https://www.hexwiki.net/api.php?action=feedcontributions&feedformat=atom&user=Kogorman
HexWiki - User contributions [en]
2026-05-07T03:42:17Z
User contributions
MediaWiki 1.23.15
https://www.hexwiki.net/index.php/Edge_template_VI1a
Edge template VI1a
2009-03-19T20:08:46Z
<p>Kogorman: Changed "handwritten" to "written out" because this is not actually handwritten. Printed text does not qualify.</p>
<hr />
<div>This template is the first one stone 6th row [[edge template|template]] for which a proof has been written out.<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
</hex><br />
<br />
== Elimination of irrelevant Blue moves ==<br />
<br />
Red has a couple of direct threats to connect, using smaller templates. Blue must play in the carrier of these threats in order to counter them. To prevent Red from connecting Blue must play in the intersection of Red's threats carriers.<br />
<br />
=== [[edge template IV1a]] ===<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ph4 Ri4<br />
Pf5 Pg5 Ph5 Pi5 Pj5 <br />
Pe6 Pf6 Pg6 Ph6 Pi6 Pj6<br />
Pd7 Pe7 Pf7 Pg7 Ph7 Pi7 Pj7<br />
</hex><br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ri4 Pj4<br />
Pg5 Ph5 Pi5 Pj5 Pk5<br />
Pf6 Pg6 Ph6 Pi6 Pj6 Pk6<br />
Pe7 Pf7 Pg7 Ph7 Pi7 Pj7 Pk7<br />
</hex><br />
<br />
=== [[edge template IV1b]] ===<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ph4 Ri4 Pj4<br />
Pf5 Pg5 Ph5 Pi5 Pj5 Pk5<br />
Pe6 Pf6 Pg6 Pi6 Pj6 Pk6<br />
Pd7 Pe7 Pf7 Pg7 Ph7 Pi7 Pj7 Pk7<br />
</hex><br />
=== Using the [[parallel ladder]] trick ===<br />
<br />
6 moves can furthermore be discarded thanks to the [[Parallel ladder]] trick. Of course, symmetry will cut our work in half!<br />
<br />
We can dispose of 3 moves on the left (and, using mirror symmetry, the corresponding 3 moves on the right), as follows:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pg5 <br />
Pf6 <br />
Pe7<br />
N:on Ri4 Bi5 Rh5 Bg7 Rh6 Bh7<br />
</hex><br />
<br />
At this point, we can use the [[Parallel ladder]] trick as follows:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pg5 <br />
Pf6 <br />
Pe7<br />
Ri4 Bi5 Rh5 Bg7 Rh6 Bh7<br />
N:on Rk5 Bj6 Ri6 Bi7 Rl4 Bj5 Rk3<br />
</hex><br />
<br />
=== [[Overlapping connections|Remaining possibilities]] for Blue ===<br />
Blue's first move must be one of the following:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
[[#The_remaining_intrusion_on_the_fifth_row|Pi3]] [[#The_remaining_intrusion_on_the_fifth_row|Pj3]]<br />
[[Template_VI1/Intrusion_on_the_4th_row|Pi4]]<br />
[[Template_VI1/Intrusion_on_the_3rd_row|Ph5]] <br />
[[Template_VI1/Intrusion_on_the_3rd_row|Pi5]]<br />
[[#The_remaining_intrusion_on_the_second_row_.28stub.29|Pg6]] [[#The_remaining_intrusion_on_the_second_row_.28stub.29|Pi6]]<br />
[[#One_remaining_intrusion_on_the_first_row_.28stub.29|Pf7]] <br />
[[#The_other_remaining_intrusion_on_the_first_row_.28stub.29|Pg7]]<br />
[[#The_other_remaining_intrusion_on_the_first_row_.28stub.29|Ph7]] [[#One_remaining_intrusion_on_the_first_row_.28stub.29|Pi7]]<br />
</hex><br />
<br />
== Specific defense ==<br />
For the moves that intersect all the carriers, Red has to find specific answers. Let's deal with the remaining intrusions!<br />
<br />
===One remaining intrusion on the first row (stub) ===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bf7 <br />
</hex><br />
<br />
Details to follow<br />
<br />
===The other remaining intrusion on the first row (stub)===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bg7 <br />
</hex><br />
<br />
Details to follow<br />
<br />
===The remaining intrusion on the second row (stub)===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bg6 <br />
</hex><br />
<br />
===The remaining intrusion on the third row (stub)===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bh5 <br />
</hex><br />
<br />
Red should go here:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bh5 MR Mi5<br />
</hex><br />
<br />
See more details [[Template VI1/Intrusion on the 3rd row| here]].<br />
<br />
===The remaining intrusion on the fourth row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 <br />
</hex><br />
<br />
Red should move here (or the equivalent mirror-image move at "+"):<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 Pk3<br />
</hex><br />
<br />
For more details, see [[Template VI1/Intrusion on the 4th row|this page]].<br />
===The remaining intrusion on the fifth row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
</hex><br />
<br />
First establish a [[double ladder]] on the right.<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
N:on Rj3 Bi5 Rk4 Bk5 Rj5 Bi7 Ri4 Bh5 <br />
</hex><br />
<br />
Then use [[Tom's move]]:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
Rj3 Bi5 Rk4 Bk5 Rj5 Bi7 Ri4 Bh5 Rf5 Bf6<br />
N:on Rf5 Bf6 Rf4 Bg5 Rh3<br />
</hex><br />
<br />
<br />
[[category:edge templates]]<br />
[[category:theory]]</div>
Kogorman
https://www.hexwiki.net/index.php/Talk:Edge_template_VI1a
Talk:Edge template VI1a
2009-03-06T14:27:50Z
<p>Kogorman: /* Size of this page */</p>
<hr />
<div>Do you think that we should have blue cells instead of stars to denote the "outer space" ? I think it would be better, because star would become usable to showing purposes. [[User:Halladba|Halladba]] 15:10, 14 January 2009 (CET)<br />
<br />
== Size of this page ==<br />
<br />
This page is getting awfully long, and it's still incomplete.<br />
Any suggestions?<br />
<br />
: We can use sub pages for the details, see for instance [[template VI1/Intrusion on the 4th row]]. [[User:Halladba|Halladba]] 16:02, 2 March 2009 (CET)<br />
<br />
: I agree--[[User:Gregorio|Gregorio]] 12:43, 3 March 2009 (CET)<br />
<br />
: I have the impression that subpages help with editing, but the pages still takes a very long time to load -- [[User:Kogorman|OHex]] 15:27, 6 March 2009 (CET)</div>
Kogorman
https://www.hexwiki.net/index.php/Talk:Edge_template_VI1a
Talk:Edge template VI1a
2009-03-06T14:27:19Z
<p>Kogorman: /* Size of this page */</p>
<hr />
<div>Do you think that we should have blue cells instead of stars to denote the "outer space" ? I think it would be better, because star would become usable to showing purposes. [[User:Halladba|Halladba]] 15:10, 14 January 2009 (CET)<br />
<br />
== Size of this page ==<br />
<br />
This page is getting awfully long, and it's still incomplete.<br />
Any suggestions?<br />
<br />
: We can use sub pages for the details, see for instance [[template VI1/Intrusion on the 4th row]]. [[User:Halladba|Halladba]] 16:02, 2 March 2009 (CET)<br />
<br />
: I agree--[[User:Gregorio|Gregorio]] 12:43, 3 March 2009 (CET)<br />
<br />
: I have the impression that subpages help with editing, but the pages still takes a very long time to load -- [[User:Kogorman|OHex]] [[User:Kogorman|OHex]] 15:27, 6 March 2009 (CET)</div>
Kogorman
https://www.hexwiki.net/index.php/Talk:Edge_template_VI1a
Talk:Edge template VI1a
2009-03-06T14:26:50Z
<p>Kogorman: /* Size of this page */</p>
<hr />
<div>Do you think that we should have blue cells instead of stars to denote the "outer space" ? I think it would be better, because star would become usable to showing purposes. [[User:Halladba|Halladba]] 15:10, 14 January 2009 (CET)<br />
<br />
== Size of this page ==<br />
<br />
This page is getting awfully long, and it's still incomplete.<br />
Any suggestions?<br />
<br />
: We can use sub pages for the details, see for instance [[template VI1/Intrusion on the 4th row]]. [[User:Halladba|Halladba]] 16:02, 2 March 2009 (CET)<br />
<br />
: I agree--[[User:Gregorio|Gregorio]] 12:43, 3 March 2009 (CET)<br />
<br />
: I have the impression that subpages help with editing, but the pages still takes a very long time to load -- ~~ [[User:Kogorman|OHex]]</div>
Kogorman
https://www.hexwiki.net/index.php/Talk:Edge_template_VI1a
Talk:Edge template VI1a
2009-03-06T14:26:16Z
<p>Kogorman: /* Size of this page */</p>
<hr />
<div>Do you think that we should have blue cells instead of stars to denote the "outer space" ? I think it would be better, because star would become usable to showing purposes. [[User:Halladba|Halladba]] 15:10, 14 January 2009 (CET)<br />
<br />
== Size of this page ==<br />
<br />
This page is getting awfully long, and it's still incomplete.<br />
Any suggestions?<br />
<br />
: We can use sub pages for the details, see for instance [[template VI1/Intrusion on the 4th row]]. [[User:Halladba|Halladba]] 16:02, 2 March 2009 (CET)<br />
<br />
: I agree--[[User:Gregorio|Gregorio]] 12:43, 3 March 2009 (CET)<br />
<br />
: I have the impression that subpages help with editing, but the pages still takes a very long time to load -- 15:26, 6 March 2009 (CET)</div>
Kogorman
https://www.hexwiki.net/index.php/Talk:Edge_template_VI1a
Talk:Edge template VI1a
2009-03-06T14:25:42Z
<p>Kogorman: /* Size of this page */</p>
<hr />
<div>Do you think that we should have blue cells instead of stars to denote the "outer space" ? I think it would be better, because star would become usable to showing purposes. [[User:Halladba|Halladba]] 15:10, 14 January 2009 (CET)<br />
<br />
== Size of this page ==<br />
<br />
This page is getting awfully long, and it's still incomplete.<br />
Any suggestions?<br />
<br />
: We can use sub pages for the details, see for instance [[template VI1/Intrusion on the 4th row]]. [[User:Halladba|Halladba]] 16:02, 2 March 2009 (CET)<br />
<br />
: I agree--[[User:Gregorio|Gregorio]] 12:43, 3 March 2009 (CET)<br />
<br />
: I have the impression that subpages help with editing, but the pages still takes a very long time to load 15:25, 6 March 2009 (CET)</div>
Kogorman
https://www.hexwiki.net/index.php/Talk:Edge_template_VI1a
Talk:Edge template VI1a
2009-03-01T22:55:58Z
<p>Kogorman: Size of this page</p>
<hr />
<div>Do you think that we should have blue cells instead of stars to denote the "outer space" ? I think it would be better, because star would become usable to showing purposes. [[User:Halladba|Halladba]] 15:10, 14 January 2009 (CET)<br />
<br />
== Size of this page ==<br />
<br />
This page is getting awfully long, and it's still incomplete.<br />
Any suggestions?</div>
Kogorman
https://www.hexwiki.net/index.php/Edge_template_VI1a
Edge template VI1a
2009-03-01T21:38:51Z
<p>Kogorman: /* Third-row followup i4 and incursion at i6 */</p>
<hr />
<div>This template is the first one stone 6th row [[edge template|template]] for which a proof has been handwritten.<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
</hex><br />
<br />
== Elimination of irrelevant Blue moves ==<br />
<br />
Red has a couple of direct threats to connect, using smaller templates. Blue must play in the carrier of these threats in order to counter them. To prevent Red from connecting Blue must play in the intersection of Red's threats carriers.<br />
<br />
=== [[edge template IV1a]] ===<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ph4 Ri4<br />
Pf5 Pg5 Ph5 Pi5 Pj5 <br />
Pe6 Pf6 Pg6 Ph6 Pi6 Pj6<br />
Pd7 Pe7 Pf7 Pg7 Ph7 Pi7 Pj7<br />
</hex><br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ri4 Pj4<br />
Pg5 Ph5 Pi5 Pj5 Pk5<br />
Pf6 Pg6 Ph6 Pi6 Pj6 Pk6<br />
Pe7 Pf7 Pg7 Ph7 Pi7 Pj7 Pk7<br />
</hex><br />
<br />
=== [[edge template IV1b]] ===<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ph4 Ri4 Pj4<br />
Pf5 Pg5 Ph5 Pi5 Pj5 Pk5<br />
Pe6 Pf6 Pg6 Pi6 Pj6 Pk6<br />
Pd7 Pe7 Pf7 Pg7 Ph7 Pi7 Pj7 Pk7<br />
</hex><br />
=== Using the [[parallel ladder]] trick ===<br />
<br />
6 moves can furthermore be discarded thanks to the [[Parallel ladder]] trick. Of course, symmetry will cut our work in half!<br />
<br />
We can dispose of 3 moves on the left (and, using mirror symmetry, the corresponding 3 moves on the right), as follows:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pg5 <br />
Pf6 <br />
Pe7<br />
N:on Ri4 Bi5 Rh5 Bg7 Rh6 Bh7<br />
</hex><br />
<br />
At this point, we can use the [[Parallel ladder]] trick as follows:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pg5 <br />
Pf6 <br />
Pe7<br />
Ri4 Bi5 Rh5 Bg7 Rh6 Bh7<br />
N:on Rk5 Bj6 Ri6 Bi7 Rl4 Bj5 Rk3<br />
</hex><br />
<br />
=== [[Overlapping connections|Remaining possibilities]] for Blue ===<br />
Blue's first move must be one of the following:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Pi4<br />
Ph5 Pi5<br />
Pg6 Pi6<br />
Pf7 Pg7 Ph7 Pi7<br />
</hex><br />
<br />
== Specific defense ==<br />
For the moves that intersect all the carriers, Red has to find specific answers. Let's deal with the remaining intrusions!<br />
<br />
===One remaining intrusion on the first row (stub) ===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bf7 <br />
</hex><br />
<br />
Details to follow<br />
<br />
===The other remaining intrusion on the first row (stub)===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bg7 <br />
</hex><br />
<br />
Details to follow<br />
<br />
===The remaining intrusion on the second row (stub)===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bg6 <br />
</hex><br />
<br />
===The remaining intrusion on the third row (stub)===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bh5 <br />
</hex><br />
<br />
Red should go here:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bh5 MR Mi5 Pi4 Pj3 <br />
</hex><br />
<br />
The Red 1 hex is connected to the bottom, and threatens to connect to the top through<br />
either one of the "+" hexes. Thus these are the only important incursions. An incursion to the right of the <br />
number 1 hex is important only in connection with the two indicated here, and will be seen in the treatement<br />
below transposed into the sequel.<br />
<br />
==== Third-row followup: i4 ====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bh5 MR Mi5 Mi4 Mk3 <br />
Pj5 Pk4 Pl4<br />
</hex><br />
<br />
Red threatens to play at "+" points above, with these two templates:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bh5 Ri5 Bi4 Rk3 <br />
Rj5<br />
Pk4 Pj4<br />
Ph6 Pi6 Pj6 Pg7 Ph7 Pi7<br />
</hex><br />
<br />
<br />
<br />
Edge template IV1a<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bh5 Ri5 Bi4 Rk3 <br />
Rl4<br />
<br />
Pl3<br />
Pk4 Pm4<br />
Pj5 Pk5 Pl5 Pm5 Pn5<br />
Pi6 Pj6 Pk6 Pl6 Pm6 Pn6<br />
Ph7 Pi7 Pj7 Pk7 Pl7 Pm7 Pn7<br />
</hex><br />
<br />
We need only consider the intersection of these two templates<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bh5 Ri5 Bi4 Rk3 <br />
Pj5<br />
Pk4<br />
Pi6 Pj6<br />
Ph7 Pi7<br />
</hex><br />
<br />
===== Third-row followup i4 and incursion at k4 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bh5 Ri5 Bi4 Rk3 <br />
MB Mk4 Mj4<br />
Pj5 Ph6 Pi6 Pj6<br />
Pg7 Ph7 Pi7 Pj7<br />
</hex><br />
<br />
===== Third-row followup i4 and incursion at j5 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bh5 Ri5 Bi4 Rk3 <br />
MB Mj5 Mj4 Mh7 Mi6 Mi7 Mk6<br />
Pj6 Pl4<br />
</hex><br />
<br />
===== Third-row followup i4 and incursion at i6 =====<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bh5 Ri5 Bi4 Rk3 <br />
MB Mi6 Mj5<br />
Ph6 Pj6<br />
</hex><br />
<br />
===== Third-row followup i4 and incursion at j6 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bh5 Ri5 Bi4 Rk3 <br />
MB Mj6 Mk4<br />
Ph7 Pl5<br />
</hex><br />
<br />
===== Third-row followup i4 and incursion at h7 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bh5 Ri5 Bi4 Rk3 <br />
MB Mh7 Mj6 Mj5 Ml4 Mk5 Ml5<br />
Pm5 <br />
Pk6 Pl6 Pm6<br />
Pj7 Pk7 Pl7 Pm7<br />
</hex><br />
<br />
===== Third-row followup i4 and incursion at i7 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bh5 Ri5 Bi4 Rk3 <br />
MB Mi7 Mj5<br />
Ph6 Pk6<br />
</hex><br />
<br />
==== Third-row followup: j3 (stub) ====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bh5 MR Mi5 Mj3<br />
</hex><br />
<br />
===The remaining intrusion on the fourth row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 <br />
</hex><br />
<br />
Red should move here (or the equivalent mirror-image move at "+"):<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 Pk3<br />
</hex><br />
<br />
==== Elimination of irrelevant Blue moves ====<br />
This gives Red several immediate threats:<br />
From III1a:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Ph5<br />
Pf6 Pg6 Ph6<br />
Pe7 Pf7 Pg7 Ph7<br />
</hex><br />
<br />
From III1a again:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Pf5<br />
Pe6 Pf6 Pg6<br />
Pd7 Pe7 Pf7 Pg7 <br />
</hex><br />
<br />
From III1b :<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Pf5 Ph5<br />
Pe6 Pf6 Pg6 Ph6<br />
Pd7 Pe7 Pg7 Ph7 <br />
</hex><br />
<br />
From IV1a:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg4<br />
Pf4<br />
Pd5 Pe5 Pf5 Pg5 Ph5<br />
Pc6 Pd6 Pe6 Pf6 Pg6 Ph6<br />
Pb7 Pc7 Pd7 Pe7 Pf7 Pg7 Ph7<br />
</hex><br />
<br />
From IV1b:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg4<br />
Pf4 Ph4<br />
Pd5 Pe5 Pf5 Pg5 Ph5 Pi5<br />
Pc6 Pd6 Pe6 Pg6 Ph6 Pi6<br />
Pb7 Pc7 Pd7 Pe7 Pf7 Pg7 Ph7 Pi7<br />
</hex><br />
<br />
The intersection of all of these leaves: <br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Pg4<br />
Pg5<br />
Pg6 <br />
Pe7 Pg7 <br />
</hex><br />
<br />
==== Specific defense ==== <br />
So we must deal with each of these responses. (Which will not be too hard!)<br />
<br />
===== Bg4 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg4 Rh4 Bg6 Rh5<br />
</hex><br />
And now either<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg4 Rh4 Bg6 Rh5<br />
N:on Bh6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
<br />
or<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg4 Rh4 Bg6 Rh5<br />
N:on Bh7 Rh6 Bg7 Rj6 Bi6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
===== Bg5 =====<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg5 Rf4<br />
</hex><br />
Threatening:<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pe4<br />
Pc5 R4d5 Pe5<br />
Pb6 Pc6 Pd6<br />
Pa7 Pb7 Pc7 Pd7<br />
</hex><br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pe5 Pf5<br />
R4e6<br />
Pd7 Pe7<br />
</hex><br />
<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pd5 R4e5 Pf5<br />
Pc6 Pd6 Pe6 Pf6<br />
Pb7 Pc7 Pe7 Pf7<br />
</hex><br />
So the only hope for Blue lies in the intersection of the threats, Be5, but it is unsufficient:<br />
<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
N:on Be5 Rf5 Be7 Rf6 Bf7 Rg6 Bg7 Rj5<br />
Pk3 Pi5<br />
</hex><br />
===== Bg6 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg6 Rg5 Bf6 Rh5<br />
Pe7<br />
</hex><br />
<br />
3 could be played at + with the same effect; in any case<br />
now either<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg6 Rg5 Bf6 Rh5<br />
N:on Bh6 Rj5<br />
Pi5 Pk3<br />
</hex><br />
<br />
or<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg6 Rg5 Bf6 Rh5<br />
N:on Bh7 Rh6 Bg7 Rj6 Bi6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
<br />
===== Be7 =====<br />
Either this<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Be7 Rg5 Bg6 Rh5 Bh6 Rj5<br />
Pi5 Pk3<br />
<br />
</hex><br />
<br />
or a minor variation<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Be7 Rg5 Bg6 Rh5 Bh7 Rh6 Bg7 Rj6 Bi6 Rj5<br />
Pi5 Pk3<br />
<br />
</hex><br />
<br />
===== Bg7 =====<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg7 Rg5 Bf6 Rh6 Bh7 Rj6 Bi6 Rj5<br />
Pi5 Pk3<br />
<br />
</hex><br />
<br />
===The remaining intrusion on the fifth row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
</hex><br />
<br />
First establish a [[double ladder]] on the right.<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
N:on Rj3 Bi5 Rk4 Bk5 Rj5 Bi7 Ri4 Bh5 <br />
</hex><br />
<br />
Then use [[Tom's move]]:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
Rj3 Bi5 Rk4 Bk5 Rj5 Bi7 Ri4 Bh5 Rf5 Bf6<br />
N:on Rf5 Bf6 Rf4 Bg5 Rh3<br />
</hex><br />
<br />
<br />
[[category:edge templates]]<br />
[[category:theory]]</div>
Kogorman
https://www.hexwiki.net/index.php/Edge_template_VI1a
Edge template VI1a
2009-03-01T21:35:00Z
<p>Kogorman: /* Third-row followup: i4 */ Filling in some details.</p>
<hr />
<div>This template is the first one stone 6th row [[edge template|template]] for which a proof has been handwritten.<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
</hex><br />
<br />
== Elimination of irrelevant Blue moves ==<br />
<br />
Red has a couple of direct threats to connect, using smaller templates. Blue must play in the carrier of these threats in order to counter them. To prevent Red from connecting Blue must play in the intersection of Red's threats carriers.<br />
<br />
=== [[edge template IV1a]] ===<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ph4 Ri4<br />
Pf5 Pg5 Ph5 Pi5 Pj5 <br />
Pe6 Pf6 Pg6 Ph6 Pi6 Pj6<br />
Pd7 Pe7 Pf7 Pg7 Ph7 Pi7 Pj7<br />
</hex><br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ri4 Pj4<br />
Pg5 Ph5 Pi5 Pj5 Pk5<br />
Pf6 Pg6 Ph6 Pi6 Pj6 Pk6<br />
Pe7 Pf7 Pg7 Ph7 Pi7 Pj7 Pk7<br />
</hex><br />
<br />
=== [[edge template IV1b]] ===<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ph4 Ri4 Pj4<br />
Pf5 Pg5 Ph5 Pi5 Pj5 Pk5<br />
Pe6 Pf6 Pg6 Pi6 Pj6 Pk6<br />
Pd7 Pe7 Pf7 Pg7 Ph7 Pi7 Pj7 Pk7<br />
</hex><br />
=== Using the [[parallel ladder]] trick ===<br />
<br />
6 moves can furthermore be discarded thanks to the [[Parallel ladder]] trick. Of course, symmetry will cut our work in half!<br />
<br />
We can dispose of 3 moves on the left (and, using mirror symmetry, the corresponding 3 moves on the right), as follows:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pg5 <br />
Pf6 <br />
Pe7<br />
N:on Ri4 Bi5 Rh5 Bg7 Rh6 Bh7<br />
</hex><br />
<br />
At this point, we can use the [[Parallel ladder]] trick as follows:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pg5 <br />
Pf6 <br />
Pe7<br />
Ri4 Bi5 Rh5 Bg7 Rh6 Bh7<br />
N:on Rk5 Bj6 Ri6 Bi7 Rl4 Bj5 Rk3<br />
</hex><br />
<br />
=== [[Overlapping connections|Remaining possibilities]] for Blue ===<br />
Blue's first move must be one of the following:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Pi4<br />
Ph5 Pi5<br />
Pg6 Pi6<br />
Pf7 Pg7 Ph7 Pi7<br />
</hex><br />
<br />
== Specific defense ==<br />
For the moves that intersect all the carriers, Red has to find specific answers. Let's deal with the remaining intrusions!<br />
<br />
===One remaining intrusion on the first row (stub) ===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bf7 <br />
</hex><br />
<br />
Details to follow<br />
<br />
