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HexWiki - User contributions [en]
2024-03-28T10:52:17Z
User contributions
MediaWiki 1.23.15
https://www.hexwiki.net/index.php/Where_to_swap_(y)
Where to swap (y)
2011-05-06T08:40:42Z
<p>Halladba: Added size 5 and 7</p>
<hr />
<div>*the red marked hexes should not be swapped<br />
*the blue marked hexes should be swapped<br />
*the star marked hexes are defining the [[Y]] board.<br />
<br />
=== Size 5===<br />
<hex> C5 R5<br />
1:SSSSR<br />
2:SSSRR<br />
3:SSRBR<br />
4:SRBBR<br />
5:RRRRR<br />
</hex><br />
<br />
=== Size 6===<br />
<hex> C6 R6<br />
1:SSSSSR<br />
2:SSSSRR<br />
3:SSS_R_<br />
4:SS_BB_<br />
5:SRRBRR<br />
6:RR__RR<br />
</hex><br />
<br />
=== Size 7===<br />
<hex> C7 R7<br />
1:SSSSSSR<br />
2:SSSSSRR<br />
3:SSSS___<br />
4:SSS_BB_<br />
5:SS_BBB_<br />
6:SR_BB_R<br />
7:RR___RR<br />
<br />
</hex><br />
[[category:Y]]</div>
Halladba
https://www.hexwiki.net/index.php/Commented_games
Commented games
2010-12-13T21:06:37Z
<p>Halladba: update for Niall games</p>
<hr />
<div>The best ways for getting better at Hex are to learn strategies, solve problems and to replay games of stronger players. The following collection of games are intended to help you get stronger.<br />
<br />
{| class="wikitable" border="1" cellpadding="2" cellspacing="0"<br />
|-<br />
! Game !! Date !! Commented by !! Intended audience<br />
|-<br />
| [[Glenn C. Rhoads vs. unknown]] || || [[Glenn C. Rhoads]] || advanced<br />
|-<br />
| [[V vs. H game 1|Vertical vs. Horizontal]] || || David Boll || ---<br />
|-<br />
| [[Bill LeBoeuf vs. Universidad de Oviedo]] || November 2003 || Bill LeBoeuf || ---<br />
|-<br />
| [[Niall vs. Halladba, November 2010 | Halladba vs. Niall]] || November 2010 || [[user:Niall | Niall]] || ---<br />
|-<br />
| [[Nietsabes vs. Niall, November 2010 | Nietsabes vs. Niall]] || November 2010 || Niall || ---<br />
|-<br />
| [[James A. Cook vs. Niall, December 2010 | James A. Cook vs. Niall]] || December 2010 || Niall || ---<br />
|}<br />
<br />
Remarks:<br />
* The '''Game''' is a link to the commented game.<br />
* The '''Commented by''' field contains the name of the person who did the commentary.<br />
* The '''Intended audience''' can be ''beginners'', ''advanced'', ''experts'', whatever.<br />
<br />
[[category:Game record]]</div>
Halladba
https://www.hexwiki.net/index.php/James_A._Cook_vs._Niall,_December_2010
James A. Cook vs. Niall, December 2010
2010-12-13T20:55:57Z
<p>Halladba: templatization</p>
<hr />
<div>== Game information ==<br />
* Size: 13x13<br />
* Red: James A. Cook<br />
* Blue: [[user:Niall | Niall]]<br />
* Result: <br />
* Comments: Niall, [[user:Halladba | Halladba]]<br />
* Location: [[Little Golem]], game [http://www.littlegolem.net/jsp/game/game.jsp?gid=1252463 1252463] in July 2010 [[monthly cup]] group 2.1<br />
<br />
== Comments ==<br />
<br />
Unfinished notes.<br />
<br />
Move 26: <br />
Red is threatening two powerful moves: (J2) [I4] and (D8) [B12].<br />
The B12 weakness of (D8) means that red can't connect (E6) to the bottom in one move.<br />
