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Edge template VI1a
2010-08-20T00:43:00Z
<p>Elemay: remove "stub"</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===<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 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 />
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 />
Bg7 MR Mh5<br />
</hex><br />
<br />
See more details [[Template VI1/Other Intrusion on the 1st row| here]].<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>
Elemay
https://www.hexwiki.net/index.php/Edge_template_VI1a
Edge template VI1a
2010-08-20T00:42:08Z
<p>Elemay: Adding link to new page, "Defending against VI1 right (other) intrusion on the 1st row"</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 />
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 />
Bg7 MR Mh5<br />
</hex><br />
<br />
See more details [[Template VI1/Other Intrusion on the 1st row| here]].<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>
Elemay
https://www.hexwiki.net/index.php/Template_VI1/Other_Intrusion_on_the_1st_row
Template VI1/Other Intrusion on the 1st row
2010-08-20T00:41:51Z
<p>Elemay: Defending against VI1 right (other) intrusion on the 1st row</p>
<hr />
<div>This article deals with a special case in [[defending against intrusions in template VI1]], namely the right-hand ('other') intrusion on the 1st that is not eliminated by [[sub-templates threat]]s.<br />
<br />
== Basic situation ==<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 />
Bg7 <br />
</hex><br />
<br />
Red should go here:<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 />
Bg7 MR Mh5 Pi3 Pi4<br />
</hex><br />
<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. It is now Blue's move.<br />
<br />
== Claim #1: Blue must move in one of the following + squares below ==<br />
<br />
If Blue moves to <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 />
Bg7 Rh5 Pi3 Pi4 Pe7 Pf6 Pf7 Pg5 Pg6 Ph6 Ph7 Pi5 Pi6 Pi7<br />
</hex><br />
<br />
If not, Red can move to either i3 or i4 and secure a connection.<br />
<br />
== Proposed first Red response ==<br />
<br />
If Blue moves to {e7, f6, f7, g5, g6}, Red should take i6 and force a Blue response in either i3 or i4.<br />
If Blue moves to {h6, h7, i5, i6, i7}, Red should take f6 and force a Blue response in either i3 or i4.<br />
If Blue takes i3 or i4 direcly, proceed with [[#Response_to_i3|Response to i3]] or [[#Response_to_i4|Response to i4]] instructions below.<br />
<br />
== Response to i3 ==<br />
<br />
If we've arrived here, Blue has just taken i3, i4 is free, h5 is securely connected to the bottom and Blue has at most one of the "+" squares below (with one exception; see [[#i3_addendum|i3 addendum]]). In this case, Red should first take j3 and force a Blue response at i4:<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 />
Bg7 Rh5 Bi3 Pe7 Pf6 Pf7 Pg5 Pg6 Ph6 Ph7 Pi5 Pi6 Pi7<br />
MV Mj3 Mi4<br />
</hex><br />
<br />
CASE #1: Blue has i5.<br />
SOLUTION: <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 />
Bg7 Rh5 Bi5 Bi3<br />
Rj3 Bi4<br />
MV Mk4 Mk5 Mj5 Mi7 Mi6 Mh7 Mh6<br />
</hex><br />
<br />
CASE #2: Blue has no tiles in {h6, h7, i5, i6, i7}, or has either {h6, h7, i6} (indicated by +).<br />
SOLUTION: <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 />
Bg7 Rh5 Bi3<br />
Rj3 Bi4<br />
MV Mj4 Mi5 Mk5<br />
Ph6, Ph7, Pi6<br />
</hex><br />
<br />
CASE #3: Blue has i7.<br />
SOLUTION:<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 />
Bg7 Rh5 Bi7 Bi3<br />
Rj3 Bi4<br />
MV Mj4 Mi5 Mj5 Pj6 Pj7 Pk5 Pk6 Pk7<br />
</hex><br />
<br />
Blue must take one of the + hexes or Red wins. Now, Red can play i6 and force h7, then play h6 and connect to h5 (which is already securely connected.<br />
<br />
== Response to i4 ==<br />
<br />
If we've arrived here, Blue has just taken i4, i3 is free, h5 is securely connected to the bottom and Blue has at most one of the "+" squares below (with one exception; see [[#i4_addendum|i4 addendum]]). In this case, Red should first take h3 and force a Blue response at h4:<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 />
Bg7 Rh5 Bi4 Pe7 Pf6 Pf7 Pg5 Pg6 Ph6 Ph7 Pi5 Pi6 Pi7<br />
MV Mh3 Mh4<br />
</hex><br />
<br />
CASE #1: Blue has g5.<br />
SOLUTION:<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 />
Bg7 Rh5 Bg5 Bi4 Rh3 Bh4<br />
MV Mf4 Me5 Mf5 Me7 Mf6 Mf7 Mg6<br />
</hex><br />
<br />
CASE #2: Blue has no tiles in {e7, f6, f7, g5, g6}, or has either {f6, f7, g6} (indicated by +).<br />
SOLUTION:<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 />
Bg7 Rh5 Bi4 Rh3 Bh4<br />
MV Mg4 Mg5 Me5<br />
Pf6, Pf7, Pg6<br />
</hex><br />
<br />
CASE #3: Blue has e7.<br />
SOLUTION:<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 />
Bg7 Rh5 Be7 Bi4 Rh3 Bh4<br />
MV Mg4 Mg5 Mf5<br />
Pc7 Pd6 Pd7 Pe5 Pe6<br />
</hex><br />
<br />
Blue must take one of the + hexes or Red wins. Now, Red can play f6 and force f7, then play g6 and connect to h5 (which is already securely connected.<br />
<br />
== i3 addendum ==<br />
<br />
I claimed that Blue can have only one of the + hexes but this is not quite true if Blue first "plays out" the secured bridge. But in this case Red definitely can acquire i6.<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 />
Bg7 Rh5 Bi3 Rh6 Bi5 Ri6 Bf6<br />
Pe7 Pf7 Pg5 Pg6 Ph7 Pi7<br />
</hex><br />
<br />
In this case, Red can still play j3 to force i4, then k4 to force j5, then l5 wins:<br />
<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 />
Bg7 Rh5 Bi3 Rh6 Bi5 Ri6 Bf6<br />
MV Mj3 Mi4 Mk4 Mj5 Ml5<br />
</hex><br />
<br />
== i4 addendum ==<br />
<br />
I claimed that Blue can have only one of the + hexes but this is not quite true if Blue first "plays out" the secured bridge. But in this case Red definitely can acquire f6.<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 />
Bg7 Rh5 Bi4 Bg5 Rg6 Rf6 Bi6<br />
Pe7 Pf7 Ph6 Ph7 Pi5 Pi7<br />
</hex><br />
<br />
In this case, Red can still play h3 to force h4, then f4 to force f5, then d5 wins:<br />
<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 />
Bg7 Rh5 Bi4 Bg5 Rg6 Rf6 Bi6<br />
MV Mh3 Mh4 Mf4 Mf5 Md5<br />
</hex><br />
<br />
<br />
<br />
[[category:edge templates]]</div>
Elemay