===The other remaining intrusion on the first row (stub)===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bg7 <br />
</hex><br />
<br />
Details to follow<br />
<br />
===The remaining intrusion on the second row (stub)===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bg6 <br />
</hex><br />
<br />
===The remaining intrusion on the third row (stub)===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bh5 <br />
</hex><br />
<br />
Red should go here:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bh5 MR Mi5 Pi4 Pj3 <br />
</hex><br />
<br />
The Red 1 hex is connected to the bottom, and threatens to connect to the top through<br />
either one of the "+" hexes. Thus these are the only important incursions. An incursion to the right of the <br />
number 1 hex is important only in connection with the two indicated here, and will be seen in the treatement<br />
below transposed into the sequel.<br />
<br />
==== Third-row followup: i4 ====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bh5 MR Mi5 Mi4 Mk3 <br />
Pj5 Pk4 Pl4<br />
</hex><br />
<br />
Red threatens to play at "+" points above, with these two templates:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bh5 Ri5 Bi4 Rk3 <br />
Rj5<br />
Pk4 Pj4<br />
Ph6 Pi6 Pj6 Pg7 Ph7 Pi7<br />
</hex><br />
<br />
<br />
<br />
Edge template IV1a<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bh5 Ri5 Bi4 Rk3 <br />
Rl4<br />
<br />
Pl3<br />
Pk4 Pm4<br />
Pj5 Pk5 Pl5 Pm5 Pn5<br />
Pi6 Pj6 Pk6 Pl6 Pm6 Pn6<br />
Ph7 Pi7 Pj7 Pk7 Pl7 Pm7 Pn7<br />
</hex><br />
<br />
We need only consider the intersection of these two templates<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bh5 Ri5 Bi4 Rk3 <br />
Pj5<br />
Pk4<br />
Pi6 Pj6<br />
Ph7 Pi7<br />
</hex><br />
<br />
===== Third-row followup i4 and incursion at k4 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bh5 Ri5 Bi4 Rk3 <br />
MB Mk4 Mj4<br />
Pj5 Ph6 Pi6 Pj6<br />
Pg7 Ph7 Pi7 Pj7<br />
</hex><br />
<br />
===== Third-row followup i4 and incursion at j5 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bh5 Ri5 Bi4 Rk3 <br />
MB Mj5 Mj4 Mh7 Mi6 Mi7 Mk6<br />
Pj6 Pl4<br />
</hex><br />
<br />
===== Third-row followup i4 and incursion at i6 =====<br />
This the hardest of the variations; the others should be obvious.<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bh5 Ri5 Bi4 Rk3 <br />
MB Mi6 Mj5<br />
Ph6 Pj6<br />
</hex><br />
<br />
===== Third-row followup i4 and incursion at j6 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bh5 Ri5 Bi4 Rk3 <br />
MB Mj6 Mk4<br />
Ph7 Pl5<br />
</hex><br />
<br />
===== Third-row followup i4 and incursion at h7 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bh5 Ri5 Bi4 Rk3 <br />
MB Mh7 Mj6 Mj5 Ml4 Mk5 Ml5<br />
Pm5 <br />
Pk6 Pl6 Pm6<br />
Pj7 Pk7 Pl7 Pm7<br />
</hex><br />
<br />
===== Third-row followup i4 and incursion at i7 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bh5 Ri5 Bi4 Rk3 <br />
MB Mi7 Mj5<br />
Ph6 Pk6<br />
</hex><br />
<br />
==== Third-row followup: j3 (stub) ====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bh5 MR Mi5 Mj3<br />
</hex><br />
<br />
===The remaining intrusion on the fourth row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 <br />
</hex><br />
<br />
Red should move here (or the equivalent mirror-image move at "+"):<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 Pk3<br />
</hex><br />
<br />
==== Elimination of irrelevant Blue moves ====<br />
This gives Red several immediate threats:<br />
From III1a:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Ph5<br />
Pf6 Pg6 Ph6<br />
Pe7 Pf7 Pg7 Ph7<br />
</hex><br />
<br />
From III1a again:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Pf5<br />
Pe6 Pf6 Pg6<br />
Pd7 Pe7 Pf7 Pg7 <br />
</hex><br />
<br />
From III1b :<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Pf5 Ph5<br />
Pe6 Pf6 Pg6 Ph6<br />
Pd7 Pe7 Pg7 Ph7 <br />
</hex><br />
<br />
From IV1a:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg4<br />
Pf4<br />
Pd5 Pe5 Pf5 Pg5 Ph5<br />
Pc6 Pd6 Pe6 Pf6 Pg6 Ph6<br />
Pb7 Pc7 Pd7 Pe7 Pf7 Pg7 Ph7<br />
</hex><br />
<br />
From IV1b:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg4<br />
Pf4 Ph4<br />
Pd5 Pe5 Pf5 Pg5 Ph5 Pi5<br />
Pc6 Pd6 Pe6 Pg6 Ph6 Pi6<br />
Pb7 Pc7 Pd7 Pe7 Pf7 Pg7 Ph7 Pi7<br />
</hex><br />
<br />
The intersection of all of these leaves: <br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Pg4<br />
Pg5<br />
Pg6 <br />
Pe7 Pg7 <br />
</hex><br />
<br />
==== Specific defense ==== <br />
So we must deal with each of these responses. (Which will not be too hard!)<br />
<br />
===== Bg4 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg4 Rh4 Bg6 Rh5<br />
</hex><br />
And now either<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg4 Rh4 Bg6 Rh5<br />
N:on Bh6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
<br />
or<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg4 Rh4 Bg6 Rh5<br />
N:on Bh7 Rh6 Bg7 Rj6 Bi6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
===== Bg5 =====<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg5 Rf4<br />
</hex><br />
Threatening:<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pe4<br />
Pc5 R4d5 Pe5<br />
Pb6 Pc6 Pd6<br />
Pa7 Pb7 Pc7 Pd7<br />
</hex><br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pe5 Pf5<br />
R4e6<br />
Pd7 Pe7<br />
</hex><br />
<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pd5 R4e5 Pf5<br />
Pc6 Pd6 Pe6 Pf6<br />
Pb7 Pc7 Pe7 Pf7<br />
</hex><br />
So the only hope for Blue lies in the intersection of the threats, Be5, but it is unsufficient:<br />
<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
N:on Be5 Rf5 Be7 Rf6 Bf7 Rg6 Bg7 Rj5<br />
Pk3 Pi5<br />
</hex><br />
===== Bg6 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg6 Rg5 Bf6 Rh5<br />
Pe7<br />
</hex><br />
<br />
3 could be played at + with the same effect; in any case<br />
now either<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg6 Rg5 Bf6 Rh5<br />
N:on Bh6 Rj5<br />
Pi5 Pk3<br />
</hex><br />
<br />
or<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg6 Rg5 Bf6 Rh5<br />
N:on Bh7 Rh6 Bg7 Rj6 Bi6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
<br />
===== Be7 =====<br />
Either this<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Be7 Rg5 Bg6 Rh5 Bh6 Rj5<br />
Pi5 Pk3<br />
<br />
</hex><br />
<br />
or a minor variation<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Be7 Rg5 Bg6 Rh5 Bh7 Rh6 Bg7 Rj6 Bi6 Rj5<br />
Pi5 Pk3<br />
<br />
</hex><br />
<br />
===== Bg7 =====<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg7 Rg5 Bf6 Rh6 Bh7 Rj6 Bi6 Rj5<br />
Pi5 Pk3<br />
<br />
</hex><br />
<br />
===The remaining intrusion on the fifth row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
</hex><br />
<br />
First establish a [[double ladder]] on the right.<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
N:on Rj3 Bi5 Rk4 Bk5 Rj5 Bi7 Ri4 Bh5 <br />
</hex><br />
<br />
Then use [[Tom's move]]:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
Rj3 Bi5 Rk4 Bk5 Rj5 Bi7 Ri4 Bh5 Rf5 Bf6<br />
N:on Rf5 Bf6 Rf4 Bg5 Rh3<br />
</hex><br />
<br />
<br />
[[category:edge templates]]<br />
[[category:theory]]</div>
Kogorman
https://www.hexwiki.net/index.php/Edge_template_VI1a
Edge template VI1a
2009-03-01T19:42:01Z
<p>Kogorman: /* The remaining intrusion on the third row (stub) */</p>
<hr />
<div>This template is the first one stone 6th row [[edge template|template]] for which a proof has been handwritten.<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
</hex><br />
<br />
== Elimination of irrelevant Blue moves ==<br />
<br />
Red has a couple of direct threats to connect, using smaller templates. Blue must play in the carrier of these threats in order to counter them. To prevent Red from connecting Blue must play in the intersection of Red's threats carriers.<br />
<br />
=== [[edge template IV1a]] ===<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ph4 Ri4<br />
Pf5 Pg5 Ph5 Pi5 Pj5 <br />
Pe6 Pf6 Pg6 Ph6 Pi6 Pj6<br />
Pd7 Pe7 Pf7 Pg7 Ph7 Pi7 Pj7<br />
</hex><br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ri4 Pj4<br />
Pg5 Ph5 Pi5 Pj5 Pk5<br />
Pf6 Pg6 Ph6 Pi6 Pj6 Pk6<br />
Pe7 Pf7 Pg7 Ph7 Pi7 Pj7 Pk7<br />
</hex><br />
<br />
=== [[edge template IV1b]] ===<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ph4 Ri4 Pj4<br />
Pf5 Pg5 Ph5 Pi5 Pj5 Pk5<br />
Pe6 Pf6 Pg6 Pi6 Pj6 Pk6<br />
Pd7 Pe7 Pf7 Pg7 Ph7 Pi7 Pj7 Pk7<br />
</hex><br />
=== Using the [[parallel ladder]] trick ===<br />
<br />
6 moves can furthermore be discarded thanks to the [[Parallel ladder]] trick. Of course, symmetry will cut our work in half!<br />
<br />
We can dispose of 3 moves on the left (and, using mirror symmetry, the corresponding 3 moves on the right), as follows:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pg5 <br />
Pf6 <br />
Pe7<br />
N:on Ri4 Bi5 Rh5 Bg7 Rh6 Bh7<br />
</hex><br />
<br />
At this point, we can use the [[Parallel ladder]] trick as follows:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pg5 <br />
Pf6 <br />
Pe7<br />
Ri4 Bi5 Rh5 Bg7 Rh6 Bh7<br />
N:on Rk5 Bj6 Ri6 Bi7 Rl4 Bj5 Rk3<br />
</hex><br />
<br />
=== [[Overlapping connections|Remaining possibilities]] for Blue ===<br />
Blue's first move must be one of the following:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Pi4<br />
Ph5 Pi5<br />
Pg6 Pi6<br />
Pf7 Pg7 Ph7 Pi7<br />
</hex><br />
<br />
== Specific defense ==<br />
For the moves that intersect all the carriers, Red has to find specific answers. Let's deal with the remaining intrusions!<br />
<br />
===One remaining intrusion on the first row (stub) ===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bf7 <br />
</hex><br />
<br />
Details to follow<br />
<br />
===The other remaining intrusion on the first row (stub)===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bg7 <br />
</hex><br />
<br />
Details to follow<br />
<br />
===The remaining intrusion on the second row (stub)===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bg6 <br />
</hex><br />
<br />
===The remaining intrusion on the third row (stub)===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bh5 <br />
</hex><br />
<br />
Red should go here:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bh5 MR Mi5 Pi4 Pj3 <br />
</hex><br />
<br />
The Red 1 hex is connected to the bottom, and threatens to connect to the top through<br />
either one of the "+" hexes. Thus these are the only important incursions. An incursion to the right of the <br />
number 1 hex is important only in connection with the two indicated here, and will be seen in the treatement<br />
below transposed into the sequel.<br />
<br />
==== Third-row followup: i4 ====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bh5 MR Mi5 Mi4 Mk3 <br />
Pj5 Pl4<br />
</hex><br />
<br />
Red threatens to play at "+" points<br />
Details to follow.<br />
==== Third-row followup: j3 (stub) ====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bh5 MR Mi5 Mj3<br />
</hex><br />
<br />
===The remaining intrusion on the fourth row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 <br />
</hex><br />
<br />
Red should move here (or the equivalent mirror-image move at "+"):<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 Pk3<br />
</hex><br />
<br />
==== Elimination of irrelevant Blue moves ====<br />
This gives Red several immediate threats:<br />
From III1a:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Ph5<br />
Pf6 Pg6 Ph6<br />
Pe7 Pf7 Pg7 Ph7<br />
</hex><br />
<br />
From III1a again:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Pf5<br />
Pe6 Pf6 Pg6<br />
Pd7 Pe7 Pf7 Pg7 <br />
</hex><br />
<br />
From III1b :<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Pf5 Ph5<br />
Pe6 Pf6 Pg6 Ph6<br />
Pd7 Pe7 Pg7 Ph7 <br />
</hex><br />
<br />
From IV1a:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg4<br />
Pf4<br />
Pd5 Pe5 Pf5 Pg5 Ph5<br />
Pc6 Pd6 Pe6 Pf6 Pg6 Ph6<br />
Pb7 Pc7 Pd7 Pe7 Pf7 Pg7 Ph7<br />
</hex><br />
<br />
From IV1b:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg4<br />
Pf4 Ph4<br />
Pd5 Pe5 Pf5 Pg5 Ph5 Pi5<br />
Pc6 Pd6 Pe6 Pg6 Ph6 Pi6<br />
Pb7 Pc7 Pd7 Pe7 Pf7 Pg7 Ph7 Pi7<br />
</hex><br />
<br />
The intersection of all of these leaves: <br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Pg4<br />
Pg5<br />
Pg6 <br />
Pe7 Pg7 <br />
</hex><br />
<br />
==== Specific defense ==== <br />
So we must deal with each of these responses. (Which will not be too hard!)<br />
<br />
===== Bg4 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg4 Rh4 Bg6 Rh5<br />
</hex><br />
And now either<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg4 Rh4 Bg6 Rh5<br />
N:on Bh6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
<br />
or<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg4 Rh4 Bg6 Rh5<br />
N:on Bh7 Rh6 Bg7 Rj6 Bi6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
===== Bg5 =====<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg5 Rf4<br />
</hex><br />
Threatening:<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pe4<br />
Pc5 R4d5 Pe5<br />
Pb6 Pc6 Pd6<br />
Pa7 Pb7 Pc7 Pd7<br />
</hex><br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pe5 Pf5<br />
R4e6<br />
Pd7 Pe7<br />
</hex><br />
<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pd5 R4e5 Pf5<br />
Pc6 Pd6 Pe6 Pf6<br />
Pb7 Pc7 Pe7 Pf7<br />
</hex><br />
So the only hope for Blue lies in the intersection of the threats, Be5, but it is unsufficient:<br />
<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
N:on Be5 Rf5 Be7 Rf6 Bf7 Rg6 Bg7 Rj5<br />
Pk3 Pi5<br />
</hex><br />
===== Bg6 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg6 Rg5 Bf6 Rh5<br />
Pe7<br />
</hex><br />
<br />
3 could be played at + with the same effect; in any case<br />
now either<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg6 Rg5 Bf6 Rh5<br />
N:on Bh6 Rj5<br />
Pi5 Pk3<br />
</hex><br />
<br />
or<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg6 Rg5 Bf6 Rh5<br />
N:on Bh7 Rh6 Bg7 Rj6 Bi6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
<br />
===== Be7 =====<br />
Either this<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Be7 Rg5 Bg6 Rh5 Bh6 Rj5<br />
Pi5 Pk3<br />
<br />
</hex><br />
<br />
or a minor variation<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Be7 Rg5 Bg6 Rh5 Bh7 Rh6 Bg7 Rj6 Bi6 Rj5<br />
Pi5 Pk3<br />
<br />
</hex><br />
<br />
===== Bg7 =====<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg7 Rg5 Bf6 Rh6 Bh7 Rj6 Bi6 Rj5<br />
Pi5 Pk3<br />
<br />
</hex><br />
<br />
===The remaining intrusion on the fifth row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
</hex><br />
<br />
First establish a [[double ladder]] on the right.<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
N:on Rj3 Bi5 Rk4 Bk5 Rj5 Bi7 Ri4 Bh5 <br />
</hex><br />
<br />
Then use [[Tom's move]]:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
Rj3 Bi5 Rk4 Bk5 Rj5 Bi7 Ri4 Bh5 Rf5 Bf6<br />
N:on Rf5 Bf6 Rf4 Bg5 Rh3<br />
</hex><br />
<br />
<br />
[[category:edge templates]]<br />
[[category:theory]]</div>
Kogorman
https://www.hexwiki.net/index.php/Edge_template_VI1a
Edge template VI1a
2009-03-01T19:10:25Z
<p>Kogorman: /* The remaining intrusion on the fourth row */</p>
<hr />
<div>This template is the first one stone 6th row [[edge template|template]] for which a proof has been handwritten.<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
</hex><br />
<br />
== Elimination of irrelevant Blue moves ==<br />
<br />
Red has a couple of direct threats to connect, using smaller templates. Blue must play in the carrier of these threats in order to counter them. To prevent Red from connecting Blue must play in the intersection of Red's threats carriers.<br />
<br />
=== [[edge template IV1a]] ===<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ph4 Ri4<br />
Pf5 Pg5 Ph5 Pi5 Pj5 <br />
Pe6 Pf6 Pg6 Ph6 Pi6 Pj6<br />
Pd7 Pe7 Pf7 Pg7 Ph7 Pi7 Pj7<br />
</hex><br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ri4 Pj4<br />
Pg5 Ph5 Pi5 Pj5 Pk5<br />
Pf6 Pg6 Ph6 Pi6 Pj6 Pk6<br />
Pe7 Pf7 Pg7 Ph7 Pi7 Pj7 Pk7<br />
</hex><br />
<br />
=== [[edge template IV1b]] ===<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ph4 Ri4 Pj4<br />
Pf5 Pg5 Ph5 Pi5 Pj5 Pk5<br />
Pe6 Pf6 Pg6 Pi6 Pj6 Pk6<br />
Pd7 Pe7 Pf7 Pg7 Ph7 Pi7 Pj7 Pk7<br />
</hex><br />
=== Using the [[parallel ladder]] trick ===<br />
<br />
6 moves can furthermore be discarded thanks to the [[Parallel ladder]] trick. Of course, symmetry will cut our work in half!<br />
<br />
We can dispose of 3 moves on the left (and, using mirror symmetry, the corresponding 3 moves on the right), as follows:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pg5 <br />
Pf6 <br />
Pe7<br />
N:on Ri4 Bi5 Rh5 Bg7 Rh6 Bh7<br />
</hex><br />
<br />
At this point, we can use the [[Parallel ladder]] trick as follows:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pg5 <br />
Pf6 <br />
Pe7<br />
Ri4 Bi5 Rh5 Bg7 Rh6 Bh7<br />
N:on Rk5 Bj6 Ri6 Bi7 Rl4 Bj5 Rk3<br />
</hex><br />
<br />
=== [[Overlapping connections|Remaining possibilities]] for Blue ===<br />
Blue's first move must be one of the following:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Pi4<br />
Ph5 Pi5<br />
Pg6 Pi6<br />
Pf7 Pg7 Ph7 Pi7<br />
</hex><br />
<br />
== Specific defense ==<br />
For the moves that intersect all the carriers, Red has to find specific answers. Let's deal with the remaining intrusions!<br />
<br />
===One remaining intrusion on the first row (stub) ===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bf7 <br />
</hex><br />
<br />
Details to follow<br />
<br />
===The other remaining intrusion on the first row (stub)===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bg7 <br />
</hex><br />
<br />
Details to follow<br />
<br />
===The remaining intrusion on the second row (stub)===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bg6 <br />
</hex><br />
<br />
===The remaining intrusion on the third row (stub)===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bh5 <br />
</hex><br />
<br />
===The remaining intrusion on the fourth row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 <br />
</hex><br />
<br />
Red should move here (or the equivalent mirror-image move at "+"):<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 Pk3<br />
</hex><br />
<br />
==== Elimination of irrelevant Blue moves ====<br />
This gives Red several immediate threats:<br />
From III1a:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Ph5<br />
Pf6 Pg6 Ph6<br />
Pe7 Pf7 Pg7 Ph7<br />
</hex><br />
<br />
From III1a again:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Pf5<br />
Pe6 Pf6 Pg6<br />
Pd7 Pe7 Pf7 Pg7 <br />
</hex><br />
<br />
From III1b :<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Pf5 Ph5<br />
Pe6 Pf6 Pg6 Ph6<br />
Pd7 Pe7 Pg7 Ph7 <br />
</hex><br />
<br />
From IV1a:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg4<br />
Pf4<br />
Pd5 Pe5 Pf5 Pg5 Ph5<br />
Pc6 Pd6 Pe6 Pf6 Pg6 Ph6<br />
Pb7 Pc7 Pd7 Pe7 Pf7 Pg7 Ph7<br />
</hex><br />
<br />
From IV1b:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg4<br />
Pf4 Ph4<br />
Pd5 Pe5 Pf5 Pg5 Ph5 Pi5<br />
Pc6 Pd6 Pe6 Pg6 Ph6 Pi6<br />
Pb7 Pc7 Pd7 Pe7 Pf7 Pg7 Ph7 Pi7<br />
</hex><br />
<br />
The intersection of all of these leaves: <br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Pg4<br />
Pg5<br />
Pg6 <br />
Pe7 Pg7 <br />
</hex><br />
<br />
==== Specific defense ==== <br />
So we must deal with each of these responses. (Which will not be too hard!)<br />
<br />
===== Bg4 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg4 Rh4 Bg6 Rh5<br />
</hex><br />
And now either<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg4 Rh4 Bg6 Rh5<br />
N:on Bh6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
<br />
or<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg4 Rh4 Bg6 Rh5<br />
N:on Bh7 Rh6 Bg7 Rj6 Bi6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
===== Bg5 =====<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg5 Rf4<br />
</hex><br />
Threatening:<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pe4<br />
Pc5 R4d5 Pe5<br />
Pb6 Pc6 Pd6<br />
Pa7 Pb7 Pc7 Pd7<br />
</hex><br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pe5 Pf5<br />
R4e6<br />
Pd7 Pe7<br />
</hex><br />
<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pd5 R4e5 Pf5<br />
Pc6 Pd6 Pe6 Pf6<br />
Pb7 Pc7 Pe7 Pf7<br />
</hex><br />
So the only hope for Blue lies in the intersection of the threats, Be5, but it is unsufficient:<br />
<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
N:on Be5 Rf5 Be7 Rf6 Bf7 Rg6 Bg7 Rj5<br />
Pk3 Pi5<br />
</hex><br />
===== Bg6 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg6 Rg5 Bf6 Rh5<br />
Pe7<br />
</hex><br />
<br />
3 could be played at + with the same effect; in any case<br />
now either<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg6 Rg5 Bf6 Rh5<br />
N:on Bh6 Rj5<br />
Pi5 Pk3<br />
</hex><br />
<br />
or<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg6 Rg5 Bf6 Rh5<br />
N:on Bh7 Rh6 Bg7 Rj6 Bi6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
<br />
===== Be7 =====<br />
Either this<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Be7 Rg5 Bg6 Rh5 Bh6 Rj5<br />
Pi5 Pk3<br />
<br />
</hex><br />
<br />
or a minor variation<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Be7 Rg5 Bg6 Rh5 Bh7 Rh6 Bg7 Rj6 Bi6 Rj5<br />
Pi5 Pk3<br />
<br />
</hex><br />
<br />
===== Bg7 =====<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg7 Rg5 Bf6 Rh6 Bh7 Rj6 Bi6 Rj5<br />
Pi5 Pk3<br />
<br />
</hex><br />
<br />
===The remaining intrusion on the fifth row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
</hex><br />
<br />
First establish a [[double ladder]] on the right.<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
N:on Rj3 Bi5 Rk4 Bk5 Rj5 Bi7 Ri4 Bh5 <br />
</hex><br />
<br />
Then use [[Tom's move]]:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
Rj3 Bi5 Rk4 Bk5 Rj5 Bi7 Ri4 Bh5 Rf5 Bf6<br />
N:on Rf5 Bf6 Rf4 Bg5 Rh3<br />
</hex><br />
<br />
<br />
[[category:edge templates]]<br />
[[category:theory]]</div>
Kogorman
https://www.hexwiki.net/index.php/Edge_template_VI1a
Edge template VI1a
2009-03-01T19:05:58Z
<p>Kogorman: /* The remaining intrusion on the fourth row */</p>
<hr />
<div>This template is the first one stone 6th row [[edge template|template]] for which a proof has been handwritten.<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