G6 <br />
- (K7) K6 (L6) L5 <(J7) I9> (L11 - pointless, as the ladder never gets that far now!) K12 <br />
- (F9 - aiming at (D8) B12 (D9) C13 (F11), and also at (G7) double peep) G8 <br />
- (F10) C9 [because (D8) is now a threat]<br />
- (D8) B12 - good for blue?<br />
- <(C9) D7> - good for blue?<br />
- (H4) I7 - gfb<br />
- (L10) K7 - gfb<br />
- (L11) L10 <br />
<br />
<F4 (E5)> G6 (D8) - <> exchange doesn't look like it helps<br />
E5 (F5) - because F2 has a weakness at (H2)<br />
F4 (F3) D5 (G3) H4 (G6) G5 (F6) F5 - blue wins<br />
H4 (G6) I7 (F8) <br />
- F9 (G8) G10 (H10) H12 (H11) G12 (F10) - red connects (F8) to the bottom<br />
H4 (D8) <br />
- B12 (D9) C13 (F10) G11 - blue wins<br />
- E5 (F5) G2 (F3) F2 (D2) D3 (C3) D4 (C5) D5 (B7) - red wins<br />
D7 (H5) I7 (F8) <br />
- G6 (F7) F5 (E5) G2 (E3) - reds connection goes: {top->E3/E4/E5 -> F7/F8 -> bottom}<br />
- <...> F2 (?) D3 (C3) D4 (C5) D5 (B7) C9 (D8) D9 (E7) - red wins<br />
D7 <(E7) D8> (I7) H4 (G6) F2 (D2) D3 (C3) D4 (C5) - now red can't connect if he has played (E7)<br />
F2 (D2) D3 (C3) H4 (G6) G5 (E7) C6 (D5) E5 (F5) F4 (H2) I1 (G2) G1 (F3) I7 (D8) B12 - now what?<br />
F2 (H2) H4<br />
<br />
Move 24: <blah> denotes possibilty of exchanging blah<br />
C2<br />
- (I7) F2 (H2) I1 (G2) G1<br />
- (B3) B2 (C3) <D5 (E4)> E1 (J2) I4 (I3) H4 (H3) G6 <br />
- (C9) D7 (E7 [G6->E8 ok]) D7 (B7) <br />
- with <D5 (E4)> get: B6 - BLUE wins<br />
- without <D5 (E4)> get: D5 (B6) D4 (D2) D1 (E2) F1 (E3) E5 (F5) - RED wins!<br />
- (D8) D9 (B10) B12 (B11) C13 - now blue wins as G11/F10 are miai<br />
- (J2) <br />
- (D2) F4 (J2) <br />
- (E4) E1 (J2) I4 (I3) H4 (H3) <br />
- (J2) C9 (I7) I4 (H5) H4 (G5) F2 (D2) E4 (D5) E5 - red has no move, blue wins<br />
- (D2) <br />
<br />
Close to repetition! From move 22 notes:<br />
I7 (C9 [B9 doesn't work with D11 because of E12]) C2<br />
- (B3) B2 (C3) F2 (I4) I3 (D2) D5 (E5 [D4 weakness, so (E4)?]) D7 (E7) D8 (F8)<br />
(note the K7) K6 (L6) L5 (J7) I9 sequence)<br />
- (D2) D7 (B7) C5, blue connects, red can play (F8), but looks like this works for blue? What if red plays (H4/G5/H5/I4), threatening an attack around (J2) before (F8)? Well, blue can play at F7 and just connect to I7 and win.<br />
I10 (C11 [threatens D8 connection]) C9 (I7) <br />
- H4 (G6) G5 (E7) F2 (E4) D3 (C3), with C9 in place blue can run down the left<br />
- C2/F2?<br />
<br />
<br />
Question: Does I7 connect E8 to the right edge? It's a series of double threats. Attacking the direct E8--> I7 connected: If red (F8) then blue walks up to I2, however this only connects by running down to J11. So can red attack the connection of E8 to the right edge by first attacking the direct route through I7 (eg. at (K7) or (L11)) and then playing (F8) having damaged the route down the RHS?<br />
Note* I was very worried, after playing move 22 that red would instead play at E10. This blocks E9-->I10 better than D11.<br />
<br />
Move 22: <br />
/ F10 (G11) \<br />
I10 (D11) I7 [[not needed (F8) F7 (G7) G6 (H6) G4]] (B9) C2 [see below]<br />
\ G11 (F10) /<br />