</hex><br />
<br />
== Elimination of irrelevant Blue moves ==<br />
<br />
Red has a couple of direct threats to connect, using smaller templates. Blue must play in the carrier of these threats in order to counter them. To prevent Red from connecting Blue must play in the intersection of Red's threats carriers.<br />
<br />
=== [[edge template IV1a]] ===<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ph4 Ri4<br />
Pf5 Pg5 Ph5 Pi5 Pj5 <br />
Pe6 Pf6 Pg6 Ph6 Pi6 Pj6<br />
Pd7 Pe7 Pf7 Pg7 Ph7 Pi7 Pj7<br />
</hex><br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ri4 Pj4<br />
Pg5 Ph5 Pi5 Pj5 Pk5<br />
Pf6 Pg6 Ph6 Pi6 Pj6 Pk6<br />
Pe7 Pf7 Pg7 Ph7 Pi7 Pj7 Pk7<br />
</hex><br />
<br />
=== [[edge template IV1b]] ===<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ph4 Ri4 Pj4<br />
Pf5 Pg5 Ph5 Pi5 Pj5 Pk5<br />
Pe6 Pf6 Pg6 Pi6 Pj6 Pk6<br />
Pd7 Pe7 Pf7 Pg7 Ph7 Pi7 Pj7 Pk7<br />
</hex><br />
=== Using the [[parallel ladder]] trick ===<br />
<br />
6 moves can furthermore be discarded thanks to the [[Parallel ladder]] trick. Of course, symmetry will cut our work in half!<br />
<br />
We can dispose of 3 moves on the left (and, using mirror symmetry, the corresponding 3 moves on the right), as follows:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pg5 <br />
Pf6 <br />
Pe7<br />
N:on Ri4 Bi5 Rh5 Bg7 Rh6 Bh7<br />
</hex><br />
<br />
At this point, we can use the [[Parallel ladder]] trick as follows:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pg5 <br />
Pf6 <br />
Pe7<br />
Ri4 Bi5 Rh5 Bg7 Rh6 Bh7<br />
N:on Rk5 Bj6 Ri6 Bi7 Rl4 Bj5 Rk3<br />
</hex><br />
<br />
=== [[Overlapping connections|Remaining possibilities]] for Blue ===<br />
Blue's first move must be one of the following:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Pi4<br />
Ph5 Pi5<br />
Pg6 Pi6<br />
Pf7 Pg7 Ph7 Pi7<br />
</hex><br />
<br />
== Specific defense ==<br />
For the moves that intersect all the carriers, Red has to find specific answers. Let's deal with the remaining intrusions!<br />
<br />
===One remaining intrusion on the first row (stub) ===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bf7 <br />
</hex><br />
<br />
Details to follow<br />
<br />
===The other remaining intrusion on the first row (stub)===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bg7 <br />
</hex><br />
<br />
Details to follow<br />
<br />
===The remaining intrusion on the second row (stub)===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bg6 <br />
</hex><br />
<br />
===The remaining intrusion on the third row (stub)===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bh5 <br />
</hex><br />
<br />
===The remaining intrusion on the fourth row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 <br />
</hex><br />
<br />
Red should move here (or the equivalent miror-image move):<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
</hex><br />
<br />
==== Elimination of irrelevant Blue moves ====<br />
This gives Red several immediate threats:<br />
From III1a:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Ph5<br />
Pf6 Pg6 Ph6<br />
Pe7 Pf7 Pg7 Ph7<br />
</hex><br />
<br />
From III1a again:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Pf5<br />
Pe6 Pf6 Pg6<br />
Pd7 Pe7 Pf7 Pg7 <br />
</hex><br />
<br />
From III1b :<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Pf5 Ph5<br />
Pe6 Pf6 Pg6 Ph6<br />
Pd7 Pe7 Pg7 Ph7 <br />
</hex><br />
<br />
From IV1a:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg4<br />
Pf4<br />
Pd5 Pe5 Pf5 Pg5 Ph5<br />
Pc6 Pd6 Pe6 Pf6 Pg6 Ph6<br />
Pb7 Pc7 Pd7 Pe7 Pf7 Pg7 Ph7<br />
</hex><br />
<br />
From IV1b:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg4<br />
Pf4 Ph4<br />
Pd5 Pe5 Pf5 Pg5 Ph5 Pi5<br />
Pc6 Pd6 Pe6 Pg6 Ph6 Pi6<br />
Pb7 Pc7 Pd7 Pe7 Pf7 Pg7 Ph7 Pi7<br />
</hex><br />
<br />
The intersection of all of these leaves: <br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Pg4<br />
Pg5<br />
Pg6 <br />
Pe7 Pg7 <br />
</hex><br />
<br />
==== Specific defense ==== <br />
So we must deal with each of these responses. (Which will not be too hard!)<br />
<br />
===== Bg4 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg4 Rh4 Bg6 Rh5<br />
</hex><br />
And now either<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg4 Rh4 Bg6 Rh5<br />
N:on Bh6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
<br />
or<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg4 Rh4 Bg6 Rh5<br />
N:on Bh7 Rh6 Bg7 Rj6 Bi6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
===== Bg5 =====<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg5 Rf4<br />
</hex><br />
Threatening:<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pe4<br />
Pc5 R4d5 Pe5<br />
Pb6 Pc6 Pd6<br />
Pa7 Pb7 Pc7 Pd7<br />
</hex><br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pe5 Pf5<br />
R4e6<br />
Pd7 Pe7<br />
</hex><br />
<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pd5 R4e5 Pf5<br />
Pc6 Pd6 Pe6 Pf6<br />
Pb7 Pc7 Pe7 Pf7<br />
</hex><br />
So the only hope for Blue lies in the intersection of the threats, Be5, but it is unsufficient:<br />
<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
N:on Be5 Rf5 Be7 Rf6 Bf7 Rg6 Bg7 Rj5<br />
Pk3 Pi5<br />
</hex><br />
===== Bg6 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg6 Rg5 Bf6 Rh5<br />
Pe7<br />
</hex><br />
<br />
3 could be played at + with the same effect; in any case<br />
now either<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg6 Rg5 Bf6 Rh5<br />
N:on Bh6 Rj5<br />
Pi5 Pk3<br />
</hex><br />
<br />
or<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg6 Rg5 Bf6 Rh5<br />
N:on Bh7 Rh6 Bg7 Rj6 Bi6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
<br />
===== Be7 =====<br />
Either this<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Be7 Rg5 Bg6 Rh5 Bh6 Rj5<br />
Pi5 Pk3<br />
<br />
</hex><br />
<br />
or a minor variation<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Be7 Rg5 Bg6 Rh5 Bh7 Rh6 Bg7 Rj6 Bi6 Rj5<br />
Pi5 Pk3<br />
<br />
</hex><br />
<br />
===== Bg7 =====<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg7 Rg5 Bf6 Rh6 Bh7 Rj6 Bi6 Rj5<br />
Pi5 Pk3<br />
<br />
</hex><br />
<br />
===The remaining intrusion on the fifth row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
</hex><br />
<br />
First establish a [[double ladder]] on the right.<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
N:on Rj3 Bi5 Rk4 Bk5 Rj5 Bi7 Ri4 Bh5 <br />
</hex><br />
<br />
Then use [[Tom's move]]:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
Rj3 Bi5 Rk4 Bk5 Rj5 Bi7 Ri4 Bh5 Rf5 Bf6<br />
N:on Rf5 Bf6 Rf4 Bg5 Rh3<br />
</hex><br />
<br />
<br />
[[category:edge templates]]<br />
[[category:theory]]</div>
Kogorman
https://www.hexwiki.net/index.php/Edge_template_VI1a
Edge template VI1a
2009-02-24T14:40:23Z
<p>Kogorman: /* The other remaining intrusion on the first row (stub) */</p>
<hr />
<div>This template is the first one stone 6th row [[edge template|template]] for which a proof has been handwritten.<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
</hex><br />
<br />
== Elimination of irrelevant Blue moves ==<br />
<br />
Red has a couple of direct threats to connect, using smaller templates. Blue must play in the carrier of these threats in order to counter them. To prevent Red from connecting Blue must play in the intersection of Red's threats carriers.<br />
<br />
=== [[edge template IV1a]] ===<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ph4 Ri4<br />
Pf5 Pg5 Ph5 Pi5 Pj5 <br />
Pe6 Pf6 Pg6 Ph6 Pi6 Pj6<br />
Pd7 Pe7 Pf7 Pg7 Ph7 Pi7 Pj7<br />
</hex><br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ri4 Pj4<br />
Pg5 Ph5 Pi5 Pj5 Pk5<br />
Pf6 Pg6 Ph6 Pi6 Pj6 Pk6<br />
Pe7 Pf7 Pg7 Ph7 Pi7 Pj7 Pk7<br />
</hex><br />
<br />
=== [[edge template IV1b]] ===<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ph4 Ri4 Pj4<br />
Pf5 Pg5 Ph5 Pi5 Pj5 Pk5<br />
Pe6 Pf6 Pg6 Pi6 Pj6 Pk6<br />
Pd7 Pe7 Pf7 Pg7 Ph7 Pi7 Pj7 Pk7<br />
</hex><br />
=== Using the [[parallel ladder]] trick ===<br />
<br />
6 moves can furthermore be discarded thanks to the [[Parallel ladder]] trick. Of course, symmetry will cut our work in half!<br />
<br />
We can dispose of 3 moves on the left (and, using mirror symmetry, the corresponding 3 moves on the right), as follows:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pg5 <br />
Pf6 <br />
Pe7<br />
N:on Ri4 Bi5 Rh5 Bg7 Rh6 Bh7<br />
</hex><br />
<br />
At this point, we can use the [[Parallel ladder]] trick as follows:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pg5 <br />
Pf6 <br />
Pe7<br />
Ri4 Bi5 Rh5 Bg7 Rh6 Bh7<br />
N:on Rk5 Bj6 Ri6 Bi7 Rl4 Bj5 Rk3<br />
</hex><br />
<br />
=== [[Overlapping connections|Remaining possibilities]] for Blue ===<br />
Blue's first move must be one of the following:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Pi4<br />
Ph5 Pi5<br />
Pg6 Pi6<br />
Pf7 Pg7 Ph7 Pi7<br />
</hex><br />
<br />
== Specific defense ==<br />
For the moves that intersect all the carriers, Red has to find specific answers. Let's deal with the remaining intrusions!<br />
<br />
===One remaining intrusion on the first row (stub) ===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bf7 <br />
</hex><br />
<br />
Details to follow<br />
<br />
===The other remaining intrusion on the first row (stub)===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bg7 <br />
</hex><br />
<br />
Details to follow<br />
<br />
===The remaining intrusion on the second row (stub)===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bg6 <br />
</hex><br />
<br />
===The remaining intrusion on the third row (stub)===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bh5 <br />
</hex><br />
<br />
===The remaining intrusion on the fourth row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 <br />
</hex><br />
<br />
Red should move here:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
</hex><br />
<br />
==== Elimination of irrelevant Blue moves ====<br />
This gives Red several immediate threats:<br />
From III1a:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Ph5<br />
Pf6 Pg6 Ph6<br />
Pe7 Pf7 Pg7 Ph7<br />
</hex><br />
<br />
From III1a again:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Pf5<br />
Pe6 Pf6 Pg6<br />
Pd7 Pe7 Pf7 Pg7 <br />
</hex><br />
<br />
From III1b :<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Pf5 Ph5<br />
Pe6 Pf6 Pg6 Ph6<br />
Pd7 Pe7 Pg7 Ph7 <br />
</hex><br />
<br />
From IV1a:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg4<br />
Pf4<br />
Pd5 Pe5 Pf5 Pg5 Ph5<br />
Pc6 Pd6 Pe6 Pf6 Pg6 Ph6<br />
Pb7 Pc7 Pd7 Pe7 Pf7 Pg7 Ph7<br />
</hex><br />
<br />
From IV1b:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg4<br />
Pf4 Ph4<br />
Pd5 Pe5 Pf5 Pg5 Ph5 Pi5<br />
Pc6 Pd6 Pe6 Pg6 Ph6 Pi6<br />
Pb7 Pc7 Pd7 Pe7 Pf7 Pg7 Ph7 Pi7<br />
</hex><br />
<br />
The intersection of all of these leaves: <br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Pg4<br />
Pg5<br />
Pg6 <br />
Pe7 Pg7 <br />
</hex><br />
<br />
==== Specific defense ==== <br />
So we must deal with each of these responses. (Which will not be too hard!)<br />
<br />
===== Bg4 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg4 Rh4 Bg6 Rh5<br />
</hex><br />
And now either<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg4 Rh4 Bg6 Rh5<br />
N:on Bh6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
<br />
or<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg4 Rh4 Bg6 Rh5<br />
N:on Bh7 Rh6 Bg7 Rj6 Bi6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
===== Bg5 =====<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg5 Rf4<br />
</hex><br />
Threatening:<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pe4<br />
Pc5 R4d5 Pe5<br />
Pb6 Pc6 Pd6<br />
Pa7 Pb7 Pc7 Pd7<br />
</hex><br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pe5 Pf5<br />
R4e6<br />
Pd7 Pe7<br />
</hex><br />
<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pd5 R4e5 Pf5<br />
Pc6 Pd6 Pe6 Pf6<br />
Pb7 Pc7 Pe7 Pf7<br />
</hex><br />
So the only hope for Blue lies in the intersection of the threats, Be5, but it is unsufficient:<br />
<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
N:on Be5 Rf5 Be7 Rf6 Bf7 Rg6 Bg7 Rj5<br />
Pk3 Pi5<br />
</hex><br />
===== Bg6 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg6 Rg5 Bf6 Rh5<br />
Pe7<br />
</hex><br />
<br />
3 could be played at + with the same effect; in any case<br />
now either<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg6 Rg5 Bf6 Rh5<br />
N:on Bh6 Rj5<br />
Pi5 Pk3<br />
</hex><br />
<br />
or<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg6 Rg5 Bf6 Rh5<br />
N:on Bh7 Rh6 Bg7 Rj6 Bi6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
<br />
===== Be7 =====<br />
Either this<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Be7 Rg5 Bg6 Rh5 Bh6 Rj5<br />
Pi5 Pk3<br />
<br />
</hex><br />
<br />
or a minor variation<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Be7 Rg5 Bg6 Rh5 Bh7 Rh6 Bg7 Rj6 Bi6 Rj5<br />
Pi5 Pk3<br />
<br />
</hex><br />
<br />
===== Bg7 =====<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg7 Rg5 Bf6 Rh6 Bh7 Rj6 Bi6 Rj5<br />
Pi5 Pk3<br />
<br />
</hex><br />
<br />
===The remaining intrusion on the fifth row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
</hex><br />
<br />
First establish a [[double ladder]] on the right.<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
N:on Rj3 Bi5 Rk4 Bk5 Rj5 Bi7 Ri4 Bh5 <br />
</hex><br />
<br />
Then use [[Tom's move]]:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
Rj3 Bi5 Rk4 Bk5 Rj5 Bi7 Ri4 Bh5 Rf5 Bf6<br />
N:on Rf5 Bf6 Rf4 Bg5 Rh3<br />
</hex><br />
<br />
<br />
[[category:edge templates]]<br />
[[category:theory]]</div>
Kogorman
https://www.hexwiki.net/index.php/Edge_template_VI1a
Edge template VI1a
2009-02-24T14:39:03Z
<p>Kogorman: /* One remaining intrusion on the first row (stub) */</p>
<hr />
<div>This template is the first one stone 6th row [[edge template|template]] for which a proof has been handwritten.<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
</hex><br />
<br />
== Elimination of irrelevant Blue moves ==<br />
<br />
Red has a couple of direct threats to connect, using smaller templates. Blue must play in the carrier of these threats in order to counter them. To prevent Red from connecting Blue must play in the intersection of Red's threats carriers.<br />
<br />
=== [[edge template IV1a]] ===<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ph4 Ri4<br />
Pf5 Pg5 Ph5 Pi5 Pj5 <br />
Pe6 Pf6 Pg6 Ph6 Pi6 Pj6<br />
Pd7 Pe7 Pf7 Pg7 Ph7 Pi7 Pj7<br />
</hex><br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ri4 Pj4<br />
Pg5 Ph5 Pi5 Pj5 Pk5<br />
Pf6 Pg6 Ph6 Pi6 Pj6 Pk6<br />
Pe7 Pf7 Pg7 Ph7 Pi7 Pj7 Pk7<br />
</hex><br />
<br />
=== [[edge template IV1b]] ===<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ph4 Ri4 Pj4<br />
Pf5 Pg5 Ph5 Pi5 Pj5 Pk5<br />
Pe6 Pf6 Pg6 Pi6 Pj6 Pk6<br />
Pd7 Pe7 Pf7 Pg7 Ph7 Pi7 Pj7 Pk7<br />
</hex><br />
=== Using the [[parallel ladder]] trick ===<br />
<br />
6 moves can furthermore be discarded thanks to the [[Parallel ladder]] trick. Of course, symmetry will cut our work in half!<br />
<br />
We can dispose of 3 moves on the left (and, using mirror symmetry, the corresponding 3 moves on the right), as follows:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pg5 <br />
Pf6 <br />
Pe7<br />
N:on Ri4 Bi5 Rh5 Bg7 Rh6 Bh7<br />
</hex><br />
<br />
At this point, we can use the [[Parallel ladder]] trick as follows:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pg5 <br />
Pf6 <br />
Pe7<br />
Ri4 Bi5 Rh5 Bg7 Rh6 Bh7<br />
N:on Rk5 Bj6 Ri6 Bi7 Rl4 Bj5 Rk3<br />
</hex><br />
<br />
=== [[Overlapping connections|Remaining possibilities]] for Blue ===<br />
Blue's first move must be one of the following:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Pi4<br />
Ph5 Pi5<br />
Pg6 Pi6<br />
Pf7 Pg7 Ph7 Pi7<br />
</hex><br />
<br />
== Specific defense ==<br />
For the moves that intersect all the carriers, Red has to find specific answers. Let's deal with the remaining intrusions!<br />
<br />
===One remaining intrusion on the first row (stub) ===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bf7 <br />
</hex><br />
<br />
Details to follow<br />
<br />
===The other remaining intrusion on the first row (stub)===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bg7 <br />
</hex><br />
<br />
===The remaining intrusion on the second row (stub)===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bg6 <br />
</hex><br />
<br />
===The remaining intrusion on the third row (stub)===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bh5 <br />
</hex><br />
<br />
===The remaining intrusion on the fourth row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 <br />
</hex><br />
<br />
Red should move here:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
</hex><br />
<br />
==== Elimination of irrelevant Blue moves ====<br />
This gives Red several immediate threats:<br />
From III1a:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Ph5<br />
Pf6 Pg6 Ph6<br />
Pe7 Pf7 Pg7 Ph7<br />
</hex><br />
<br />
From III1a again:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Pf5<br />
Pe6 Pf6 Pg6<br />
Pd7 Pe7 Pf7 Pg7 <br />
</hex><br />
<br />
From III1b :<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Pf5 Ph5<br />
Pe6 Pf6 Pg6 Ph6<br />
Pd7 Pe7 Pg7 Ph7 <br />
</hex><br />
<br />
From IV1a:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg4<br />
Pf4<br />
Pd5 Pe5 Pf5 Pg5 Ph5<br />
Pc6 Pd6 Pe6 Pf6 Pg6 Ph6<br />
Pb7 Pc7 Pd7 Pe7 Pf7 Pg7 Ph7<br />
</hex><br />
<br />
From IV1b:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg4<br />
Pf4 Ph4<br />
Pd5 Pe5 Pf5 Pg5 Ph5 Pi5<br />
Pc6 Pd6 Pe6 Pg6 Ph6 Pi6<br />
Pb7 Pc7 Pd7 Pe7 Pf7 Pg7 Ph7 Pi7<br />
</hex><br />
<br />
The intersection of all of these leaves: <br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Pg4<br />
Pg5<br />
Pg6 <br />
Pe7 Pg7 <br />
</hex><br />
<br />
==== Specific defense ==== <br />
So we must deal with each of these responses. (Which will not be too hard!)<br />
<br />
===== Bg4 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg4 Rh4 Bg6 Rh5<br />
</hex><br />
And now either<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg4 Rh4 Bg6 Rh5<br />
N:on Bh6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
<br />
or<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg4 Rh4 Bg6 Rh5<br />
N:on Bh7 Rh6 Bg7 Rj6 Bi6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
===== Bg5 =====<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg5 Rf4<br />
</hex><br />
Threatening:<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pe4<br />
Pc5 R4d5 Pe5<br />
Pb6 Pc6 Pd6<br />
Pa7 Pb7 Pc7 Pd7<br />
</hex><br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pe5 Pf5<br />
R4e6<br />
Pd7 Pe7<br />
</hex><br />
<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pd5 R4e5 Pf5<br />
Pc6 Pd6 Pe6 Pf6<br />
Pb7 Pc7 Pe7 Pf7<br />
</hex><br />
So the only hope for Blue lies in the intersection of the threats, Be5, but it is unsufficient:<br />
<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
N:on Be5 Rf5 Be7 Rf6 Bf7 Rg6 Bg7 Rj5<br />
Pk3 Pi5<br />
</hex><br />
===== Bg6 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg6 Rg5 Bf6 Rh5<br />
Pe7<br />
</hex><br />
<br />
3 could be played at + with the same effect; in any case<br />
now either<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg6 Rg5 Bf6 Rh5<br />
N:on Bh6 Rj5<br />
Pi5 Pk3<br />
</hex><br />
<br />
or<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg6 Rg5 Bf6 Rh5<br />
N:on Bh7 Rh6 Bg7 Rj6 Bi6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
<br />
===== Be7 =====<br />
Either this<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Be7 Rg5 Bg6 Rh5 Bh6 Rj5<br />
Pi5 Pk3<br />
<br />
</hex><br />
<br />
or a minor variation<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Be7 Rg5 Bg6 Rh5 Bh7 Rh6 Bg7 Rj6 Bi6 Rj5<br />
Pi5 Pk3<br />
<br />
</hex><br />
<br />
===== Bg7 =====<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg7 Rg5 Bf6 Rh6 Bh7 Rj6 Bi6 Rj5<br />
Pi5 Pk3<br />
<br />
</hex><br />
<br />
===The remaining intrusion on the fifth row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
</hex><br />
<br />
First establish a [[double ladder]] on the right.<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
N:on Rj3 Bi5 Rk4 Bk5 Rj5 Bi7 Ri4 Bh5 <br />
</hex><br />
<br />
Then use [[Tom's move]]:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
Rj3 Bi5 Rk4 Bk5 Rj5 Bi7 Ri4 Bh5 Rf5 Bf6<br />
N:on Rf5 Bf6 Rf4 Bg5 Rh3<br />
</hex><br />
<br />
<br />
[[category:edge templates]]<br />
[[category:theory]]</div>
Kogorman
https://www.hexwiki.net/index.php/Edge_template_VI1a
Edge template VI1a
2009-02-17T10:36:16Z
<p>Kogorman: /* Be7 */ A variation added</p>
<hr />
<div>This template is the first one stone 6th row [[edge template|template]] for which a proof has been handwritten.<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
</hex><br />
<br />
== Elimination of irrelevant Blue moves ==<br />
<br />
Red has a couple of direct threats to connect, using smaller templates. Blue must play in the carrier of these threats in order to counter them. To prevent Red from connecting Blue must play in the intersection of Red's threats carriers.<br />
<br />
=== [[edge template IV1a]] ===<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ph4 Ri4<br />
Pf5 Pg5 Ph5 Pi5 Pj5 <br />
Pe6 Pf6 Pg6 Ph6 Pi6 Pj6<br />
Pd7 Pe7 Pf7 Pg7 Ph7 Pi7 Pj7<br />
</hex><br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ri4 Pj4<br />
Pg5 Ph5 Pi5 Pj5 Pk5<br />
Pf6 Pg6 Ph6 Pi6 Pj6 Pk6<br />
Pe7 Pf7 Pg7 Ph7 Pi7 Pj7 Pk7<br />
</hex><br />
<br />
=== [[edge template IV1b]] ===<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ph4 Ri4 Pj4<br />
Pf5 Pg5 Ph5 Pi5 Pj5 Pk5<br />
Pe6 Pf6 Pg6 Pi6 Pj6 Pk6<br />
Pd7 Pe7 Pf7 Pg7 Ph7 Pi7 Pj7 Pk7<br />
</hex><br />
=== Using the [[parallel ladder]] trick ===<br />
<br />
6 moves can furthermore be discarded thanks to the [[Parallel ladder]] trick. Of course, symmetry will cut our work in half!<br />
<br />
We can dispose of 3 moves on the left (and, using mirror symmetry, the corresponding 3 moves on the right), as follows:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pg5 <br />
Pf6 <br />
Pe7<br />
N:on Ri4 Bi5 Rh5 Bg7 Rh6 Bh7<br />
</hex><br />
<br />
At this point, we can use the [[Parallel ladder]] trick as follows:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pg5 <br />
Pf6 <br />
Pe7<br />
Ri4 Bi5 Rh5 Bg7 Rh6 Bh7<br />
N:on Rk5 Bj6 Ri6 Bi7 Rl4 Bj5 Rk3<br />
</hex><br />
<br />
=== [[Overlapping connections|Remaining possibilities]] for Blue ===<br />
Blue's first move must be one of the following:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Pi4<br />
Ph5 Pi5<br />
Pg6 Pi6<br />
Pf7 Pg7 Ph7 Pi7<br />
</hex><br />
<br />
== Specific defense ==<br />
For the moves that intersect all the carriers, Red has to find specific answers. Let's deal with the remaining intrusions!<br />
<br />
===One remaining intrusion on the first row (stub) ===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bf7 <br />
</hex><br />
<br />
===The other remaining intrusion on the first row (stub)===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bg7 <br />
</hex><br />
<br />
===The remaining intrusion on the second row (stub)===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bg6 <br />
</hex><br />
<br />
===The remaining intrusion on the third row (stub)===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bh5 <br />
</hex><br />
<br />
===The remaining intrusion on the fourth row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 <br />
</hex><br />
<br />
Red should move here:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
</hex><br />
<br />
==== Elimination of irrelevant Blue moves ====<br />
This gives Red several immediate threats:<br />
From III1a:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Ph5<br />
Pf6 Pg6 Ph6<br />
Pe7 Pf7 Pg7 Ph7<br />
</hex><br />
<br />
From III1a again:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Pf5<br />
Pe6 Pf6 Pg6<br />
Pd7 Pe7 Pf7 Pg7 <br />
</hex><br />
<br />
From III1b :<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Pf5 Ph5<br />
Pe6 Pf6 Pg6 Ph6<br />
Pd7 Pe7 Pg7 Ph7 <br />
</hex><br />
<br />
From IV1a:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg4<br />
Pf4<br />
Pd5 Pe5 Pf5 Pg5 Ph5<br />
Pc6 Pd6 Pe6 Pf6 Pg6 Ph6<br />
Pb7 Pc7 Pd7 Pe7 Pf7 Pg7 Ph7<br />
</hex><br />
<br />
From IV1b:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg4<br />
Pf4 Ph4<br />
Pd5 Pe5 Pf5 Pg5 Ph5 Pi5<br />
Pc6 Pd6 Pe6 Pg6 Ph6 Pi6<br />
Pb7 Pc7 Pd7 Pe7 Pf7 Pg7 Ph7 Pi7<br />
</hex><br />
<br />
The intersection of all of these leaves: <br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Pg4<br />
Pg5<br />
Pg6 <br />
Pe7 Pg7 <br />
</hex><br />
<br />
==== Specific defense ==== <br />
So we must deal with each of these responses. (Which will not be too hard!)<br />
<br />
===== Bg4 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg4 Rh4 Bg6 Rh5<br />
</hex><br />
And now either<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg4 Rh4 Bg6 Rh5<br />
N:on Bh6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
<br />
or<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg4 Rh4 Bg6 Rh5<br />
N:on Bh7 Rh6 Bg7 Rj6 Bi6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
===== Bg5 =====<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg5 Rf4<br />
</hex><br />
Threatening:<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pe4<br />
Pc5 R4d5 Pe5<br />
Pb6 Pc6 Pd6<br />
Pa7 Pb7 Pc7 Pd7<br />
</hex><br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pe5 Pf5<br />
R4e6<br />
Pd7 Pe7<br />
</hex><br />
<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pd5 R4e5 Pf5<br />
Pc6 Pd6 Pe6 Pf6<br />
Pb7 Pc7 Pe7 Pf7<br />
</hex><br />
So the only hope for Blue lies in the intersection of the threats, Be5, but it is unsufficient:<br />
<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
N:on Be5 Rf5 Be7 Rf6 Bf7 Rg6 Bg7 Rj5<br />
Pk3 Pi5<br />
</hex><br />
===== Bg6 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg6 Rg5 Bf6 Rh5<br />
Pe7<br />
</hex><br />
<br />
3 could be played at + with the same effect; in any case<br />
now either<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg6 Rg5 Bf6 Rh5<br />
N:on Bh6 Rj5<br />
Pi5 Pk3<br />
</hex><br />
<br />
or<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg6 Rg5 Bf6 Rh5<br />
N:on Bh7 Rh6 Bg7 Rj6 Bi6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
<br />
===== Be7 =====<br />
Either this<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Be7 Rg5 Bg6 Rh5 Bh6 Rj5<br />
Pi5 Pk3<br />
<br />
</hex><br />
<br />
or a minor variation<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Be7 Rg5 Bg6 Rh5 Bh7 Rh6 Bg7 Rj6 Bi6 Rj5<br />
Pi5 Pk3<br />
<br />
</hex><br />
<br />
===== Bg7 =====<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg7 Rg5 Bf6 Rh6 Bh7 Rj6 Bi6 Rj5<br />
Pi5 Pk3<br />
<br />
</hex><br />
<br />
===The remaining intrusion on the fifth row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
</hex><br />
<br />
First establish a [[double ladder]] on the right.<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
N:on Rj3 Bi5 Rk4 Bk5 Rj5 Bi7 Ri4 Bh5 <br />
</hex><br />
<br />
Then use [[Tom's move]]:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
Rj3 Bi5 Rk4 Bk5 Rj5 Bi7 Ri4 Bh5 Rf5 Bf6<br />
N:on Rf5 Bf6 Rf4 Bg5 Rh3<br />
</hex><br />
<br />
<br />
[[category:edge templates]]<br />
[[category:theory]]</div>
Kogorman
https://www.hexwiki.net/index.php/Edge_template_VI1a
Edge template VI1a
2009-02-17T10:29:03Z
<p>Kogorman: /* Specific defense */ spelling</p>
<hr />
<div>This template is the first one stone 6th row [[edge template|template]] for which a proof has been handwritten.<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
</hex><br />
<br />
== Elimination of irrelevant Blue moves ==<br />
<br />
Red has a couple of direct threats to connect, using smaller templates. Blue must play in the carrier of these threats in order to counter them. To prevent Red from connecting Blue must play in the intersection of Red's threats carriers.<br />
<br />
=== [[edge template IV1a]] ===<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ph4 Ri4<br />
Pf5 Pg5 Ph5 Pi5 Pj5 <br />
Pe6 Pf6 Pg6 Ph6 Pi6 Pj6<br />
Pd7 Pe7 Pf7 Pg7 Ph7 Pi7 Pj7<br />
</hex><br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ri4 Pj4<br />
Pg5 Ph5 Pi5 Pj5 Pk5<br />
Pf6 Pg6 Ph6 Pi6 Pj6 Pk6<br />
Pe7 Pf7 Pg7 Ph7 Pi7 Pj7 Pk7<br />
</hex><br />
<br />
=== [[edge template IV1b]] ===<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ph4 Ri4 Pj4<br />
Pf5 Pg5 Ph5 Pi5 Pj5 Pk5<br />
Pe6 Pf6 Pg6 Pi6 Pj6 Pk6<br />
Pd7 Pe7 Pf7 Pg7 Ph7 Pi7 Pj7 Pk7<br />
</hex><br />
=== Using the [[parallel ladder]] trick ===<br />
<br />
6 moves can furthermore be discarded thanks to the [[Parallel ladder]] trick. Of course, symmetry will cut our work in half!<br />
<br />
We can dispose of 3 moves on the left (and, using mirror symmetry, the corresponding 3 moves on the right), as follows:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pg5 <br />
Pf6 <br />
Pe7<br />
N:on Ri4 Bi5 Rh5 Bg7 Rh6 Bh7<br />
</hex><br />
<br />
At this point, we can use the [[Parallel ladder]] trick as follows:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pg5 <br />
Pf6 <br />
Pe7<br />
Ri4 Bi5 Rh5 Bg7 Rh6 Bh7<br />
N:on Rk5 Bj6 Ri6 Bi7 Rl4 Bj5 Rk3<br />
</hex><br />
<br />
=== [[Overlapping connections|Remaining possibilities]] for Blue ===<br />
Blue's first move must be one of the following:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Pi4<br />
Ph5 Pi5<br />
Pg6 Pi6<br />
Pf7 Pg7 Ph7 Pi7<br />
</hex><br />
<br />
== Specific defense ==<br />
For the moves that intersect all the carriers, Red has to find specific answers. Let's deal with the remaining intrusions!<br />
<br />
===One remaining intrusion on the first row (stub) ===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bf7 <br />
</hex><br />
<br />
===The other remaining intrusion on the first row (stub)===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bg7 <br />
</hex><br />
<br />
===The remaining intrusion on the second row (stub)===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bg6 <br />
</hex><br />
<br />
===The remaining intrusion on the third row (stub)===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bh5 <br />
</hex><br />
<br />
===The remaining intrusion on the fourth row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 <br />
</hex><br />
<br />
Red should move here:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
</hex><br />
<br />
==== Elimination of irrelevant Blue moves ====<br />
This gives Red several immediate threats:<br />
From III1a:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Ph5<br />
Pf6 Pg6 Ph6<br />
Pe7 Pf7 Pg7 Ph7<br />
</hex><br />
<br />
From III1a again:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Pf5<br />
Pe6 Pf6 Pg6<br />
Pd7 Pe7 Pf7 Pg7 <br />
</hex><br />
<br />
From III1b :<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Pf5 Ph5<br />
Pe6 Pf6 Pg6 Ph6<br />
Pd7 Pe7 Pg7 Ph7 <br />
</hex><br />
<br />
From IV1a:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg4<br />
Pf4<br />
Pd5 Pe5 Pf5 Pg5 Ph5<br />
Pc6 Pd6 Pe6 Pf6 Pg6 Ph6<br />
Pb7 Pc7 Pd7 Pe7 Pf7 Pg7 Ph7<br />
</hex><br />
<br />
From IV1b:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg4<br />
Pf4 Ph4<br />
Pd5 Pe5 Pf5 Pg5 Ph5 Pi5<br />
Pc6 Pd6 Pe6 Pg6 Ph6 Pi6<br />
Pb7 Pc7 Pd7 Pe7 Pf7 Pg7 Ph7 Pi7<br />
</hex><br />
<br />
The intersection of all of these leaves: <br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Pg4<br />
Pg5<br />
Pg6 <br />
Pe7 Pg7 <br />
</hex><br />
<br />
==== Specific defense ==== <br />
So we must deal with each of these responses. (Which will not be too hard!)<br />
<br />
===== Bg4 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg4 Rh4 Bg6 Rh5<br />
</hex><br />
And now either<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg4 Rh4 Bg6 Rh5<br />
N:on Bh6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
<br />
or<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg4 Rh4 Bg6 Rh5<br />
N:on Bh7 Rh6 Bg7 Rj6 Bi6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
===== Bg5 =====<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg5 Rf4<br />
</hex><br />
Threatening:<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pe4<br />
Pc5 R4d5 Pe5<br />
Pb6 Pc6 Pd6<br />
Pa7 Pb7 Pc7 Pd7<br />
</hex><br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pe5 Pf5<br />
R4e6<br />
Pd7 Pe7<br />
</hex><br />
<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pd5 R4e5 Pf5<br />
Pc6 Pd6 Pe6 Pf6<br />
Pb7 Pc7 Pe7 Pf7<br />
</hex><br />
So the only hope for Blue lies in the intersection of the threats, Be5, but it is unsufficient:<br />
<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
N:on Be5 Rf5 Be7 Rf6 Bf7 Rg6 Bg7 Rj5<br />
Pk3 Pi5<br />
</hex><br />
===== Bg6 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg6 Rg5 Bf6 Rh5<br />
Pe7<br />
</hex><br />
<br />
3 could be played at + with the same effect; in any case<br />
now either<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg6 Rg5 Bf6 Rh5<br />
N:on Bh6 Rj5<br />
Pi5 Pk3<br />
</hex><br />
<br />
or<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg6 Rg5 Bf6 Rh5<br />
N:on Bh7 Rh6 Bg7 Rj6 Bi6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
<br />
===== Be7 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Be7 Rg5 Bg6 Rh5 Bh6 Rj5<br />
Pi5 Pk3<br />
<br />
</hex><br />
<br />
===== Bg7 =====<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg7 Rg5 Bf6 Rh6 Bh7 Rj6 Bi6 Rj5<br />
Pi5 Pk3<br />
<br />
</hex><br />
<br />
===The remaining intrusion on the fifth row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
</hex><br />
<br />
First establish a [[double ladder]] on the right.<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
N:on Rj3 Bi5 Rk4 Bk5 Rj5 Bi7 Ri4 Bh5 <br />
</hex><br />
<br />
Then use [[Tom's move]]:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
Rj3 Bi5 Rk4 Bk5 Rj5 Bi7 Ri4 Bh5 Rf5 Bf6<br />
N:on Rf5 Bf6 Rf4 Bg5 Rh3<br />
</hex><br />
<br />
<br />
[[category:edge templates]]<br />
[[category:theory]]</div>
Kogorman
https://www.hexwiki.net/index.php/Edge_template_VI1a
Edge template VI1a
2009-02-17T10:27:11Z
<p>Kogorman: /* Specific defense */ spelling</p>
<hr />
<div>This template is the first one stone 6th row [[edge template|template]] for which a proof has been handwritten.<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
</hex><br />
<br />
== Elimination of irrelevant Blue moves ==<br />
<br />
Red has a couple of direct threats to connect, using smaller templates. Blue must play in the carrier of these threats in order to counter them. To prevent Red from connecting Blue must play in the intersection of Red's threats carriers.<br />
<br />
=== [[edge template IV1a]] ===<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ph4 Ri4<br />
Pf5 Pg5 Ph5 Pi5 Pj5 <br />
Pe6 Pf6 Pg6 Ph6 Pi6 Pj6<br />
Pd7 Pe7 Pf7 Pg7 Ph7 Pi7 Pj7<br />
</hex><br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ri4 Pj4<br />
Pg5 Ph5 Pi5 Pj5 Pk5<br />
Pf6 Pg6 Ph6 Pi6 Pj6 Pk6<br />
Pe7 Pf7 Pg7 Ph7 Pi7 Pj7 Pk7<br />
</hex><br />
<br />
=== [[edge template IV1b]] ===<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ph4 Ri4 Pj4<br />
Pf5 Pg5 Ph5 Pi5 Pj5 Pk5<br />
Pe6 Pf6 Pg6 Pi6 Pj6 Pk6<br />
Pd7 Pe7 Pf7 Pg7 Ph7 Pi7 Pj7 Pk7<br />
</hex><br />
=== Using the [[parallel ladder]] trick ===<br />
<br />
6 moves can furthermore be discarded thanks to the [[Parallel ladder]] trick. Of course, symmetry will cut our work in half!<br />
<br />
We can dispose of 3 moves on the left (and, using mirror symmetry, the corresponding 3 moves on the right), as follows:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pg5 <br />
Pf6 <br />
Pe7<br />
N:on Ri4 Bi5 Rh5 Bg7 Rh6 Bh7<br />
</hex><br />
<br />
At this point, we can use the [[Parallel ladder]] trick as follows:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pg5 <br />
Pf6 <br />
Pe7<br />
Ri4 Bi5 Rh5 Bg7 Rh6 Bh7<br />
N:on Rk5 Bj6 Ri6 Bi7 Rl4 Bj5 Rk3<br />
</hex><br />
<br />
=== [[Overlapping connections|Remaining possibilities]] for Blue ===<br />
Blue's first move must be one of the following:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Pi4<br />
Ph5 Pi5<br />
Pg6 Pi6<br />
Pf7 Pg7 Ph7 Pi7<br />
</hex><br />
<br />
== Specific defense ==<br />
For the moves that intersect all the carriers, Red has to find specific answers. Let's deal with the remaining intrusions!<br />
<br />
===One remaining intrusion on the first row (stub) ===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bf7 <br />
</hex><br />
<br />
===The other remaining intrusion on the first row (stub)===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bg7 <br />
</hex><br />
<br />
===The remaining intrusion on the second row (stub)===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bg6 <br />
</hex><br />
<br />
===The remaining intrusion on the third row (stub)===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bh5 <br />
</hex><br />
<br />
===The remaining intrusion on the fourth row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 <br />
</hex><br />
<br />
Red should move here:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
</hex><br />
<br />
==== Elimination of irrelevant Blue moves ====<br />
This gives Red several immediate threats:<br />
From III1a:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Ph5<br />
Pf6 Pg6 Ph6<br />
Pe7 Pf7 Pg7 Ph7<br />
</hex><br />
<br />
From III1a again:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Pf5<br />
Pe6 Pf6 Pg6<br />
Pd7 Pe7 Pf7 Pg7 <br />
</hex><br />
<br />
From III1b :<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Pf5 Ph5<br />
Pe6 Pf6 Pg6 Ph6<br />
Pd7 Pe7 Pg7 Ph7 <br />
</hex><br />
<br />
From IV1a:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg4<br />
Pf4<br />
Pd5 Pe5 Pf5 Pg5 Ph5<br />
Pc6 Pd6 Pe6 Pf6 Pg6 Ph6<br />
Pb7 Pc7 Pd7 Pe7 Pf7 Pg7 Ph7<br />
</hex><br />
<br />
From IV1b:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg4<br />
Pf4 Ph4<br />
Pd5 Pe5 Pf5 Pg5 Ph5 Pi5<br />
Pc6 Pd6 Pe6 Pg6 Ph6 Pi6<br />
Pb7 Pc7 Pd7 Pe7 Pf7 Pg7 Ph7 Pi7<br />
</hex><br />
<br />
The intersection of all of these leaves: <br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Pg4<br />
Pg5<br />
Pg6 <br />
Pe7 Pg7 <br />
</hex><br />
<br />
==== Specific defence ==== <br />
So we must deal with each of these responses. (Which will not be too hard!)<br />
<br />
===== Bg4 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg4 Rh4 Bg6 Rh5<br />
</hex><br />
And now either<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg4 Rh4 Bg6 Rh5<br />
N:on Bh6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
<br />
or<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg4 Rh4 Bg6 Rh5<br />
N:on Bh7 Rh6 Bg7 Rj6 Bi6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
===== Bg5 =====<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg5 Rf4<br />
</hex><br />
Threatening:<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pe4<br />
Pc5 R4d5 Pe5<br />
Pb6 Pc6 Pd6<br />
Pa7 Pb7 Pc7 Pd7<br />
</hex><br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pe5 Pf5<br />
R4e6<br />
Pd7 Pe7<br />
</hex><br />
<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pd5 R4e5 Pf5<br />
Pc6 Pd6 Pe6 Pf6<br />
Pb7 Pc7 Pe7 Pf7<br />
</hex><br />
So the only hope for Blue lies in the intersection of the threats, Be5, but it is unsufficient:<br />
<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
N:on Be5 Rf5 Be7 Rf6 Bf7 Rg6 Bg7 Rj5<br />
Pk3 Pi5<br />
</hex><br />
===== Bg6 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg6 Rg5 Bf6 Rh5<br />
Pe7<br />
</hex><br />
<br />
3 could be played at + with the same effect; in any case<br />
now either<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg6 Rg5 Bf6 Rh5<br />
N:on Bh6 Rj5<br />
Pi5 Pk3<br />
</hex><br />
<br />
or<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg6 Rg5 Bf6 Rh5<br />
N:on Bh7 Rh6 Bg7 Rj6 Bi6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
<br />
===== Be7 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Be7 Rg5 Bg6 Rh5 Bh6 Rj5<br />
Pi5 Pk3<br />
<br />
</hex><br />
<br />
===== Bg7 =====<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg7 Rg5 Bf6 Rh6 Bh7 Rj6 Bi6 Rj5<br />
Pi5 Pk3<br />
<br />
</hex><br />
<br />
===The remaining intrusion on the fifth row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
</hex><br />
<br />
First establish a [[double ladder]] on the right.<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
N:on Rj3 Bi5 Rk4 Bk5 Rj5 Bi7 Ri4 Bh5 <br />
</hex><br />
<br />
Then use [[Tom's move]]:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
Rj3 Bi5 Rk4 Bk5 Rj5 Bi7 Ri4 Bh5 Rf5 Bf6<br />
N:on Rf5 Bf6 Rf4 Bg5 Rh3<br />
</hex><br />
<br />
<br />
[[category:edge templates]]<br />
[[category:theory]]</div>
Kogorman
https://www.hexwiki.net/index.php/Edge_template_VI1a
Edge template VI1a
2009-02-17T10:26:09Z
<p>Kogorman: /* The remaining intrusion on the third row */ mark as incomplete</p>
<hr />
<div>This template is the first one stone 6th row [[edge template|template]] for which a proof has been handwritten.<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
</hex><br />
<br />
== Elimination of irrelevant Blue moves ==<br />
<br />
Red has a couple of direct threats to connect, using smaller templates. Blue must play in the carrier of these threats in order to counter them. To prevent Red from connecting Blue must play in the intersection of Red's threats carriers.<br />
<br />
=== [[edge template IV1a]] ===<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ph4 Ri4<br />
Pf5 Pg5 Ph5 Pi5 Pj5 <br />
Pe6 Pf6 Pg6 Ph6 Pi6 Pj6<br />
Pd7 Pe7 Pf7 Pg7 Ph7 Pi7 Pj7<br />
</hex><br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ri4 Pj4<br />
Pg5 Ph5 Pi5 Pj5 Pk5<br />
Pf6 Pg6 Ph6 Pi6 Pj6 Pk6<br />
Pe7 Pf7 Pg7 Ph7 Pi7 Pj7 Pk7<br />
</hex><br />
<br />
=== [[edge template IV1b]] ===<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ph4 Ri4 Pj4<br />
Pf5 Pg5 Ph5 Pi5 Pj5 Pk5<br />
Pe6 Pf6 Pg6 Pi6 Pj6 Pk6<br />
Pd7 Pe7 Pf7 Pg7 Ph7 Pi7 Pj7 Pk7<br />
</hex><br />
=== Using the [[parallel ladder]] trick ===<br />
<br />
6 moves can furthermore be discarded thanks to the [[Parallel ladder]] trick. Of course, symmetry will cut our work in half!<br />
<br />
We can dispose of 3 moves on the left (and, using mirror symmetry, the corresponding 3 moves on the right), as follows:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pg5 <br />
Pf6 <br />
Pe7<br />
N:on Ri4 Bi5 Rh5 Bg7 Rh6 Bh7<br />
</hex><br />
<br />
At this point, we can use the [[Parallel ladder]] trick as follows:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pg5 <br />
Pf6 <br />
Pe7<br />
Ri4 Bi5 Rh5 Bg7 Rh6 Bh7<br />
N:on Rk5 Bj6 Ri6 Bi7 Rl4 Bj5 Rk3<br />
</hex><br />
<br />
=== [[Overlapping connections|Remaining possibilities]] for Blue ===<br />
Blue's first move must be one of the following:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Pi4<br />
Ph5 Pi5<br />
Pg6 Pi6<br />
Pf7 Pg7 Ph7 Pi7<br />
</hex><br />
<br />
== Specific defence ==<br />
For the moves that intersect all the carriers, Red has to find specific answers. Let's deal with the remaining intrusions!<br />
<br />
===One remaining intrusion on the first row (stub) ===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bf7 <br />
</hex><br />
<br />
===The other remaining intrusion on the first row (stub)===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bg7 <br />
</hex><br />
<br />
===The remaining intrusion on the second row (stub)===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bg6 <br />
</hex><br />
<br />
===The remaining intrusion on the third row (stub)===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bh5 <br />
</hex><br />
<br />
===The remaining intrusion on the fourth row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 <br />
</hex><br />
<br />
Red should move here:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
</hex><br />
<br />
==== Elimination of irrelevant Blue moves ====<br />
This gives Red several immediate threats:<br />
From III1a:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Ph5<br />
Pf6 Pg6 Ph6<br />
Pe7 Pf7 Pg7 Ph7<br />
</hex><br />
<br />
From III1a again:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Pf5<br />
Pe6 Pf6 Pg6<br />
Pd7 Pe7 Pf7 Pg7 <br />
</hex><br />
<br />
From III1b :<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Pf5 Ph5<br />