- (B3) B2 (C3) F2 (I4) I3 (D2) D5 (E5 [D4 weakness, so (E4)?]) D7 (E7) D8 (F8) - blue *almost* wins here. The complication is J3, leading to a ladder down the right hand side, and the possibility of a double threat earlier. Something like (K7) K6 (L6) L5 (J7) I9. So it looks like it doesn't work for red. <br />
- (D2) D7 (B7) C5, blue connects, red can play (F8), but looks like this works for blue? What if red plays (H4/G5/H5/I4), threatening an attack around (J2) before (F8)? Well, blue can play at F7 and just connect to I7 and win.<br />
I10 (C11 [threatens D8 connection]) C9 (I7) <br />
- H4 (G6) G5 (E7) F2 (E4) D3 (C3), with C9 in place blue can run down the left<br />
- C2/F2?<br />
I10 (I7) G11 (C11) <br />
<br />
C11 (B12) D11 (B11) C9 (E10) C10<br />
- (G11) <br />
- (A10), and a ladder<br />
C11 (D9 - cuts off E8 pieces fairly thoroughly) I10 (G11) <br />
C11 (B10) C9 (D11) - confusing...<br />
<br />
D8s connection to both the top and the bottom?<br />
[E3/F2 - looking at C2? C2? - ignoring F2 too much?] H4 [protect against F2, sets up G6 related moves, like C9?]<br />
Can I get J5 in as a forcing move?<br />
J5 (J4) - looks bad for blue<br />
Red is in danger of playing J2 and chopping through the top. After red J2 blue can get to the E8 stones, but not to the left edge yet. <br />
<br />
Move 20: <br />
D6 (C9? B7? D7? F4?)<br />
E4 (D5) C2 (D2) D6 (B7) C5 <br />
E4 (D5) C2 (B3) B2 (C3) F2 (D2) C9 (G11) F6 - looks good for blue<br />
E4 (D5) C2 (D2) D6 - seems to work for blue <br />
Red can pull out (J2) at any time - that looks like a big problem!<br />
<br />
Problem is that if I play C9, red will play a testing move like (G8). If I play G7 red can play (I7) and I10 no longer threatens anything. So red can focus on the top, with something like (K4). Then when blue plays G11 red can answer at (E10), connecting to the bottom.<br />
<br />
Move 18:<br />
E5 (F5) F2[say] (I4) I3 (B6) - looks good for red, F5 seems basically connected to top and bottom<br />
E5 (D6) D5 (B6) C7 (D8) C6 (B10) B8 - good for blue, red has no way to the top<br />
D5 (F4) - red seems to connect to the top and benefit substantially from this exchange.<br />
E4 (D5) G5 (B10) - good for red?<br />
<br />
Move 14: <br />
C5?<br />
E8 (F8) F5 [looking at I4 and C5, or even D6, with E8?] <br />
E8 (F8) F7 (G7) G6 (H6) I4 - doesn't look like quite enough for blue?<br />
E8 (I7) H4 <br />
E10 (I7) I6 (J6) J5 (F8) F10 (G8) G11 (H11) - now (I7) forcing sequence connects red around to (F8)! - Bad for blue<br />
I7 (F8) <br />
D6 - doesn't connect to the left, can that be ok?<br />
F11 (D10) - goes badly for blue when red [later] plays E11<br />
<br />
Move 12: Should arguably have been at J3, as this still connects with J11. Should always stretch as much as you can (Jonatan Rydh)<br />
<br />
Move 10: I8?<br />
<br />
[[category:game record]]</div>
Halladba
https://www.hexwiki.net/index.php/James_A._Cook_vs._Niall,_December_2010
James A. Cook vs. Niall, December 2010
2010-12-13T20:52:12Z
<p>Halladba: NiallVsJamesACook 1252463 moved to James A. Cook vs. Niall, December 2010: uniformisation</p>