Pe6 Pf6 Pg6 Ph6<br />
Pd7 Pe7 Pg7 Ph7 <br />
</hex><br />
<br />
From IV1a:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg4<br />
Pf4<br />
Pd5 Pe5 Pf5 Pg5 Ph5<br />
Pc6 Pd6 Pe6 Pf6 Pg6 Ph6<br />
Pb7 Pc7 Pd7 Pe7 Pf7 Pg7 Ph7<br />
</hex><br />
<br />
From IV1b:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg4<br />
Pf4 Ph4<br />
Pd5 Pe5 Pf5 Pg5 Ph5 Pi5<br />
Pc6 Pd6 Pe6 Pg6 Ph6 Pi6<br />
Pb7 Pc7 Pd7 Pe7 Pf7 Pg7 Ph7 Pi7<br />
</hex><br />
<br />
The intersection of all of these leaves: <br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Pg4<br />
Pg5<br />
Pg6 <br />
Pe7 Pg7 <br />
</hex><br />
<br />
==== Specific defence ==== <br />
So we must deal with each of these responses. (Which will not be too hard!)<br />
<br />
===== Bg4 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg4 Rh4 Bg6 Rh5<br />
</hex><br />
And now either<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg4 Rh4 Bg6 Rh5<br />
N:on Bh6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
<br />
or<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg4 Rh4 Bg6 Rh5<br />
N:on Bh7 Rh6 Bg7 Rj6 Bi6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
===== Bg5 =====<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg5 Rf4<br />
</hex><br />
Threatening:<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pe4<br />
Pc5 R4d5 Pe5<br />
Pb6 Pc6 Pd6<br />
Pa7 Pb7 Pc7 Pd7<br />
</hex><br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pe5 Pf5<br />
R4e6<br />
Pd7 Pe7<br />
</hex><br />
<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pd5 R4e5 Pf5<br />
Pc6 Pd6 Pe6 Pf6<br />
Pb7 Pc7 Pe7 Pf7<br />
</hex><br />
So the only hope for Blue lies in the intersection of the threats, Be5, but it is unsufficient:<br />
<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
N:on Be5 Rf5 Be7 Rf6 Bf7 Rg6 Bg7 Rj5<br />
Pk3 Pi5<br />
</hex><br />
===== Bg6 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg6 Rg5 Bf6 Rh5<br />
Pe7<br />
</hex><br />
<br />
3 could be played at + with the same effect; in any case<br />
now either<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg6 Rg5 Bf6 Rh5<br />
N:on Bh6 Rj5<br />
Pi5 Pk3<br />
</hex><br />
<br />
or<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg6 Rg5 Bf6 Rh5<br />
N:on Bh7 Rh6 Bg7 Rj6 Bi6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
<br />
===== Be7 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Be7 Rg5 Bg6 Rh5 Bh6 Rj5<br />
Pi5 Pk3<br />
<br />
</hex><br />
<br />
===== Bg7 =====<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg7 Rg5 Bf6 Rh6 Bh7 Rj6 Bi6 Rj5<br />
Pi5 Pk3<br />
<br />
</hex><br />
<br />
===The remaining intrusion on the fifth row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
</hex><br />
<br />
First establish a [[double ladder]] on the right.<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
N:on Rj3 Bi5 Rk4 Bk5 Rj5 Bi7 Ri4 Bh5 <br />
</hex><br />
<br />
Then use [[Tom's move]]:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
Rj3 Bi5 Rk4 Bk5 Rj5 Bi7 Ri4 Bh5 Rf5 Bf6<br />
N:on Rf5 Bf6 Rf4 Bg5 Rh3<br />
</hex><br />
<br />
<br />
[[category:edge templates]]<br />
[[category:theory]]</div>
Kogorman
https://www.hexwiki.net/index.php/Edge_template_VI1a
Edge template VI1a
2009-02-17T10:24:56Z
<p>Kogorman: /* The remaining intrusion on the second row */ mark as incomplete</p>
<hr />
<div>This template is the first one stone 6th row [[edge template|template]] for which a proof has been handwritten.<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
</hex><br />
<br />
== Elimination of irrelevant Blue moves ==<br />
<br />
Red has a couple of direct threats to connect, using smaller templates. Blue must play in the carrier of these threats in order to counter them. To prevent Red from connecting Blue must play in the intersection of Red's threats carriers.<br />
<br />
=== [[edge template IV1a]] ===<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ph4 Ri4<br />
Pf5 Pg5 Ph5 Pi5 Pj5 <br />
Pe6 Pf6 Pg6 Ph6 Pi6 Pj6<br />
Pd7 Pe7 Pf7 Pg7 Ph7 Pi7 Pj7<br />
</hex><br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ri4 Pj4<br />
Pg5 Ph5 Pi5 Pj5 Pk5<br />
Pf6 Pg6 Ph6 Pi6 Pj6 Pk6<br />
Pe7 Pf7 Pg7 Ph7 Pi7 Pj7 Pk7<br />
</hex><br />
<br />
=== [[edge template IV1b]] ===<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ph4 Ri4 Pj4<br />
Pf5 Pg5 Ph5 Pi5 Pj5 Pk5<br />
Pe6 Pf6 Pg6 Pi6 Pj6 Pk6<br />
Pd7 Pe7 Pf7 Pg7 Ph7 Pi7 Pj7 Pk7<br />
</hex><br />
=== Using the [[parallel ladder]] trick ===<br />
<br />
6 moves can furthermore be discarded thanks to the [[Parallel ladder]] trick. Of course, symmetry will cut our work in half!<br />
<br />
We can dispose of 3 moves on the left (and, using mirror symmetry, the corresponding 3 moves on the right), as follows:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pg5 <br />
Pf6 <br />
Pe7<br />
N:on Ri4 Bi5 Rh5 Bg7 Rh6 Bh7<br />
</hex><br />
<br />
At this point, we can use the [[Parallel ladder]] trick as follows:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pg5 <br />
Pf6 <br />
Pe7<br />
Ri4 Bi5 Rh5 Bg7 Rh6 Bh7<br />
N:on Rk5 Bj6 Ri6 Bi7 Rl4 Bj5 Rk3<br />
</hex><br />
<br />
=== [[Overlapping connections|Remaining possibilities]] for Blue ===<br />
Blue's first move must be one of the following:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Pi4<br />
Ph5 Pi5<br />
Pg6 Pi6<br />
Pf7 Pg7 Ph7 Pi7<br />
</hex><br />
<br />
== Specific defence ==<br />
For the moves that intersect all the carriers, Red has to find specific answers. Let's deal with the remaining intrusions!<br />
<br />
===One remaining intrusion on the first row (stub) ===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bf7 <br />
</hex><br />
<br />
===The other remaining intrusion on the first row (stub)===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bg7 <br />
</hex><br />
<br />
===The remaining intrusion on the second row (stub)===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bg6 <br />
</hex><br />
<br />
===The remaining intrusion on the third row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bh5 <br />
</hex><br />
<br />
===The remaining intrusion on the fourth row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 <br />
</hex><br />
<br />
Red should move here:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
</hex><br />
<br />
==== Elimination of irrelevant Blue moves ====<br />
This gives Red several immediate threats:<br />
From III1a:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Ph5<br />
Pf6 Pg6 Ph6<br />
Pe7 Pf7 Pg7 Ph7<br />
</hex><br />
<br />
From III1a again:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Pf5<br />
Pe6 Pf6 Pg6<br />
Pd7 Pe7 Pf7 Pg7 <br />
</hex><br />
<br />
From III1b :<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Pf5 Ph5<br />
Pe6 Pf6 Pg6 Ph6<br />
Pd7 Pe7 Pg7 Ph7 <br />
</hex><br />
<br />
From IV1a:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg4<br />
Pf4<br />
Pd5 Pe5 Pf5 Pg5 Ph5<br />
Pc6 Pd6 Pe6 Pf6 Pg6 Ph6<br />
Pb7 Pc7 Pd7 Pe7 Pf7 Pg7 Ph7<br />
</hex><br />
<br />
From IV1b:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg4<br />
Pf4 Ph4<br />
Pd5 Pe5 Pf5 Pg5 Ph5 Pi5<br />
Pc6 Pd6 Pe6 Pg6 Ph6 Pi6<br />
Pb7 Pc7 Pd7 Pe7 Pf7 Pg7 Ph7 Pi7<br />
</hex><br />
<br />
The intersection of all of these leaves: <br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Pg4<br />
Pg5<br />
Pg6 <br />
Pe7 Pg7 <br />
</hex><br />
<br />
==== Specific defence ==== <br />
So we must deal with each of these responses. (Which will not be too hard!)<br />
<br />
===== Bg4 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg4 Rh4 Bg6 Rh5<br />
</hex><br />
And now either<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg4 Rh4 Bg6 Rh5<br />
N:on Bh6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
<br />
or<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg4 Rh4 Bg6 Rh5<br />
N:on Bh7 Rh6 Bg7 Rj6 Bi6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
===== Bg5 =====<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg5 Rf4<br />
</hex><br />
Threatening:<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pe4<br />
Pc5 R4d5 Pe5<br />
Pb6 Pc6 Pd6<br />
Pa7 Pb7 Pc7 Pd7<br />
</hex><br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pe5 Pf5<br />
R4e6<br />
Pd7 Pe7<br />
</hex><br />
<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pd5 R4e5 Pf5<br />
Pc6 Pd6 Pe6 Pf6<br />
Pb7 Pc7 Pe7 Pf7<br />
</hex><br />
So the only hope for Blue lies in the intersection of the threats, Be5, but it is unsufficient:<br />
<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
N:on Be5 Rf5 Be7 Rf6 Bf7 Rg6 Bg7 Rj5<br />
Pk3 Pi5<br />
</hex><br />
===== Bg6 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg6 Rg5 Bf6 Rh5<br />
Pe7<br />
</hex><br />
<br />
3 could be played at + with the same effect; in any case<br />
now either<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg6 Rg5 Bf6 Rh5<br />
N:on Bh6 Rj5<br />
Pi5 Pk3<br />
</hex><br />
<br />
or<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg6 Rg5 Bf6 Rh5<br />
N:on Bh7 Rh6 Bg7 Rj6 Bi6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
<br />
===== Be7 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Be7 Rg5 Bg6 Rh5 Bh6 Rj5<br />
Pi5 Pk3<br />
<br />
</hex><br />
<br />
===== Bg7 =====<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg7 Rg5 Bf6 Rh6 Bh7 Rj6 Bi6 Rj5<br />
Pi5 Pk3<br />
<br />
</hex><br />
<br />
===The remaining intrusion on the fifth row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
</hex><br />
<br />
First establish a [[double ladder]] on the right.<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
N:on Rj3 Bi5 Rk4 Bk5 Rj5 Bi7 Ri4 Bh5 <br />
</hex><br />
<br />
Then use [[Tom's move]]:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
Rj3 Bi5 Rk4 Bk5 Rj5 Bi7 Ri4 Bh5 Rf5 Bf6<br />
N:on Rf5 Bf6 Rf4 Bg5 Rh3<br />
</hex><br />
<br />
<br />
[[category:edge templates]]<br />
[[category:theory]]</div>
Kogorman
https://www.hexwiki.net/index.php/Edge_template_VI1a
Edge template VI1a
2009-02-17T10:23:48Z
<p>Kogorman: /* The other remaining intrusion on the first row */ mark as incomplete</p>
<hr />
<div>This template is the first one stone 6th row [[edge template|template]] for which a proof has been handwritten.<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
</hex><br />
<br />
== Elimination of irrelevant Blue moves ==<br />
<br />
Red has a couple of direct threats to connect, using smaller templates. Blue must play in the carrier of these threats in order to counter them. To prevent Red from connecting Blue must play in the intersection of Red's threats carriers.<br />
<br />
=== [[edge template IV1a]] ===<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ph4 Ri4<br />
Pf5 Pg5 Ph5 Pi5 Pj5 <br />
Pe6 Pf6 Pg6 Ph6 Pi6 Pj6<br />
Pd7 Pe7 Pf7 Pg7 Ph7 Pi7 Pj7<br />
</hex><br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ri4 Pj4<br />
Pg5 Ph5 Pi5 Pj5 Pk5<br />
Pf6 Pg6 Ph6 Pi6 Pj6 Pk6<br />
Pe7 Pf7 Pg7 Ph7 Pi7 Pj7 Pk7<br />
</hex><br />
<br />
=== [[edge template IV1b]] ===<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ph4 Ri4 Pj4<br />
Pf5 Pg5 Ph5 Pi5 Pj5 Pk5<br />
Pe6 Pf6 Pg6 Pi6 Pj6 Pk6<br />
Pd7 Pe7 Pf7 Pg7 Ph7 Pi7 Pj7 Pk7<br />
</hex><br />
=== Using the [[parallel ladder]] trick ===<br />
<br />
6 moves can furthermore be discarded thanks to the [[Parallel ladder]] trick. Of course, symmetry will cut our work in half!<br />
<br />
We can dispose of 3 moves on the left (and, using mirror symmetry, the corresponding 3 moves on the right), as follows:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pg5 <br />
Pf6 <br />
Pe7<br />
N:on Ri4 Bi5 Rh5 Bg7 Rh6 Bh7<br />
</hex><br />
<br />
At this point, we can use the [[Parallel ladder]] trick as follows:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pg5 <br />
Pf6 <br />
Pe7<br />
Ri4 Bi5 Rh5 Bg7 Rh6 Bh7<br />
N:on Rk5 Bj6 Ri6 Bi7 Rl4 Bj5 Rk3<br />
</hex><br />
<br />
=== [[Overlapping connections|Remaining possibilities]] for Blue ===<br />
Blue's first move must be one of the following:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Pi4<br />
Ph5 Pi5<br />
Pg6 Pi6<br />
Pf7 Pg7 Ph7 Pi7<br />
</hex><br />
<br />
== Specific defence ==<br />
For the moves that intersect all the carriers, Red has to find specific answers. Let's deal with the remaining intrusions!<br />
<br />
===One remaining intrusion on the first row (stub) ===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bf7 <br />
</hex><br />
<br />
===The other remaining intrusion on the first row (stub)===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bg7 <br />
</hex><br />
<br />
===The remaining intrusion on the second row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bg6 <br />
</hex><br />
<br />
===The remaining intrusion on the third row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bh5 <br />
</hex><br />
<br />
===The remaining intrusion on the fourth row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 <br />
</hex><br />
<br />
Red should move here:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
</hex><br />
<br />
==== Elimination of irrelevant Blue moves ====<br />
This gives Red several immediate threats:<br />
From III1a:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Ph5<br />
Pf6 Pg6 Ph6<br />
Pe7 Pf7 Pg7 Ph7<br />
</hex><br />
<br />
From III1a again:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Pf5<br />
Pe6 Pf6 Pg6<br />
Pd7 Pe7 Pf7 Pg7 <br />
</hex><br />
<br />
From III1b :<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Pf5 Ph5<br />
Pe6 Pf6 Pg6 Ph6<br />
Pd7 Pe7 Pg7 Ph7 <br />
</hex><br />
<br />
From IV1a:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg4<br />
Pf4<br />
Pd5 Pe5 Pf5 Pg5 Ph5<br />
Pc6 Pd6 Pe6 Pf6 Pg6 Ph6<br />
Pb7 Pc7 Pd7 Pe7 Pf7 Pg7 Ph7<br />
</hex><br />
<br />
From IV1b:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg4<br />
Pf4 Ph4<br />
Pd5 Pe5 Pf5 Pg5 Ph5 Pi5<br />
Pc6 Pd6 Pe6 Pg6 Ph6 Pi6<br />
Pb7 Pc7 Pd7 Pe7 Pf7 Pg7 Ph7 Pi7<br />
</hex><br />
<br />
The intersection of all of these leaves: <br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Pg4<br />
Pg5<br />
Pg6 <br />
Pe7 Pg7 <br />
</hex><br />
<br />
==== Specific defence ==== <br />
So we must deal with each of these responses. (Which will not be too hard!)<br />
<br />
===== Bg4 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg4 Rh4 Bg6 Rh5<br />
</hex><br />
And now either<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg4 Rh4 Bg6 Rh5<br />
N:on Bh6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
<br />
or<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg4 Rh4 Bg6 Rh5<br />
N:on Bh7 Rh6 Bg7 Rj6 Bi6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
===== Bg5 =====<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg5 Rf4<br />
</hex><br />
Threatening:<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pe4<br />
Pc5 R4d5 Pe5<br />
Pb6 Pc6 Pd6<br />
Pa7 Pb7 Pc7 Pd7<br />
</hex><br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pe5 Pf5<br />
R4e6<br />
Pd7 Pe7<br />
</hex><br />
<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pd5 R4e5 Pf5<br />
Pc6 Pd6 Pe6 Pf6<br />
Pb7 Pc7 Pe7 Pf7<br />
</hex><br />
So the only hope for Blue lies in the intersection of the threats, Be5, but it is unsufficient:<br />
<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
N:on Be5 Rf5 Be7 Rf6 Bf7 Rg6 Bg7 Rj5<br />
Pk3 Pi5<br />
</hex><br />
===== Bg6 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg6 Rg5 Bf6 Rh5<br />
Pe7<br />
</hex><br />
<br />
3 could be played at + with the same effect; in any case<br />
now either<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg6 Rg5 Bf6 Rh5<br />
N:on Bh6 Rj5<br />
Pi5 Pk3<br />
</hex><br />
<br />
or<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg6 Rg5 Bf6 Rh5<br />
N:on Bh7 Rh6 Bg7 Rj6 Bi6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
<br />
===== Be7 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Be7 Rg5 Bg6 Rh5 Bh6 Rj5<br />
Pi5 Pk3<br />
<br />
</hex><br />
<br />
===== Bg7 =====<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg7 Rg5 Bf6 Rh6 Bh7 Rj6 Bi6 Rj5<br />
Pi5 Pk3<br />
<br />
</hex><br />
<br />
===The remaining intrusion on the fifth row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
</hex><br />
<br />
First establish a [[double ladder]] on the right.<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
N:on Rj3 Bi5 Rk4 Bk5 Rj5 Bi7 Ri4 Bh5 <br />
</hex><br />
<br />
Then use [[Tom's move]]:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
Rj3 Bi5 Rk4 Bk5 Rj5 Bi7 Ri4 Bh5 Rf5 Bf6<br />
N:on Rf5 Bf6 Rf4 Bg5 Rh3<br />
</hex><br />
<br />
<br />
[[category:edge templates]]<br />
[[category:theory]]</div>
Kogorman
https://www.hexwiki.net/index.php/Edge_template_VI1a
Edge template VI1a
2009-02-17T10:22:33Z
<p>Kogorman: /* One remaining intrusion on the first row */ mark as incomplete</p>
<hr />
<div>This template is the first one stone 6th row [[edge template|template]] for which a proof has been handwritten.<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
</hex><br />
<br />
== Elimination of irrelevant Blue moves ==<br />
<br />
Red has a couple of direct threats to connect, using smaller templates. Blue must play in the carrier of these threats in order to counter them. To prevent Red from connecting Blue must play in the intersection of Red's threats carriers.<br />
<br />
=== [[edge template IV1a]] ===<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ph4 Ri4<br />
Pf5 Pg5 Ph5 Pi5 Pj5 <br />
Pe6 Pf6 Pg6 Ph6 Pi6 Pj6<br />
Pd7 Pe7 Pf7 Pg7 Ph7 Pi7 Pj7<br />
</hex><br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ri4 Pj4<br />
Pg5 Ph5 Pi5 Pj5 Pk5<br />
Pf6 Pg6 Ph6 Pi6 Pj6 Pk6<br />
Pe7 Pf7 Pg7 Ph7 Pi7 Pj7 Pk7<br />
</hex><br />
<br />
=== [[edge template IV1b]] ===<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ph4 Ri4 Pj4<br />
Pf5 Pg5 Ph5 Pi5 Pj5 Pk5<br />
Pe6 Pf6 Pg6 Pi6 Pj6 Pk6<br />
Pd7 Pe7 Pf7 Pg7 Ph7 Pi7 Pj7 Pk7<br />
</hex><br />
=== Using the [[parallel ladder]] trick ===<br />
<br />
6 moves can furthermore be discarded thanks to the [[Parallel ladder]] trick. Of course, symmetry will cut our work in half!<br />
<br />
We can dispose of 3 moves on the left (and, using mirror symmetry, the corresponding 3 moves on the right), as follows:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pg5 <br />
Pf6 <br />
Pe7<br />
N:on Ri4 Bi5 Rh5 Bg7 Rh6 Bh7<br />
</hex><br />
<br />
At this point, we can use the [[Parallel ladder]] trick as follows:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pg5 <br />
Pf6 <br />
Pe7<br />
Ri4 Bi5 Rh5 Bg7 Rh6 Bh7<br />
N:on Rk5 Bj6 Ri6 Bi7 Rl4 Bj5 Rk3<br />
</hex><br />
<br />
=== [[Overlapping connections|Remaining possibilities]] for Blue ===<br />
Blue's first move must be one of the following:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Pi4<br />
Ph5 Pi5<br />
Pg6 Pi6<br />
Pf7 Pg7 Ph7 Pi7<br />
</hex><br />
<br />
== Specific defence ==<br />
For the moves that intersect all the carriers, Red has to find specific answers. Let's deal with the remaining intrusions!<br />
<br />
===One remaining intrusion on the first row (stub) ===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bf7 <br />
</hex><br />
<br />
===The other remaining intrusion on the first row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bg7 <br />
</hex><br />
<br />
===The remaining intrusion on the second row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bg6 <br />
</hex><br />
<br />
===The remaining intrusion on the third row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bh5 <br />
</hex><br />
<br />
===The remaining intrusion on the fourth row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 <br />
</hex><br />
<br />
Red should move here:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
</hex><br />
<br />
==== Elimination of irrelevant Blue moves ====<br />
This gives Red several immediate threats:<br />
From III1a:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Ph5<br />
Pf6 Pg6 Ph6<br />
Pe7 Pf7 Pg7 Ph7<br />
</hex><br />
<br />
From III1a again:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Pf5<br />
Pe6 Pf6 Pg6<br />
Pd7 Pe7 Pf7 Pg7 <br />
</hex><br />
<br />
From III1b :<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Pf5 Ph5<br />
Pe6 Pf6 Pg6 Ph6<br />
Pd7 Pe7 Pg7 Ph7 <br />
</hex><br />
<br />
From IV1a:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg4<br />
Pf4<br />
Pd5 Pe5 Pf5 Pg5 Ph5<br />
Pc6 Pd6 Pe6 Pf6 Pg6 Ph6<br />
Pb7 Pc7 Pd7 Pe7 Pf7 Pg7 Ph7<br />
</hex><br />
<br />
From IV1b:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg4<br />
Pf4 Ph4<br />
Pd5 Pe5 Pf5 Pg5 Ph5 Pi5<br />
Pc6 Pd6 Pe6 Pg6 Ph6 Pi6<br />
Pb7 Pc7 Pd7 Pe7 Pf7 Pg7 Ph7 Pi7<br />
</hex><br />
<br />
The intersection of all of these leaves: <br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Pg4<br />
Pg5<br />
Pg6 <br />
Pe7 Pg7 <br />
</hex><br />
<br />
==== Specific defence ==== <br />
So we must deal with each of these responses. (Which will not be too hard!)<br />
<br />
===== Bg4 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg4 Rh4 Bg6 Rh5<br />
</hex><br />
And now either<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg4 Rh4 Bg6 Rh5<br />
N:on Bh6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
<br />
or<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg4 Rh4 Bg6 Rh5<br />
N:on Bh7 Rh6 Bg7 Rj6 Bi6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
===== Bg5 =====<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg5 Rf4<br />
</hex><br />
Threatening:<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pe4<br />
Pc5 R4d5 Pe5<br />
Pb6 Pc6 Pd6<br />
Pa7 Pb7 Pc7 Pd7<br />
</hex><br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pe5 Pf5<br />
R4e6<br />
Pd7 Pe7<br />
</hex><br />
<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pd5 R4e5 Pf5<br />
Pc6 Pd6 Pe6 Pf6<br />
Pb7 Pc7 Pe7 Pf7<br />
</hex><br />
So the only hope for Blue lies in the intersection of the threats, Be5, but it is unsufficient:<br />
<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
N:on Be5 Rf5 Be7 Rf6 Bf7 Rg6 Bg7 Rj5<br />
Pk3 Pi5<br />
</hex><br />
===== Bg6 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg6 Rg5 Bf6 Rh5<br />
Pe7<br />
</hex><br />
<br />
3 could be played at + with the same effect; in any case<br />
now either<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg6 Rg5 Bf6 Rh5<br />