<hr />
<div>Unfinished notes for game: http://www.littlegolem.net/jsp/game/game.jsp?gid=1252463<br />
<br />
Move 26: <br />
Red is threatening two powerful moves: (J2) [I4] and (D8) [B12].<br />
The B12 weakness of (D8) means that red can't connect (E6) to the bottom in one move.<br />
G6 <br />
- (K7) K6 (L6) L5 <(J7) I9> (L11 - pointless, as the ladder never gets that far now!) K12 <br />
- (F9 - aiming at (D8) B12 (D9) C13 (F11), and also at (G7) double peep) G8 <br />
- (F10) C9 [because (D8) is now a threat]<br />
- (D8) B12 - good for blue?<br />
- <(C9) D7> - good for blue?<br />
- (H4) I7 - gfb<br />
- (L10) K7 - gfb<br />
- (L11) L10 <br />
<br />
<F4 (E5)> G6 (D8) - <> exchange doesn't look like it helps<br />
E5 (F5) - because F2 has a weakness at (H2)<br />
F4 (F3) D5 (G3) H4 (G6) G5 (F6) F5 - blue wins<br />
H4 (G6) I7 (F8) <br />
- F9 (G8) G10 (H10) H12 (H11) G12 (F10) - red connects (F8) to the bottom<br />
H4 (D8) <br />
- B12 (D9) C13 (F10) G11 - blue wins<br />
- E5 (F5) G2 (F3) F2 (D2) D3 (C3) D4 (C5) D5 (B7) - red wins<br />
D7 (H5) I7 (F8) <br />
- G6 (F7) F5 (E5) G2 (E3) - reds connection goes: {top->E3/E4/E5 -> F7/F8 -> bottom}<br />
- <...> F2 (?) D3 (C3) D4 (C5) D5 (B7) C9 (D8) D9 (E7) - red wins<br />
D7 <(E7) D8> (I7) H4 (G6) F2 (D2) D3 (C3) D4 (C5) - now red can't connect if he has played (E7)<br />
F2 (D2) D3 (C3) H4 (G6) G5 (E7) C6 (D5) E5 (F5) F4 (H2) I1 (G2) G1 (F3) I7 (D8) B12 - now what?<br />
F2 (H2) H4<br />
<br />
Move 24: <blah> denotes possibilty of exchanging blah<br />
C2<br />
- (I7) F2 (H2) I1 (G2) G1<br />
- (B3) B2 (C3) <D5 (E4)> E1 (J2) I4 (I3) H4 (H3) G6 <br />
- (C9) D7 (E7 [G6->E8 ok]) D7 (B7) <br />
- with <D5 (E4)> get: B6 - BLUE wins<br />
- without <D5 (E4)> get: D5 (B6) D4 (D2) D1 (E2) F1 (E3) E5 (F5) - RED wins!<br />
- (D8) D9 (B10) B12 (B11) C13 - now blue wins as G11/F10 are miai<br />
- (J2) <br />
- (D2) F4 (J2) <br />
- (E4) E1 (J2) I4 (I3) H4 (H3) <br />
- (J2) C9 (I7) I4 (H5) H4 (G5) F2 (D2) E4 (D5) E5 - red has no move, blue wins<br />
- (D2) <br />
<br />
Close to repetition! From move 22 notes:<br />
I7 (C9 [B9 doesn't work with D11 because of E12]) C2<br />
- (B3) B2 (C3) F2 (I4) I3 (D2) D5 (E5 [D4 weakness, so (E4)?]) D7 (E7) D8 (F8)<br />
(note the K7) K6 (L6) L5 (J7) I9 sequence)<br />
- (D2) D7 (B7) C5, blue connects, red can play (F8), but looks like this works for blue? What if red plays (H4/G5/H5/I4), threatening an attack around (J2) before (F8)? Well, blue can play at F7 and just connect to I7 and win.<br />
I10 (C11 [threatens D8 connection]) C9 (I7) <br />
- H4 (G6) G5 (E7) F2 (E4) D3 (C3), with C9 in place blue can run down the left<br />
- C2/F2?<br />
<br />
<br />
Question: Does I7 connect E8 to the right edge? It's a series of double threats. Attacking the direct E8--> I7 connected: If red (F8) then blue walks up to I2, however this only connects by running down to J11. So can red attack the connection of E8 to the right edge by first attacking the direct route through I7 (eg. at (K7) or (L11)) and then playing (F8) having damaged the route down the RHS?<br />