N:on Bh6 Rj5<br />
Pi5 Pk3<br />
</hex><br />
<br />
or<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg6 Rg5 Bf6 Rh5<br />
N:on Bh7 Rh6 Bg7 Rj6 Bi6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
<br />
===== Be7 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Be7 Rg5 Bg6 Rh5 Bh6 Rj5<br />
Pi5 Pk3<br />
<br />
</hex><br />
<br />
===== Bg7 =====<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg7 Rg5 Bf6 Rh6 Bh7 Rj6 Bi6 Rj5<br />
Pi5 Pk3<br />
<br />
</hex><br />
<br />
===The remaining intrusion on the fifth row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
</hex><br />
<br />
First establish a [[double ladder]] on the right.<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
N:on Rj3 Bi5 Rk4 Bk5 Rj5 Bi7 Ri4 Bh5 <br />
</hex><br />
<br />
Then use [[Tom's move]]:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
Rj3 Bi5 Rk4 Bk5 Rj5 Bi7 Ri4 Bh5 Rf5 Bf6<br />
N:on Rf5 Bf6 Rf4 Bg5 Rh3<br />
</hex><br />
<br />
<br />
[[category:edge templates]]<br />
[[category:theory]]</div>
Kogorman
https://www.hexwiki.net/index.php/Edge_template_VI1a
Edge template VI1a
2009-02-15T04:52:13Z
<p>Kogorman: /* Be7 */ Filled in the details</p>
<hr />
<div>This template is the first one stone 6th row [[edge template|template]] for which a proof has been handwritten.<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
</hex><br />
<br />
== Elimination of irrelevant Blue moves ==<br />
<br />
Red has a couple of direct threats to connect, using smaller templates. Blue must play in the carrier of these threats in order to counter them. To prevent Red from connecting Blue must play in the intersection of Red's threats carriers.<br />
<br />
=== [[edge template IV1a]] ===<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ph4 Ri4<br />
Pf5 Pg5 Ph5 Pi5 Pj5 <br />
Pe6 Pf6 Pg6 Ph6 Pi6 Pj6<br />
Pd7 Pe7 Pf7 Pg7 Ph7 Pi7 Pj7<br />
</hex><br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ri4 Pj4<br />
Pg5 Ph5 Pi5 Pj5 Pk5<br />
Pf6 Pg6 Ph6 Pi6 Pj6 Pk6<br />
Pe7 Pf7 Pg7 Ph7 Pi7 Pj7 Pk7<br />
</hex><br />
<br />
=== [[edge template IV1b]] ===<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ph4 Ri4 Pj4<br />
Pf5 Pg5 Ph5 Pi5 Pj5 Pk5<br />
Pe6 Pf6 Pg6 Pi6 Pj6 Pk6<br />
Pd7 Pe7 Pf7 Pg7 Ph7 Pi7 Pj7 Pk7<br />
</hex><br />
=== Using the [[parallel ladder]] trick ===<br />
<br />
6 moves can furthermore be discarded thanks to the [[Parallel ladder]] trick. Of course, symmetry will cut our work in half!<br />
<br />
We can dispose of 3 moves on the left (and, using mirror symmetry, the corresponding 3 moves on the right), as follows:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pg5 <br />
Pf6 <br />
Pe7<br />
N:on Ri4 Bi5 Rh5 Bg7 Rh6 Bh7<br />
</hex><br />
<br />
At this point, we can use the [[Parallel ladder]] trick as follows:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pg5 <br />
Pf6 <br />
Pe7<br />
Ri4 Bi5 Rh5 Bg7 Rh6 Bh7<br />
N:on Rk5 Bj6 Ri6 Bi7 Rl4 Bj5 Rk3<br />
</hex><br />
<br />
=== [[Overlapping connections|Remaining possibilities]] for Blue ===<br />
Blue's first move must be one of the following:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Pi4<br />
Ph5 Pi5<br />
Pg6 Pi6<br />
Pf7 Pg7 Ph7 Pi7<br />
</hex><br />
<br />
== Specific defence ==<br />
For the moves that intersect all the carriers, Red has to find specific answers. Let's deal with the remaining intrusions!<br />
<br />
===One remaining intrusion on the first row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bf7 <br />
</hex><br />
<br />
===The other remaining intrusion on the first row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bg7 <br />
</hex><br />
<br />
===The remaining intrusion on the second row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bg6 <br />
</hex><br />
<br />
===The remaining intrusion on the third row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bh5 <br />
</hex><br />
<br />
===The remaining intrusion on the fourth row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 <br />
</hex><br />
<br />
Red should move here:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
</hex><br />
<br />
==== Elimination of irrelevant Blue moves ====<br />
This gives Red several immediate threats:<br />
From III1a:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Ph5<br />
Pf6 Pg6 Ph6<br />
Pe7 Pf7 Pg7 Ph7<br />
</hex><br />
<br />
From III1a again:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Pf5<br />
Pe6 Pf6 Pg6<br />
Pd7 Pe7 Pf7 Pg7 <br />
</hex><br />
<br />
From III1b :<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Pf5 Ph5<br />
Pe6 Pf6 Pg6 Ph6<br />
Pd7 Pe7 Pg7 Ph7 <br />
</hex><br />
<br />
From IV1a:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg4<br />
Pf4<br />
Pd5 Pe5 Pf5 Pg5 Ph5<br />
Pc6 Pd6 Pe6 Pf6 Pg6 Ph6<br />
Pb7 Pc7 Pd7 Pe7 Pf7 Pg7 Ph7<br />
</hex><br />
<br />
From IV1b:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg4<br />
Pf4 Ph4<br />
Pd5 Pe5 Pf5 Pg5 Ph5 Pi5<br />
Pc6 Pd6 Pe6 Pg6 Ph6 Pi6<br />
Pb7 Pc7 Pd7 Pe7 Pf7 Pg7 Ph7 Pi7<br />
</hex><br />
<br />
The intersection of all of these leaves: <br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Pg4<br />
Pg5<br />
Pg6 <br />
Pe7 Pg7 <br />
</hex><br />
<br />
==== Specific defence ==== <br />
So we must deal with each of these responses. (Which will not be too hard!)<br />
<br />
===== Bg4 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg4 Rh4 Bg6 Rh5<br />
</hex><br />
And now either<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg4 Rh4 Bg6 Rh5<br />
N:on Bh6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
<br />
or<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg4 Rh4 Bg6 Rh5<br />
N:on Bh7 Rh6 Bg7 Rj6 Bi6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
===== Bg5 =====<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg5 Rf4<br />
</hex><br />
Threatening:<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pe4<br />
Pc5 R4d5 Pe5<br />
Pb6 Pc6 Pd6<br />
Pa7 Pb7 Pc7 Pd7<br />
</hex><br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pe5 Pf5<br />
R4e6<br />
Pd7 Pe7<br />
</hex><br />
<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pd5 R4e5 Pf5<br />
Pc6 Pd6 Pe6 Pf6<br />
Pb7 Pc7 Pe7 Pf7<br />
</hex><br />
So the only hope for Blue lies in the intersection of the threats, Be5, but it is unsufficient:<br />
<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
N:on Be5 Rf5 Be7 Rf6 Bf7 Rg6 Bg7 Rj5<br />
Pk3 Pi5<br />
</hex><br />
===== Bg6 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg6 Rg5 Bf6 Rh5<br />
Pe7<br />
</hex><br />
<br />
3 could be played at + with the same effect; in any case<br />
now either<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg6 Rg5 Bf6 Rh5<br />
N:on Bh6 Rj5<br />
Pi5 Pk3<br />
</hex><br />
<br />
or<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg6 Rg5 Bf6 Rh5<br />
N:on Bh7 Rh6 Bg7 Rj6 Bi6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
<br />
===== Be7 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Be7 Rg5 Bg6 Rh5 Bh6 Rj5<br />
Pi5 Pk3<br />
<br />
</hex><br />
<br />
===== Bg7 =====<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg7 Rg5 Bf6 Rh6 Bh7 Rj6 Bi6 Rj5<br />
Pi5 Pk3<br />
<br />
</hex><br />
<br />
===The remaining intrusion on the fifth row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
</hex><br />
<br />
First establish a [[double ladder]] on the right.<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
N:on Rj3 Bi5 Rk4 Bk5 Rj5 Bi7 Ri4 Bh5 <br />
</hex><br />
<br />
Then use [[Tom's move]]:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
Rj3 Bi5 Rk4 Bk5 Rj5 Bi7 Ri4 Bh5 Rf5 Bf6<br />
N:on Rf5 Bf6 Rf4 Bg5 Rh3<br />
</hex><br />
<br />
<br />
[[category:edge templates]]<br />
[[category:theory]]</div>
Kogorman
https://www.hexwiki.net/index.php/Edge_template_VI1a
Edge template VI1a
2009-02-15T04:48:13Z
<p>Kogorman: /* Bg7 */ filled in the details</p>
<hr />
<div>This template is the first one stone 6th row [[edge template|template]] for which a proof has been handwritten.<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
</hex><br />
<br />
== Elimination of irrelevant Blue moves ==<br />
<br />
Red has a couple of direct threats to connect, using smaller templates. Blue must play in the carrier of these threats in order to counter them. To prevent Red from connecting Blue must play in the intersection of Red's threats carriers.<br />
<br />
=== [[edge template IV1a]] ===<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ph4 Ri4<br />
Pf5 Pg5 Ph5 Pi5 Pj5 <br />
Pe6 Pf6 Pg6 Ph6 Pi6 Pj6<br />
Pd7 Pe7 Pf7 Pg7 Ph7 Pi7 Pj7<br />
</hex><br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ri4 Pj4<br />
Pg5 Ph5 Pi5 Pj5 Pk5<br />
Pf6 Pg6 Ph6 Pi6 Pj6 Pk6<br />
Pe7 Pf7 Pg7 Ph7 Pi7 Pj7 Pk7<br />
</hex><br />
<br />
=== [[edge template IV1b]] ===<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ph4 Ri4 Pj4<br />
Pf5 Pg5 Ph5 Pi5 Pj5 Pk5<br />
Pe6 Pf6 Pg6 Pi6 Pj6 Pk6<br />
Pd7 Pe7 Pf7 Pg7 Ph7 Pi7 Pj7 Pk7<br />
</hex><br />
=== Using the [[parallel ladder]] trick ===<br />
<br />
6 moves can furthermore be discarded thanks to the [[Parallel ladder]] trick. Of course, symmetry will cut our work in half!<br />
<br />
We can dispose of 3 moves on the left (and, using mirror symmetry, the corresponding 3 moves on the right), as follows:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pg5 <br />
Pf6 <br />
Pe7<br />
N:on Ri4 Bi5 Rh5 Bg7 Rh6 Bh7<br />
</hex><br />
<br />
At this point, we can use the [[Parallel ladder]] trick as follows:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pg5 <br />
Pf6 <br />
Pe7<br />
Ri4 Bi5 Rh5 Bg7 Rh6 Bh7<br />
N:on Rk5 Bj6 Ri6 Bi7 Rl4 Bj5 Rk3<br />
</hex><br />
<br />
=== [[Overlapping connections|Remaining possibilities]] for Blue ===<br />
Blue's first move must be one of the following:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Pi4<br />
Ph5 Pi5<br />
Pg6 Pi6<br />
Pf7 Pg7 Ph7 Pi7<br />
</hex><br />
<br />
== Specific defence ==<br />
For the moves that intersect all the carriers, Red has to find specific answers. Let's deal with the remaining intrusions!<br />
<br />
===One remaining intrusion on the first row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bf7 <br />
</hex><br />
<br />
===The other remaining intrusion on the first row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bg7 <br />
</hex><br />
<br />
===The remaining intrusion on the second row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bg6 <br />
</hex><br />
<br />
===The remaining intrusion on the third row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bh5 <br />
</hex><br />
<br />
===The remaining intrusion on the fourth row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 <br />
</hex><br />
<br />
Red should move here:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
</hex><br />
<br />
==== Elimination of irrelevant Blue moves ====<br />
This gives Red several immediate threats:<br />
From III1a:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Ph5<br />
Pf6 Pg6 Ph6<br />
Pe7 Pf7 Pg7 Ph7<br />
</hex><br />
<br />
From III1a again:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Pf5<br />
Pe6 Pf6 Pg6<br />
Pd7 Pe7 Pf7 Pg7 <br />
</hex><br />
<br />
From III1b :<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Pf5 Ph5<br />
Pe6 Pf6 Pg6 Ph6<br />
Pd7 Pe7 Pg7 Ph7 <br />
</hex><br />
<br />
From IV1a:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg4<br />
Pf4<br />
Pd5 Pe5 Pf5 Pg5 Ph5<br />
Pc6 Pd6 Pe6 Pf6 Pg6 Ph6<br />
Pb7 Pc7 Pd7 Pe7 Pf7 Pg7 Ph7<br />
</hex><br />
<br />
From IV1b:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg4<br />
Pf4 Ph4<br />
Pd5 Pe5 Pf5 Pg5 Ph5 Pi5<br />
Pc6 Pd6 Pe6 Pg6 Ph6 Pi6<br />
Pb7 Pc7 Pd7 Pe7 Pf7 Pg7 Ph7 Pi7<br />
</hex><br />
<br />
The intersection of all of these leaves: <br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Pg4<br />
Pg5<br />
Pg6 <br />
Pe7 Pg7 <br />
</hex><br />
<br />
==== Specific defence ==== <br />
So we must deal with each of these responses. (Which will not be too hard!)<br />
<br />
===== Bg4 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg4 Rh4 Bg6 Rh5<br />
</hex><br />
And now either<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg4 Rh4 Bg6 Rh5<br />
N:on Bh6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
<br />
or<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg4 Rh4 Bg6 Rh5<br />
N:on Bh7 Rh6 Bg7 Rj6 Bi6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
===== Bg5 =====<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg5 Rf4<br />
</hex><br />
Threatening:<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pe4<br />
Pc5 R4d5 Pe5<br />
Pb6 Pc6 Pd6<br />
Pa7 Pb7 Pc7 Pd7<br />
</hex><br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pe5 Pf5<br />
R4e6<br />
Pd7 Pe7<br />
</hex><br />
<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pd5 R4e5 Pf5<br />
Pc6 Pd6 Pe6 Pf6<br />
Pb7 Pc7 Pe7 Pf7<br />
</hex><br />
So the only hope for Blue lies in the intersection of the threats, Be5, but it is unsufficient:<br />
<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
N:on Be5 Rf5 Be7 Rf6 Bf7 Rg6 Bg7 Rj5<br />
Pk3 Pi5<br />
</hex><br />
===== Bg6 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg6 Rg5 Bf6 Rh5<br />
Pe7<br />
</hex><br />
<br />
3 could be played at + with the same effect; in any case<br />
now either<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg6 Rg5 Bf6 Rh5<br />
N:on Bh6 Rj5<br />
Pi5 Pk3<br />
</hex><br />
<br />
or<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg6 Rg5 Bf6 Rh5<br />
N:on Bh7 Rh6 Bg7 Rj6 Bi6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
<br />
===== Be7 =====<br />
===== Bg7 =====<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg7 Rg5 Bf6 Rh6 Bh7 Rj6 Bi6 Rj5<br />
Pi5 Pk3<br />
<br />
</hex><br />
<br />
===The remaining intrusion on the fifth row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
</hex><br />
<br />
First establish a [[double ladder]] on the right.<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
N:on Rj3 Bi5 Rk4 Bk5 Rj5 Bi7 Ri4 Bh5 <br />
</hex><br />
<br />
Then use [[Tom's move]]:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
Rj3 Bi5 Rk4 Bk5 Rj5 Bi7 Ri4 Bh5 Rf5 Bf6<br />
N:on Rf5 Bf6 Rf4 Bg5 Rh3<br />
</hex><br />
<br />
<br />
[[category:edge templates]]<br />
[[category:theory]]</div>
Kogorman
https://www.hexwiki.net/index.php/Edge_template_VI1a
Edge template VI1a
2009-02-15T04:39:25Z
<p>Kogorman: /* Bg6 */ Filled in the details.</p>
<hr />
<div>This template is the first one stone 6th row [[edge template|template]] for which a proof has been handwritten.<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
</hex><br />
<br />
== Elimination of irrelevant Blue moves ==<br />
<br />
Red has a couple of direct threats to connect, using smaller templates. Blue must play in the carrier of these threats in order to counter them. To prevent Red from connecting Blue must play in the intersection of Red's threats carriers.<br />
<br />
=== [[edge template IV1a]] ===<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ph4 Ri4<br />
Pf5 Pg5 Ph5 Pi5 Pj5 <br />
Pe6 Pf6 Pg6 Ph6 Pi6 Pj6<br />
Pd7 Pe7 Pf7 Pg7 Ph7 Pi7 Pj7<br />
</hex><br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ri4 Pj4<br />
Pg5 Ph5 Pi5 Pj5 Pk5<br />
Pf6 Pg6 Ph6 Pi6 Pj6 Pk6<br />
Pe7 Pf7 Pg7 Ph7 Pi7 Pj7 Pk7<br />
</hex><br />
<br />
=== [[edge template IV1b]] ===<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ph4 Ri4 Pj4<br />
Pf5 Pg5 Ph5 Pi5 Pj5 Pk5<br />
Pe6 Pf6 Pg6 Pi6 Pj6 Pk6<br />
Pd7 Pe7 Pf7 Pg7 Ph7 Pi7 Pj7 Pk7<br />
</hex><br />
=== Using the [[parallel ladder]] trick ===<br />
<br />
6 moves can furthermore be discarded thanks to the [[Parallel ladder]] trick. Of course, symmetry will cut our work in half!<br />
<br />
We can dispose of 3 moves on the left (and, using mirror symmetry, the corresponding 3 moves on the right), as follows:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pg5 <br />
Pf6 <br />
Pe7<br />
N:on Ri4 Bi5 Rh5 Bg7 Rh6 Bh7<br />
</hex><br />
<br />
At this point, we can use the [[Parallel ladder]] trick as follows:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pg5 <br />
Pf6 <br />
Pe7<br />
Ri4 Bi5 Rh5 Bg7 Rh6 Bh7<br />
N:on Rk5 Bj6 Ri6 Bi7 Rl4 Bj5 Rk3<br />
</hex><br />
<br />
=== [[Overlapping connections|Remaining possibilities]] for Blue ===<br />
Blue's first move must be one of the following:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Pi4<br />
Ph5 Pi5<br />
Pg6 Pi6<br />
Pf7 Pg7 Ph7 Pi7<br />
</hex><br />
<br />
== Specific defence ==<br />
For the moves that intersect all the carriers, Red has to find specific answers. Let's deal with the remaining intrusions!<br />
<br />
===One remaining intrusion on the first row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bf7 <br />
</hex><br />
<br />
===The other remaining intrusion on the first row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bg7 <br />
</hex><br />
<br />
===The remaining intrusion on the second row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bg6 <br />
</hex><br />
<br />
===The remaining intrusion on the third row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bh5 <br />
</hex><br />
<br />
===The remaining intrusion on the fourth row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 <br />
</hex><br />
<br />
Red should move here:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
</hex><br />
<br />
==== Elimination of irrelevant Blue moves ====<br />
This gives Red several immediate threats:<br />
From III1a:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Ph5<br />
Pf6 Pg6 Ph6<br />
Pe7 Pf7 Pg7 Ph7<br />
</hex><br />
<br />
From III1a again:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Pf5<br />
Pe6 Pf6 Pg6<br />
Pd7 Pe7 Pf7 Pg7 <br />
</hex><br />
<br />
From III1b :<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Pf5 Ph5<br />
Pe6 Pf6 Pg6 Ph6<br />
Pd7 Pe7 Pg7 Ph7 <br />
</hex><br />
<br />
From IV1a:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg4<br />
Pf4<br />
Pd5 Pe5 Pf5 Pg5 Ph5<br />
Pc6 Pd6 Pe6 Pf6 Pg6 Ph6<br />
Pb7 Pc7 Pd7 Pe7 Pf7 Pg7 Ph7<br />
</hex><br />
<br />
From IV1b:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg4<br />
Pf4 Ph4<br />
Pd5 Pe5 Pf5 Pg5 Ph5 Pi5<br />
Pc6 Pd6 Pe6 Pg6 Ph6 Pi6<br />
Pb7 Pc7 Pd7 Pe7 Pf7 Pg7 Ph7 Pi7<br />
</hex><br />
<br />
The intersection of all of these leaves: <br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Pg4<br />
Pg5<br />
Pg6 <br />
Pe7 Pg7 <br />
</hex><br />
<br />
==== Specific defence ==== <br />
So we must deal with each of these responses. (Which will not be too hard!)<br />
<br />
===== Bg4 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg4 Rh4 Bg6 Rh5<br />
</hex><br />
And now either<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg4 Rh4 Bg6 Rh5<br />
N:on Bh6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
<br />
or<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg4 Rh4 Bg6 Rh5<br />
N:on Bh7 Rh6 Bg7 Rj6 Bi6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
===== Bg5 =====<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg5 Rf4<br />
</hex><br />
Threatening:<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pe4<br />
Pc5 R4d5 Pe5<br />
Pb6 Pc6 Pd6<br />
Pa7 Pb7 Pc7 Pd7<br />
</hex><br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pe5 Pf5<br />
R4e6<br />
Pd7 Pe7<br />
</hex><br />
<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pd5 R4e5 Pf5<br />
Pc6 Pd6 Pe6 Pf6<br />
Pb7 Pc7 Pe7 Pf7<br />
</hex><br />
So the only hope for Blue lies in the intersection of the threats, Be5, but it is unsufficient:<br />
<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
N:on Be5 Rf5 Be7 Rf6 Bf7 Rg6 Bg7 Rj5<br />
Pk3 Pi5<br />
</hex><br />
===== Bg6 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg6 Rg5 Bf6 Rh5<br />
Pe7<br />
</hex><br />
<br />
3 could be played at + with the same effect; in any case<br />
now either<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg6 Rg5 Bf6 Rh5<br />
N:on Bh6 Rj5<br />
Pi5 Pk3<br />
</hex><br />
<br />
or<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg6 Rg5 Bf6 Rh5<br />
N:on Bh7 Rh6 Bg7 Rj6 Bi6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
<br />
===== Be7 =====<br />
===== Bg7 =====<br />
'''To be continued...'''<br />
<br />
===The remaining intrusion on the fifth row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
</hex><br />
<br />
First establish a [[double ladder]] on the right.<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
N:on Rj3 Bi5 Rk4 Bk5 Rj5 Bi7 Ri4 Bh5 <br />
</hex><br />
<br />
Then use [[Tom's move]]:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
Rj3 Bi5 Rk4 Bk5 Rj5 Bi7 Ri4 Bh5 Rf5 Bf6<br />
N:on Rf5 Bf6 Rf4 Bg5 Rh3<br />
</hex><br />
<br />
<br />
[[category:edge templates]]<br />
[[category:theory]]</div>
Kogorman
https://www.hexwiki.net/index.php/Edge_template_VI1a
Edge template VI1a
2009-02-12T18:24:05Z
<p>Kogorman: /* Using the parallel ladder trick */ spelling</p>
<hr />
<div>This template is the first one stone 6th row [[edge template|template]] for which a proof has been handwritten.<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
</hex><br />
<br />
== Elimination of irrelevant Blue moves ==<br />
<br />
Red has a couple of direct threats to connect, using smaller templates. Blue must play in the carrier of these threats in order to counter them. To prevent Red from connecting Blue must play in the intersection of Red's threats carriers.<br />
<br />
=== [[edge template IV1a]] ===<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ph4 Ri4<br />
Pf5 Pg5 Ph5 Pi5 Pj5 <br />
Pe6 Pf6 Pg6 Ph6 Pi6 Pj6<br />
Pd7 Pe7 Pf7 Pg7 Ph7 Pi7 Pj7<br />
</hex><br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ri4 Pj4<br />
Pg5 Ph5 Pi5 Pj5 Pk5<br />
Pf6 Pg6 Ph6 Pi6 Pj6 Pk6<br />
Pe7 Pf7 Pg7 Ph7 Pi7 Pj7 Pk7<br />
</hex><br />
<br />
=== [[edge template IV1b]] ===<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Ph4 Ri4 Pj4<br />
Pf5 Pg5 Ph5 Pi5 Pj5 Pk5<br />
Pe6 Pf6 Pg6 Pi6 Pj6 Pk6<br />
Pd7 Pe7 Pf7 Pg7 Ph7 Pi7 Pj7 Pk7<br />
</hex><br />
=== Using the [[parallel ladder]] trick ===<br />
<br />
6 moves can furthermore be discarded thanks to the [[Parallel ladder]] trick. Of course, symmetry will cut our work in half!<br />
<br />
We can dispose of 3 moves on the left (and, using mirror symmetry, the corresponding 3 moves on the right), as follows:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pg5 <br />
Pf6 <br />
Pe7<br />
N:on Ri4 Bi5 Rh5 Bg7 Rh6 Bh7<br />
</hex><br />
<br />
At this point, we can use the [[Parallel ladder]] trick as follows:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pg5 <br />
Pf6 <br />
Pe7<br />
Ri4 Bi5 Rh5 Bg7 Rh6 Bh7<br />
N:on Rk5 Bj6 Ri6 Bi7 Rl4 Bj5 Rk3<br />
</hex><br />
<br />
=== [[Overlapping connections|Remaining possibilities]] for Blue ===<br />
Blue's first move must be one of the following:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Pi3 Pj3<br />
Pi4<br />
Ph5 Pi5<br />
Pg6 Pi6<br />
Pf7 Pg7 Ph7 Pi7<br />
</hex><br />
<br />
== Specific defence ==<br />
For the moves that intersect all the carriers, Red has to find specific answers. Let's deal with the remaining intrusions!<br />
<br />
===One remaining intrusion on the first row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bf7 <br />
</hex><br />
<br />
===The other remaining intrusion on the first row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bg7 <br />
</hex><br />
<br />
===The remaining intrusion on the second row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bg6 <br />
</hex><br />
<br />
===The remaining intrusion on the third row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bh5 <br />
</hex><br />
<br />
===The remaining intrusion on the fourth row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 <br />
</hex><br />
<br />
Red should move here:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
</hex><br />
<br />
==== Elimination of irrelevant Blue moves ====<br />
This gives Red several immediate threats:<br />
From III1a:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Ph5<br />
Pf6 Pg6 Ph6<br />
Pe7 Pf7 Pg7 Ph7<br />
</hex><br />
<br />
From III1a again:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Pf5<br />
Pe6 Pf6 Pg6<br />
Pd7 Pe7 Pf7 Pg7 <br />
</hex><br />
<br />
From III1b :<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg5<br />
Pg4 Ph4<br />
Pf5 Ph5<br />
Pe6 Pf6 Pg6 Ph6<br />
Pd7 Pe7 Pg7 Ph7 <br />
</hex><br />
<br />
From IV1a:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg4<br />
Pf4<br />
Pd5 Pe5 Pf5 Pg5 Ph5<br />
Pc6 Pd6 Pe6 Pf6 Pg6 Ph6<br />
Pb7 Pc7 Pd7 Pe7 Pf7 Pg7 Ph7<br />
</hex><br />
<br />
From IV1b:<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Rg4<br />
Pf4 Ph4<br />
Pd5 Pe5 Pf5 Pg5 Ph5 Pi5<br />
Pc6 Pd6 Pe6 Pg6 Ph6 Pi6<br />
Pb7 Pc7 Pd7 Pe7 Pf7 Pg7 Ph7 Pi7<br />
</hex><br />
<br />
The intersection of all of these leaves: <br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3<br />
Pg4<br />
Pg5<br />
Pg6 <br />
Pe7 Pg7 <br />
</hex><br />
<br />
==== Specific defence ==== <br />
So we must deal with each of these responses. (Which will not be too hard!)<br />
<br />
===== Bg4 =====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg4 Rh4 Bg6 Rh5<br />
</hex><br />
And now either<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg4 Rh4 Bg6 Rh5<br />
N:on Bh6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
<br />
or<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
Bg4 Rh4 Bg6 Rh5<br />
N:on Bh7 Rh6 Bg7 Rj6 Bi6 Rj5<br />
Pk3 Pi5<br />
</hex><br />
===== Bg5 =====<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
<br />
N:on Bg5 Rf4<br />
</hex><br />
Threatening:<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pe4<br />
Pc5 R4d5 Pe5<br />
Pb6 Pc6 Pd6<br />
Pa7 Pb7 Pc7 Pd7<br />
</hex><br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pe5 Pf5<br />
R4e6<br />
Pd7 Pe7<br />
</hex><br />
<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
Pd5 R4e5 Pf5<br />
Pc6 Pd6 Pe6 Pf6<br />
Pb7 Pc7 Pe7 Pf7<br />
</hex><br />
So the only hope for Blue lies in the intersection of the threats, Be5, but it is unsufficient:<br />
<br />
<hex><br />
R7 C14 Q1<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi4 Rh3 <br />
Bg5 Rf4<br />
N:on Be5 Rf5 Be7 Rf6 Bf7 Rg6 Bg7 Rj5<br />
Pk3 Pi5<br />
</hex><br />
===== Bg6 =====<br />
===== Be7 =====<br />
===== Bg7 =====<br />
'''To be continued...'''<br />
<br />
===The remaining intrusion on the fifth row===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
</hex><br />
<br />
First establish a [[double ladder]] on the right.<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
N:on Rj3 Bi5 Rk4 Bk5 Rj5 Bi7 Ri4 Bh5 <br />
</hex><br />
<br />
Then use [[Tom's move]]:<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 <br />
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3<br />
Sa4 Sb4 Sc4 Sd4 Sn4<br />
Sa5 Sb5<br />
Sa6<br />
<br />
Bi3 <br />
Rj3 Bi5 Rk4 Bk5 Rj5 Bi7 Ri4 Bh5 Rf5 Bf6<br />
N:on Rf5 Bf6 Rf4 Bg5 Rh3<br />
</hex><br />
<br />
<br />
[[category:edge templates]]<br />
[[category:theory]]</div>
Kogorman
https://www.hexwiki.net/index.php/User:Kogorman
User:Kogorman
2007-07-02T00:36:57Z
<p>Kogorman: </p>
<hr />
<div>I'm Kevin O'Gorman. You can find my hex database [http://hex.kosmanor.com/hex-bin/board].<br />
<br />
The database hasn't been updated since around 2004-2005 because it needs a major overhaul. But I've still been collecting games, I'm hoping to do the overhaul during the Summer of 2007.<br />
<br />
++ kevin</div>
Kogorman
https://www.hexwiki.net/index.php/Current_events
Current events
2007-07-02T00:31:32Z
<p>Kogorman: </p>
<hr />
<div>Add new things at the top.<br />
<br />
1 July 2007: A couple dozen pages were hit by spam, apparently automated, in the last 3 days. I reverted what I could, but some of the pages' history was incomplete (such as the disclaimer), and all I could do was blank it out.<br />
<br />
-- kogorman<br />
<br />
----<br />
<br />
13 Aug 2005: I notice that several pages have been defaced by something like spam:<br />
a genuine entry has been erased by some hotel advertising. Is there some way to<br />
indicate that one or more diffs should be un-done?<br />
<br />
I'm not that familiar with the wiki way of doing things. Is there a better place<br />
to put comments like this?<br />
<br />
-- kogorman<br />
<br />
''The wiki way is to "Be Bold" and [http://communitywiki.org/WhyWikiWorks fix simple problems yourself], rather than talking about the problem.''<br />
''To revert a page to a previous version after a bad edit (or after someone has mistakenly reverted a good edit), follow the directions at http://en.wikipedia.org/wiki/Help:Revert .''<br />
''This [[current events]] page or the [[community portal]] is a great place to discuss problems like this that affect the entire wiki. (Problems that affect only one page should be discussed using the "discussion" tab for that page).''<br />
<br />
----<br />
<br />
I've just added the HexWiki to the WikiIndex:<br />
http://wikiindex.com/HexWiki<br />
. I hope you don't mind.<br />
--[[User:DavidCary|DavidCary]] 04:01, 4 Dec 2006 (CET)<br />
<br />
----</div>
Kogorman
https://www.hexwiki.net/index.php/Hex_theory
Hex theory
2007-07-02T00:28:02Z
<p>Kogorman: revert again</p>
<hr />
<div>Unlike many other games, it is possible to say certain things about [[Hex]], with absolute certainty. While, for example, nobody seriously believes that black has a winning strategy in [http://en.wikipedia.org/wiki/Chess chess], nobody has been able to prove that such a strategy doesn't exist. In Hex, on the other hand, a simple argument can show that the [[second player]] certainly does not have a winning strategy from the [[starting position]] (when the [[Swap rule|swap option]] is not used). Whether this makes Hex a better game is of course debatable, but many find this attribute charming.<br />
<br />
The most important properties of Hex are the following:<br />
<br />
* The game can not end in a [[draw]]. ([http://javhar1.googlepages.com/hexcannotendinadraw Proofs] on Javhar's page)<br />
* The [[first player]] has a [[winning strategy]].<br />
* When playing with the swap option, the second player has a winning strategy.<br />
<br />
== See also ==<br />
<br />
[[Open problems]]</div>
Kogorman
https://www.hexwiki.net/index.php/Piet_Hein
Piet Hein
2007-07-02T00:22:25Z
<p>Kogorman: revert again</p>
<hr />
<div>'''Piet Hein''' (1905-1996) was a Danish poet and mathematician, and the first inventor of Hex.<br />
<br />
In Denmark, and in the rest of Scandinavia, he is most famous for his collections of short poems, which he called [http://en.wikipedia.org/wiki/Grook grooks]. Most of them are written in Danish, but some he himself translated into English. The following is an example of these poems, which ought to be taken to heart by all [[Hex]] players.<br />
<br />
The road to wisdom?<br />
Well, it's plain<br />
and simple to express:<br />
Err<br />
and err<br />
and err again<br />
but less<br />
and less<br />
and less<br />
<br />
==External links==<br />
<br />
* [http://www.piethein.com Piet Hein Homepage]<br />
* [http://www.ctaz.com/~dmn1/hein.htm Notes on Piet Hein]<br />
* [http://chat.carleton.ca/~tcstewar/grooks/grooks.html Grooks by Piet Hein]</div>
Kogorman
https://www.hexwiki.net/index.php/File:Hexposition02.jpg
File:Hexposition02.jpg
2007-07-02T00:18:51Z
<p>Kogorman: </p>
<hr />
<div>POV-Ray generated image, using modified source code for a Go board. The position is from Little Golem game 247486.</div>
Kogorman
https://www.hexwiki.net/index.php/Intermediate_(strategy_guide)
Intermediate (strategy guide)
2007-07-02T00:16:15Z
<p>Kogorman: revert</p>
<hr />
<div>''Adapted with permission from Glenn C. Rhoads strategy guide.''<br />
<br />
== Loose connections ==<br />
''(See also the article [[Loose connection]])''<br />
<br />
[[Adjacent move]]s provide a guaranteed connection but cover little ground. [[Bridge|Two-bridges]] cover twice the distance and are almost as strong. The next best connection when even more distance is required is called the '''loose connection''' &mdash; a [[Hex (board element)|hex]] that is a two-bridge plus an adjacent step away.<br />
<br />
<hex>R4 C5 Vb2 Sc2 Sc3 Vd3</hex><br />
<br />
The [[piece]]s of the loose connection [[threat]]en to connect via a two-bridge plus an adjacent step [[Multiple threats|in two different ways]] &mdash; by playing at either of the marked hexes. Also, the two marked hexes are the only ones that are in the [[overlap]] of the two [[Template|connection patterns]]. Thus, to break a loose connection, one must play in one of the marked hexes.<br />
<br />
Another connection pattern that is useful to be aware of is two pieces in the same row or column that are three hexes apart.<br />
<br />
<hex>R5 C6 Sd2 Vb3 Pc3 Pd3 Ve3 Sc4</hex><br />
<br />
The pieces threaten to connect via 2 two-bridge steps in two different ways, namely by playing at piece at one of the hexes marked with a *. There are two hexes that are in the overlap between these two connection threats and a move played in either of them breaks the immediate connection (these two hexes are marked with a +). This connection pattern is not as strong as the loose connection.<br />
<br />
== The useless triangle ==<br />
''(See also the article [[Useless triangle]])''<br />
<br />
When a piece's neighboring hexes are [[occupied hex|filled]] by the [[opponent]] such that that piece has only two empty neighboring hexes that are also [[adjacent]] to each other, then the piece is said to lie in a "'''useless triangle'''."<br />
<br />
<hex>R7 C7 Q1 Vc5 Hd4 Hc4 Hb5 Hd5 Vd7 He7 Vf7</hex><br />
<br />
In the above diagram, the red piece at c5 and the [[empty hex]]es b6 and c6 form a useless triangle. The blue piece at e7 and the empty hexes e6 and f6 also form a useless triangle. The important point is that unless the piece in a useless triangle is in that player's [[First row|border row]], the piece has effectively been removed from the game &mdash; that is, it cannot have any effect on the rest of the game regardless of the rest of the position.<br />
<br />
== Minimal edge templates ==<br />
(See also the page [[Edge templates]])<br />
<br />
An '''edge template''' is a pattern of empty hexes that will allow a piece to be [[Connection|connected]] to the [[edge]] even if the opponent has the next move. Just as the two-bridge is a useful connection pattern to know, so are minimal edge templates &mdash; the ones of the smallest size. (The templates are numbered according to row of the [[connecting piece]]).<br />
<br />
=== [[Template I]] ===<br />
<br />
Trivially, a piece on an edge row is connected to the edge.<br />
<br />
<hex>R3 C3 Vb3</hex><br />
<br />
=== [[Template II]] ===<br />
<br />
<hex>R3 C3 Vb2 Sa3 Sb3</hex><br />
<br />
If the opponent plays inside the template, [[Red (player)|Red]] plays the other move in the template restoring the connection to the edge.<br />
<br />
For templates farther away, the general strategy to apply when the opponent intrudes on the template is to make a move in the template that reduces to a smaller and closer template.<br />
<br />
=== [[Template IIIa]] ===<br />
''(Also called [[Ziggurat]])''<br />
<br />
<hex>R4 C4 Q1 Vc2 Sb3 Sd3</hex><br />
<br />
If the opponent intrudes on the template, then Red plays at one of the two marked points achieving [[template II]]. Since the b3 template and the two-chain/d3 template combination don't overlap, the opponent cannot stop both. (This template exists in a mirror image form with the red piece at d2).<br />
<br />
=== [[Template IIIb]] ===<br />
<br />
<hex>R4 C5 Vd2 Sb3 Se3 Pc4</hex><br />
<br />
The [[Hex (board element)|hex]] marked with an '+' can be occupied by the opponent! If the opponent intrudes on the template, then Red two-chains to either of the marked hexes and in either case forms [[template II]]. Since the two-chain/template II combinations don't [[overlap]] with each other, the opponent cannot stop both.<br />
<br />
=== [[Template IVa]] ===<br />
<br />
<hex>R5 C7 Q1 Ve2 Sd3 Se3 Sf3 PD5</hex><br />
<br />
If the opponent intrudes on the template, Red plays to one of hexes marked with '*' forming [[template IIIa]]. The one exception is if the opponent plays at d5, then Red plays to e3 and connects via [[template IIIb]]. (This template has a mirror image form with the red piece at f2.)<br />
<br />
=== [[Template IVb]] ===<br />
<br />
<hex>R5 C8 Vf2 Sd3 Sg3 Pe4</hex><br />
<br />
The hex marked with a '+' can be occupied by the opponent! If the opponent intrudes on the template, Red two-chains to one of the marked hexes forming [[template IIIa]].<br />
<br />
== Forming ladders ==<br />
''(See also the article [[Ladder]])''<br />
<br />
A '''ladder''' occurs when one player tries to force a connection to an edge but is kept a constant distance away by the opponent, resulting in a sequence of moves parallel to the edge. The following is an example with Red to play.<br />
<br />
<hex>R9 C9 Q1 Ve3 Vd4 Vd5 Vc6 Vc7 Hb8 Hb9 Hd7 He6 Hf6</hex><br />
<br />
Suppose Red plays c8 which forces c9 in reply. Now Red can play the following forcing sequence. d8, d9, e8, e9, f8, f9, etc. A sequence of such plays parallel to an edge is called a ladder. Note that the [[Blue (player)|Blue]]'s responses are forced. If Red blindly continues the ladder all the way to end, then he will simply lose (Blue will get pieces in row 9 from b9 through i9). There is no good reason to ever force a ladder all the way through to end, it only helps your opponent.<br />
<br />
=== Ladder escapes ===<br />
''(See also the article [[Ladder escape]])''<br />
<br />
Consider the same position as before but suppose Red has an additional piece at h8.<br />
<br />
<hex>R9 C9 Q1 Ve3 Vd4 Vd5 Vc6 Vc7 Hb8 Hb9 Hd7 He6 Hf6 Vh8</hex><br />
<br />
This additional piece forms a '''ladder escape''' which allows Red to jump a move ahead of the ladder and win the game. The piece at h2 is called the "[[escape piece]]." Red should now play along the ladder as before, forcing Blue's response at each step. After c8, c9, d8, d9, e8, e9, f8, f9, g8 Red is connected to the bottom.<br />
<br />
<hex>R9 C9 Q1 Ve3 Vd4 Vd5 Vc6 Vc7 Hb8 Hb9 Hd7 He6 Hf6 Vh8 Vc8 Hc9 Vd8 Hd9 Ve8 He9 Vf8 Hf9 Vg8</hex><br />
<br />
In general, for a ladder escape to be successful, it should be safely connected to the edge and not interfere with the ladder's [[Projected ladder path|projected path]].<br />
<br />
=== Ladder escape templates ===<br />
''(See also the article [[Ladder escape templates]])<br />
<br />
* [[Second row|Row-2]] ladders: All of the [[edge template]]s described earlier are valid.<br />
* [[Third row|Row-3]] ladders: Templates [[Template II|II]], [[Template IIIa|IIIa]], and [[Template IVa|IVa]] are valid.<br />
* [[Fourth row|Row-4]] ladders: [[Template IIIa]] is valid. Also [[template IVa]] is valid if you can double two-bridge to the [[escape piece]] as follows.<br />
<br />
<hex>R6 C9 Vb3 Vc3 Vd3 Sf2 Vg3 Ha4 Hb4 Hc4 Hd4</hex><br />
<br />
Red can jump ahead to the escape template by playing at the marked hex.<br />
<br />
=== The ladder escape fork ===<br />
''(See also the article [[Ladder escape fork]])''<br />
<br />
If you are forced onto a ladder and no convenient escape is present, then you must create one. The best way is to play one of the valid ladder escape templates that threatens another strong connection. Such a move is called a '''ladder escape fork'''. For an example, see the first example in the upcoming section "forcing moves." The first forcing move is a ladder escape fork played just prior to the formation of the ladder (and a very short ladder at that). A ladder escape fork is frequently a [[killer move]].<br />
<br />
=== Foiling ladder escapes ===<br />
''(See also the article [[Foiling ladder escapes]])''<br />
<br />
In order to successfully stop a ladder escape, you must either block the [[projected ladder path]] from connecting to the escape piece or intrude on the ladder escape template. To successfully stop a ladder escape fork, you need to do both with a single move and almost always with a move that is [[Adjacent move|adjacent]] to the escape piece. The following is an example of foiling a ladder escape fork.<br />
<br />
<hex>R9 C9 Q1 Vg3 Vf4 Vf5 Vg5 Vh6 Vh7 Vd7 Hc6 Hd6 He7 Hf7 Hg7 Hi7 Hg9 Sc7 Sb8 Sc8 Sd8 Sa9 Sb9 Sc9 Sd9</hex><br />
<br />
Red has just played a forking ladder escape at d7. This piece is connected to the edge via template IIIa as shown by the marked hexes. Red is threatening to create an unbeatable chain by playing at E6 and the edge template is a valid ladder escape for the row-2 ladder starting G8, F9, F8, etc. To stop this, Blue needs to play a move that blocks the ladder path from connecting to the escape piece and that also intrudes on the escape template. Blue can achieve both aims by playing at D8 (which is adjacent to the escape piece). Red responds by playing C8 re-establishing the connection to the edge (there is nothing better). Now Blue continues by playing E6 blocking the forking path obtaining a [[win|winning position]].<br />
<br />
<hex>R9 C9 Q1 Vg3 Vf4 Vf5 Vg5 Vh6 Vh7 Vd7 Ve6 Hc6 Hd6 Hd8 He6 He7 Hf7 Hg7 Hi7 Hg9 Vc8</hex><br />
<br />
Consider the same initial position but with Blue's piece on e7 removed.<br />
<br />
<hex>R9 C9 Q1 Vg3 Vf4 Vf5 Vg5 Vh6 Vh7 Vd7 Hc6 Hd6 Hf7 Hg7 Hi7 Hg9 Sc7 Sb8 Sc8 Sd8 Sa9 Sb9 Sc9 Sd9</hex><br />
<br />
This change may look inconsequential but now Blue cannot foil the forking ladder escape. Suppose the play goes d8, c8, e6 as before.<br />
<br />
<hex>R9 C9 Q1 Vg3 Vf4 Vf5 Vg5 Vh6 Vh7 Vd7 Ve6 Hc6 Hd6 Hd8 He6 Hf7 Hg7 Hi7 Hg9 Vc8</hex><br />
<br />
Now Red can ladder up to E8 by the sequence G8, F9, F8, E9, E8 achieving the following position.<br />
<br />
<hex>R9 C9 Q1 Vg3 Vf4 Vf5 Vg5 Vh6 Vh7 Vd7 Ve6 Hc6 Hd6 Hd8 He6 Hf7 Hg7 Hi7 Hg9 Vg8 Hf9 Vf8 He9 Ve8 Vc8</hex><br />
<br />
Now if Blue stops the e8 piece from connecting to the [[Bottom edge|bottom]] by playing d9, Red responds by playing e7 connecting to the bottom anyway. This example illustrates that a potential foiling move that leaves vulnerable points is unlikely to succeed against a forking ladder escape. The proper handling of ladders and ladder escapes is a complex matter and it is where many games are won or lost.<br />
<br />
=== Pre-ladder formations ===<br />
<br />
It's important to recognize situations in which a ladder is about to form or which could be formed. Such recognition allows you to play pieces that also serve as ladder escapes before the ladder occurs. It also allows you to play defensive moves that also block potential ladder paths prior to the existence of the ladder. By far the most common pre-ladder formation is the following "[[Bottleneck]] formation."<br />
<br />
<hex>R5 C7 Q1 Hd3 Ve3 Hf3 Hd5</hex><br />
<br />
Red can now form a ladder by playing e4, e5, f4, f5, etc. or by playing d4, c5, c4, b5, etc. Such formations typically occur due to blocking a player from directly connecting to an edge as in the following example.<br />
<br />
<hex>R5 C7 Q1 Vg1 Ve2 Hf3</hex><br />
<br />
In order to block Red from connecting to the bottom edge, Blue plays d3 creating a [[bottleneck]]. Red responds with e3 squeezing through and then Blue blocks with d5 completing the formation in the previous diagram.<br />
<br />
The other common pre-ladder formation occurs when the defender is blocking the connection to an edge via a classic block as in the following diagram.<br />
<br />
<hex>R5 C7 Q1 Ve1 Hd4</hex><br />
<br />
Red can form a ladder by playing d3, c4 and then laddering either to the left or right (c3, b4, b3, a4 or e3, e4, f3, f4, etc.)<br />
<br />
== Forcing moves ==<br />
''(See also the article [[Forcing move]])''<br />
<br />
'''Forcing moves''' are moves that make a threat that your opponent must reply to on their next turn. Common forcing moves include playing in one of the [[Empty hex|open hexes]] in a two-chain (threatening to break the link), intrusion into an edge template, or threatening an immediate strong connection or win. Consider the following position with the [[vertical player]] to move.<br />
<br />
<hex>R9 C9 Q1 Vg3 Vg4 Vf5 Vh5 Hc7 Hd8 Hf7 Hh7</hex><br />
<br />
At first glance, the position looks bad for Red, but Red can win by making a couple of forcing moves. He plays at e8 threatening to play at e7 on his next turn which would create an unbeatable winning chain. Blue has little choice but to stop this threat by playing e7 (there is nothing better). The move e8 is a forcing move.<br />
<br />
The forcing nature of the move allows Red to place a piece on the other side of Blue's line without giving Blue any time to do anything constructive. The e8 piece on the other side is connected to the bottom and is of critical importance.<br />
<br />
Red continues by playing another forcing move at g7. The only move that stops this piece from immediately connecting to the bottom edge is f9. But after f9, Red completes the win by playing at f8.<br />
<br />
<hex>R9 C9 Q1 Vg3 Vg4 Vf5 Vh5 Hc7 Hd8 Hf7 Hh7 Ve8 He7 Vg7 Hf9 Vf8</hex><br />
<br />
The group of red pieces near the bottom are connected to the bottom edge. These pieces are connected via two-chains to the [[group]] g3-g4-f5 which is in turn connected to the top edge via edge [[template IIIa]].<br />
<br />
(Note: the two forcing moves could just as easily be played in the reverse order. That is Red plays g7, Blue is forced to respond with f9, and then Red plays e8 which threatens to form an unbeatable chain in two distinct ways.)<br />
<br />
In general terms, you have three options when responding to a forcing move in a [[Bridge|two-chain]].<br />
<br />
# [[Saving a connection|Save]] the link by playing the other move in the two-chain.<br />
# [[Ignoring a threat|Play elsewhere]] (e.g. playing another move may give another way of meeting the threat thus rendering it harmless)<br />
# [[Counterthreat|Respond]] with a forcing move of your own.<br />
<br />
=== Breaking edge templates via forcing moves ===<br />
<br />
Forcing moves are also the only way to successfully defeat an edge template. This is done by making a [[template intrusion]] that is also a more threatening forcing move. After the opponent responds to the greater threat, you can play another move within the template and destroy the connection to the edge. For example, consider the following position with the vertical player to move.<br />
<br />
<hex>R9 C9 Q1 Hc3 Hd3 He3 Hf2 Hg1 Hg3 Vd7 Ve6 Ve5 Ve4 Vf3 Vh5 Si1 Si2 Si3 Si4 Sh2 Sh3 Sh4 Sg4</hex><br />
<br />
The piece on g3 is connected to the right edge via [[template IIIa]] indicated by the '*'s. Red's best move is to play at h2. This intrudes on the edge template, is connected to the top via edge [[template II]], and threatens to complete an unbeatable chain by playing at g2 next turn. Blue can stop this threat only by playing at g2. Then Red Plays i3 breaking Blue's connection to the right.<br />
<br />
<hex>R9 C9 Q1 Hc3 Hd3 He3 Hf2 Hg1 Hg3 Vd7 Ve6 Ve5 Ve4 Vf3 Vh5 Vh2 Hg2 Vi3</hex><br />
<br />
=== Using forcing moves to steal territory ===<br />
''(See also the article [[Stealing territory]])''<br />
<br />
I'll define '''territory''' to be the number of empty hexes adjacent to your pieces. By playing a forcing move in one of the empty hexes in a two-chain, a player can steal territory at no cost.<br />
<br />
<hex>R5 C5 Hc2 Hb4 Vd2 Vd3 Sb3</hex><br />
<br />
In this position, Blue has two more hexes of territory than Red (9 vs. 7 [[adjacent hex]]es). Suppose Red makes the forcing move at the indicated hex and Blue saves the link.<br />
<br />
<hex>R5 C5 Hc2 Hb4 Vd2 Vd3 Vb3 Hc3</hex><br />
<br />
Now Red has two more hexes of territory; i.e. Red has stolen 4 hexes of territory without disturbing either player's connections. Significantly, the additional territory is on the other side of Blue's connection where it may potentially be used for a future threat. The additional territory can't hurt and sometimes it makes a crucial difference.<br />
<br />
A forcing move is [[Irrelevant move|harmless]] if it gains no territory for the opponent. You should not be worried at all about leaving harmless forcing moves available for your opponent. When you have more than one way of completing a connection with a two-bridge, e.g. when completing the loose connection described previously, you should consider which forcing move is least valuable for your opponent. Consider the following position with Red to play.<br />
<br />
<hex>R5 C6 Q1 Vd2 He3 Hb4 Vd4 Hb5</hex><br />
<br />
Red wants to connect the d4 piece to the d2 piece. There are three distinct moves that accomplish this, d3, c4 (two-chaining to d2), and c3 (two-chaining to d4).<br />
<br />
There is not much to be said about d3; it [[Direct connection|directly connects]] without altering anything else. c4 connects but gives a potentially useful forcing move to Blue. Blue can respond with c3 and suppose Red saves the connection with d3. Now Blue has gained a free hex of territory, the hex c2 is now directly adjacent to the c3/b4/b5 group when it wasn't previously. Hence, c4 is worse than d3.<br />
<br />
Now consider the last remaining possibility c3. This leaves two forcing moves for Blue but both of them are completely harmless! If after c3, Blue plays one of the forcing moves c4 or d3, then Red can save the link and Blue will not have gained any territory at all &mdash; any empty hexes adjacent to the forcing piece were already adjacent to Blue's existing pieces. Hence, c3 is just as safe as d3 but significantly, c3 ''gains'' one hex! &mdash; b3 is now adjacent to Red's d2/b3 group when it wasn't before. Thus, c3 is better than d3 and is the best of three choices.<br />
<br />
== Using edge templates to block your opponent ==<br />
<br />
If your opponent has not completed an [[edge template]] but is threatening to do so in multiple ways, then the only defensive moves that stop the immediate threatened connections are those in the overlap between all threatened template connections. Suppose you are trying to stop the vertical player from connecting to the [[bottom edge]] in the following example.<br />
<br />
<hex>R5 C6 Q1 Ve2 Hf3</hex><br />
<br />
The vertical player has not formed an edge template but is threatening to do so in the following four different ways.<br />
<br />
{|<br />
| <hex>R5 C6 Q1 Ve2 Hf3 Sd3 Se3 Sd4 Sc5 Sd5</hex> || <hex>R5 C6 Q1 Ve2 Hf3 Sd3 Se3 Sc4 Sd4 Se4 Sb5 Sc5 Sd5 Se5</hex><br />
|-<br />
| <center>''Two-chain to [[template II]] at d4''</center> || <center>''Adjacent move to [[template IIIa]] at d3 and e3''</center><br />
|-<br />
| <hex>R5 C6 Q1 Ve2 Hf3 Sc3 Sd3 Sb4 Sc4 Sd4 Sa5 Sb5 Sc5 Sd5</hex> || <hex>R5 C6 Q1 Ve2 Hf3 Sc3 Sd3 Se3 Sb4 Sc4 Sd4 Se4 Sa5 Sb5 Sd5 Se5</hex><br />
|-<br />
| <center>''Adjacent move to template IIIa at d3'' || <center>''Adjacent move to [[template IIIb]] at d3''</center><br />
|}<br />
<br />
The only three [[Hex (board element)|hexes]] in the overlap among all these edge templates are marked on the following diagram. To stop the immediate connection, the horizontal player must play at one of them.<br />
<br />
<hex>R5 C6 Q1 Ve2 Hf3 Sd3 Sd4 Sd5</hex><br />
<br />
== On connectivity ==<br />
<br />
=== Overlapping connections ===<br />
''(See also the article [[Overlapping connections]])''<br />
<br />
One should be alert to the situations where various connections, edge templates, and potential connections overlap at some hex(es). Consider the following position with Blue to move.<br />
<br />
<hex>R11 C11 Vj2 Vi4 Vj5 Vi7 Vi9 Vh9 Vg9 Vf9 Se9 Ve8 Vd10 Hg7 Hf7 He6 Hc7 Hc9 He10 Hf10 Hg10 Hh10 Hi10</hex><br />
<br />
At first glance, it appears that Red has an unbreakable winning path. j2 cannot be stopped from connecting to the [[Top edge|top]], j2 is connected the [[group]] f9-g9-h9-i9 through a series of unbreakable two-chains, this group is connected to e8 via a two-chain, e8 is connected to d10 via another two-chain, and d10 cannot be stopped from connecting to the [[Bottom edge|bottom]].<br />
<br />
Appearances are deceiving; it is Blue that has a forced win! The [[Weakest link|flaw]] in Red's formation is that the two-chain from f9 to e8 and the two-chain from e8 to d10 [[overlap]] at the hex marked by a '*' in the diagram (e9). Blue should play at e9. By playing in the overlap, Blue is threatening to break ''both'' two-chains containing this hex. Red cannot save them both.<br />
<br />
If Red responds with f8, then Blue plays d9 breaking the two-chain and establishing an unbeatable chain. If Red saves the other link by responding with d9, then Blue breaks through with f8 again establishing an unbeatable chain.<br />
<br />
=== Disjoint steps ===<br />
<br />
When a piece can be connected to a group of pieces in one move in two non-overlapping ways, then they can be thought of as already connected to the group. Consider the following position.<br />
<br />
<hex>R5 C5 Q1 Vc2 Vd2 Vb3 Hc3 Ha5 Hd4</hex><br />
<br />
Red's three pieces are connected to the top. How can Red extend this connection downward? By playing at c4! The piece at c4 is connected to the group of three vertical pieces in two non-overlapping ways; namely, through the hexes b4 and d3. The diagrammed connection pattern is a fairly common occurrence and the connection to the piece at c4 is just as strongly connected as the pieces in a two-chain.<br />
<br />
=== Groups ===<br />
''(See also the article [[Group]])''<br />
<br />
A '''group''' is a collection of pieces that, considered in isolation from the rest of the position, have an unbreakable connection with each other. As you improve, it is important to learn to think in terms of safely connected groups of pieces. To illustrate why, consider the following two hex puzzles taken from [[Cameron Browne]]'s book "[[Hex Strategy]]."<br />
<br />
<hex>R11 C11 Q1 Hj2 Hh3 Hc4 Vd4 Hf4 Vi4 Vj4 Vd5 Vg5 Hh5 Vi5 Vk5 Ve6 Hf6 Hg6 Hh6 Hi6 He7 Vg7 Hi7 Vj7 Vc8 Vi9</hex><br />
<br />
It is Blue's turn; how can he win?. The chain of pieces j2-h3-f4 is connected to the right edge and furthermore, Blue has no other way of connecting to the right edge. So to win, Blue has to extend this chain to the left edge. Looked at in isolation, there doesn't seem to be any way to do this, yet by thinking in terms of connected groups, the solution falls out easily.<br />
<br />
Notice that the j2-h3-f4 chain threatens to connect to the i7-i6-h6-h5-g6-f6-e7 group in two non-overlapping ways, through locations h4 and f5. Hence, these two groups can be thought of as a single group of pieces already connected to the right edge (this is another example of "'''disjoint steps'''"). Now notice the key hex d6. This hex threatens to connect to Blue's big group in two distinct non-overlapping ways (through e5 and d7) hence a piece played at d6 would be part of the big group (disjoint steps again!). Furthermore, a blue piece at d6 could not be stopped from connecting to the left because the b4 piece acts as a ladder escape. Therefore, d6 wins.<br />
<br />
<hex>R11 C11 Q1 Hj2 Vc3 Hd3 Vg3 Hj3 Hc4 He4 Vc5 Vd5 Hg5 Vi5 Vd6 He6 Vd7 Ve7 Vh7 Hb9</hex><br />
<br />
Again, it is Blue's turn and the task is to [[win]]. The c4 piece cannot be stopped from connecting to the left edge since after the block a5, Red can ladder down row B to the escape piece at b9. Hence, the group c4-d3-e4 is connected to the [[left edge]]. The group j2-j3 is connected to the [[right edge]]. Blue has a third group e6-g5. If Blue can play a single move that connects the e6-g5 group to both other groups, then this would be a winning move. Blue has a unique move which does this, namely play at g4. The g4-g5-e6 group is connected to the left group through f4 and e5. It threatens to connect to the j2-j3 group via h3 and i4. h3 is directly connected to g4 and two-chains to j2. None of the hexes involved, h3, i2, and i3, is involved in the connection threat i4 plus the two chain to g5. I.e. the threats don't overlap and hence the connection cannot be stopped. Therefore, g4 wins.<br />
<br />
There is another way of coming up with this move. Red threatens to cut off the e6-g5 group to the left by two-chaining from g3 to f5. Red is also threatening to cut off the e6-g5 from the right by two-chaining from g3 to h4. However, these threats overlap and hence, Blue can stop them both by playing in the unique hex contained in the overlap, namely g4 again.<br />
<br />
This illustrates that [[Offence equals defense]] in hex. Playing in regions of overlapping threats in order to stop all the threats is a defensive way of thinking. Trying to establish unbreakable connections between groups of your pieces is an offensive way of thinking. In this example, both offensive and defensive thinking techniques lead you to the unique best move. A lot of times defensive thinking is easier but sometimes offensive thinking is.<br />
<br />
== Conclusion ==<br />
<br />
The first two strategy guides cover what I consider to be the fundamentals of [[hex strategy]]. This information should be enough to move up into the 1800s or 1900s on [[PlaySite]]. To move up the ranks of the red guys (the topmost group) requires the following. First you need to improve your [[opening play]]. Playing any reasonable looking moves during the initial phase of the game is enough for an orange player, but to compete with the reds, you need to [[Consistency|consistently]] play one of the top two or maybe three moves. Unfortunately, I don't know a good way to describe how to do this; I'm not convinced the necessary information can be verbalized. After that, you need to know the [[Minimax]] principle (described in the [[Advanced (strategy guide)|Advanced strategy guide]]).<br />
<br />
Also you need a certain mindset, call it [[willpower]] if you like, to move towards the top ranks. You have to try to hold onto every little [[Hex (board element)|hex]] the way a miser hoards gold pieces and you have use every optimization you can no matter how minor it may seem. The most useful optimizations, tricks, and special situations that I've learned so far are included in the Advanced strategy guide. But surely there are other things out there waiting to be discovered.</div>
Kogorman
https://www.hexwiki.net/index.php/Connection_game
Connection game
2007-07-02T00:10:38Z
<p>Kogorman: revert</p>
<hr />
<div>A '''connection game''' is a [[game]] where the goal is to use the [[Piece (general)|piece]]s to create a connection between some parts of the [[Board (general)|board]]. The first connection game was [[Hex]], which was invented in [http://en.wikipedia.org/wiki/1942 1942], after which several other connection games have been created.<br />
<br />
== Timeline ==<br />
<br />
;[[Hex]] ([[Piet Hein]] [http://en.wikipedia.org/wiki/1942 1942] and [[John Nash]] [http://en.wikipedia.org/wiki/1948 1948])<br />
:The original connection game. Played on a [[rhombic hex grid]].<br />
;[[Y]] ([[Craige Schenstead]] and [[Charles Titus]], [http://en.wikipedia.org/wiki/1950s 1950s])<br />
:Played on a [[triangluar grid of hexagons]]<br />
;[[Twixt]] ([[Alex Randolph]], [http://en.wikipedia.org/wiki/1960s 1960s])<br />
:Played on a [[square grid]] of holes into which the players place [[peg]]s. The pegs can be connected via [[Bridge (general)|bridges]].<br />
;[[Havannah]] ([[Christian Freeling]], [http://en.wikipedia.org/wiki/1980 1980])<br />
;[[Onyx]] ([[Larry Back]], [http://en.wikipedia.org/wiki/2000 2000])<br />
:Played on an original grid consisting of both triangles and squares. It is the first connection game with a [[capturing rule]].<br />
;[[Gonnect]] ([[João Pedro Neto]], [http://en.wikipedia.org/wiki/2000 2000])<br />
:This game is simply [[Go]], but with a different goal, namely to create a connection between any two opposite sides.<br />
;[[Unlur]] ([[Jorge Gómez Arrausi]], [http://en.wikipedia.org/wiki/2001 2001])<br />
:Played on a [[hexagonal hex grid]]. Unique in the way that the players have [[different objectives]].<br />
<br />
== References ==<br />
<br />
;[[Cameron Browne]], [http://www.amazon.com/Connection-Games-Variations-Cameron-Browne/dp/1568812248/ref=pd_bbs_sr_1/104-1532904-9846317?ie=UTF8&s=books&qid=1177663469&sr=8-1 "Connection Games: Variations on a Theme"]</div>
Kogorman
https://www.hexwiki.net/index.php/Win
Win
2007-07-02T00:04:32Z
<p>Kogorman: rv ads, to blank state. I wish I could just delete it.</p>
<hr />
<div>The game is won when there's a path between opposite sides of the board. The player owning those sides is the winner.<br />
<br />
Back to the [[Rules_(Hex)|rules]]</div>
Kogorman
https://www.hexwiki.net/index.php/HexWiki:Community_Portal
HexWiki:Community Portal
2007-07-01T20:55:22Z
<p>Kogorman: </p>
<hr />
<div>Does anyone know how to contact the sysop for this wiki? I and a few others are interested in contributing new content with hex diagrams, and note that the markup that used to work no longer does. Perhaps we can fix that.<br />
<br />
-- kogorman</div>
Kogorman
https://www.hexwiki.net/index.php/HexWiki:About
HexWiki:About
2007-07-01T20:47:44Z
<p>Kogorman: rv ads, to last version by Taral.</p>
<hr />
<div>HexWiki is a community initiative aimed at creating a central knowledge-base on the game [[Hex]]. The idea came about during discussions in the [http://www.littlegolem.net/jsp/forum/forum.jsp?forum=50 Hex forum] on [[Little Golem]].<br />
<br />
HexWiki formerly ran on [[QwikiWiki]], but now uses the [[MediaWiki]] engine, known for serving, among other sites, [http://wikipedia.org Wikipedia].</div>
Kogorman
https://www.hexwiki.net/index.php/HexWiki:Community_Portal
HexWiki:Community Portal
2007-07-01T19:26:47Z
<p>Kogorman: </p>
<hr />
<div></div>
Kogorman
https://www.hexwiki.net/index.php/User_talk:Kogorman
User talk:Kogorman
2005-08-14T23:08:55Z
<p>Kogorman: </p>
<hr />
<div>Aug 14: Reverting a community page: was overlaid by some hotel-related advertising.<br />
<br />
Aug 14: What are these <hex> and </hex> annotations? Are they supposed to be<br />
compiled into images? It does not appear to be working.</div>
Kogorman
https://www.hexwiki.net/index.php/Board_size
Board size
2005-08-14T21:41:00Z
<p>Kogorman: </p>
<hr />
<div>The '''board size''' in [[Hex]] varies, and no size is considered standard. 10 &times; 10 is considered by many a lower bound for interesting games.<br />
<br />
See also the article [[Small boards]].<br />
<br />
; 10 &times; 10<br />
: Standard size on [[Kurnik]].<br />
; 11 &times; 11<br />
: The size [[Piet Hein]] used.<br />
: The standard size on [[pbmserv]].<br />
; 13 &times; 13<br />
: The original size on [[Little Golem]]. (Games with this size are still called "hex" by the site engine, while 19 &times; 19 Hex games are named "hex19".)<br />
; 14 &times; 14<br />
: The size [[John Nash]] used.<br />
: Used to be offered on [[Playsite]] and [[Lycos]] but they no longer offer hex.<br />
; 18 &times; 18<br />
: Used to be offerec on [[Playsite]] and [[Lycos]] but they no longer offer hex.<br />
; 19 &times; 19<br />
: Offered on [[Little Golem]].</div>
Kogorman
https://www.hexwiki.net/index.php/Board_size
Board size
2005-08-14T21:39:24Z
<p>Kogorman: Changed "Playsite" to "Kurnik" because Playsite no longer carries hex, and the size is right.</p>
<hr />
<div>The '''board size''' in [[Hex]] varies, and no size is considered standard. 10 &times; 10 is considered by many a lower bound for interesting games.<br />
<br />
See also the article [[Small boards]].<br />
<br />
; 10 &times; 10<br />
: Standard size on [[Kurnik]].<br />
; 11 &times; 11<br />
: The size [[Piet Hein]] used.<br />
: The standard size on [[pbmserv]].<br />
; 13 &times; 13<br />
: The original size on [[Little Golem]]. (Games with this size are still called "hex" by the site engine, while 19 &times; 19 Hex games are named "hex19".)<br />
; 14 &times; 14<br />
: The size [[John Nash]] used.<br />
: Offered on [[Playsite]].<br />
; 18 &times; 18<br />
: Offered on [[Playsite]].<br />
; 19 &times; 19<br />
: Offered on [[Little Golem]].</div>
Kogorman
https://www.hexwiki.net/index.php/Board_size
Board size
2005-08-14T16:25:54Z
<p>Kogorman: </p>
<hr />
<div>The '''board size''' in [[Hex]] varies, and no size is considered standard. 10 &times; 10 is considered by many a lower bound for interesting games.<br />
<br />
See also the article [[Small boards]].<br />
<br />
; 10 &times; 10<br />
: Standard size on [[Playsite]] and [[Kurnik]].<br />
; 11 &times; 11<br />
: The size [[Piet Hein]] used.<br />
: The standard size on [[pbmserv]].<br />
; 13 &times; 13<br />
: The original size on [[Little Golem]]. (Games with this size are still called "hex" by the site engine, while 19 &times; 19 Hex games are named "hex19".)<br />
; 14 &times; 14<br />
: The size [[John Nash]] used.<br />
: Offered on [[Playsite]].<br />
; 18 &times; 18<br />
: Offered on [[Playsite]].<br />
; 19 &times; 19<br />
: Offered on [[Little Golem]].</div>
Kogorman
https://www.hexwiki.net/index.php/Board_size
Board size
2005-08-14T16:24:47Z
<p>Kogorman: </p>
<hr />
<div>The '''board size''' in [[Hex]] varies, and no size is considered standard. 10 &times; 10 is considered by many a lower bound for interesting games.<br />
<br />
See also the article [[Small boards]].<br />
<br />
; 10 &times; 10<br />
: Standard size on [[Playsite]].<br />
; 11 &times; 11<br />
: The size [[Piet Hein]] used.<br />
: The standard size on [[pbmserv]].<br />
; 13 &times; 13<br />
: The original size on [[Little Golem]]. (Games with this size are still called "hex" by the site engine, while 19 &times; 19 Hex games are named "hex19".)<br />
; 14 &times; 14<br />
: The size [[John Nash]] used.<br />
: Offered on [[Playsite]].<br />
; 18 &times; 18<br />
: Offered on [[Playsite]].<br />
; 19 &times; 19<br />
: Offered on [[Little Golem]].</div>
Kogorman
https://www.hexwiki.net/index.php/User:Kogorman
User:Kogorman
2005-08-14T16:23:18Z
<p>Kogorman: </p>
<hr />
<div>14 Aug 2005: Reverted a community page to undo advertising.</div>
Kogorman
https://www.hexwiki.net/index.php/User_talk:Kogorman
User talk:Kogorman
2005-08-14T16:22:15Z
<p>Kogorman: explaining revert</p>
<hr />
<div>Reverting a community page: was overlaid by some hotel-related advertising.</div>
Kogorman
https://www.hexwiki.net/index.php/HexWiki_talk:Community_Portal
HexWiki talk:Community Portal
2005-08-14T16:20:28Z
<p>Kogorman: Reverting: overlaid by inappropriate advertising</p>
<hr />
<div>I really like DJ's comments, but I think a better place for them would be on his [[User:Dj13|user page]]. A community portal, at least on the wikis I've seen, is something else:<br />
<br />
* [http://en.wikipedia.org/wiki/Wikipedia:Community_Portal Wikipedia's community portal]<br />
* [http://meta.wikimedia.org/wiki/Goings-on Meta-Wikipedia's "Goings-on page"]<br />
<br />
Not wishing to offend or to seem elitist, merely suggesting that personal expressions of happiness be placed on user pages, where they belong. [[User:Turing|turing]] 09:46, 17 Feb 2005 (CET)</div>
Kogorman