Note* I was very worried, after playing move 22 that red would instead play at E10. This blocks E9-->I10 better than D11.<br />
<br />
Move 22: <br />
/ F10 (G11) \<br />
I10 (D11) I7 [[not needed (F8) F7 (G7) G6 (H6) G4]] (B9) C2 [see below]<br />
\ G11 (F10) /<br />
- (B3) B2 (C3) F2 (I4) I3 (D2) D5 (E5 [D4 weakness, so (E4)?]) D7 (E7) D8 (F8) - blue *almost* wins here. The complication is J3, leading to a ladder down the right hand side, and the possibility of a double threat earlier. Something like (K7) K6 (L6) L5 (J7) I9. So it looks like it doesn't work for red. <br />
- (D2) D7 (B7) C5, blue connects, red can play (F8), but looks like this works for blue? What if red plays (H4/G5/H5/I4), threatening an attack around (J2) before (F8)? Well, blue can play at F7 and just connect to I7 and win.<br />
I10 (C11 [threatens D8 connection]) C9 (I7) <br />
- H4 (G6) G5 (E7) F2 (E4) D3 (C3), with C9 in place blue can run down the left<br />
- C2/F2?<br />
I10 (I7) G11 (C11) <br />
<br />
C11 (B12) D11 (B11) C9 (E10) C10<br />
- (G11) <br />
- (A10), and a ladder<br />
C11 (D9 - cuts off E8 pieces fairly thoroughly) I10 (G11) <br />
C11 (B10) C9 (D11) - confusing...<br />
<br />
D8s connection to both the top and the bottom?<br />
[E3/F2 - looking at C2? C2? - ignoring F2 too much?] H4 [protect against F2, sets up G6 related moves, like C9?]<br />
Can I get J5 in as a forcing move?<br />
J5 (J4) - looks bad for blue<br />
Red is in danger of playing J2 and chopping through the top. After red J2 blue can get to the E8 stones, but not to the left edge yet. <br />
<br />
Move 20: <br />
D6 (C9? B7? D7? F4?)<br />
E4 (D5) C2 (D2) D6 (B7) C5 <br />
E4 (D5) C2 (B3) B2 (C3) F2 (D2) C9 (G11) F6 - looks good for blue<br />
E4 (D5) C2 (D2) D6 - seems to work for blue <br />
Red can pull out (J2) at any time - that looks like a big problem!<br />
<br />
Problem is that if I play C9, red will play a testing move like (G8). If I play G7 red can play (I7) and I10 no longer threatens anything. So red can focus on the top, with something like (K4). Then when blue plays G11 red can answer at (E10), connecting to the bottom.<br />
<br />
Move 18:<br />
E5 (F5) F2[say] (I4) I3 (B6) - looks good for red, F5 seems basically connected to top and bottom<br />
E5 (D6) D5 (B6) C7 (D8) C6 (B10) B8 - good for blue, red has no way to the top<br />
D5 (F4) - red seems to connect to the top and benefit substantially from this exchange.<br />
E4 (D5) G5 (B10) - good for red?<br />
<br />
Move 14: <br />
C5?<br />
E8 (F8) F5 [looking at I4 and C5, or even D6, with E8?] <br />
E8 (F8) F7 (G7) G6 (H6) I4 - doesn't look like quite enough for blue?<br />
E8 (I7) H4 <br />
E10 (I7) I6 (J6) J5 (F8) F10 (G8) G11 (H11) - now (I7) forcing sequence connects red around to (F8)! - Bad for blue<br />
I7 (F8) <br />
D6 - doesn't connect to the left, can that be ok?<br />
F11 (D10) - goes badly for blue when red [later] plays E11<br />
<br />
Move 12: Should arguably have been at J3, as this still connects with J11. Should always stretch as much as you can (Jonatan Rydh)<br />
<br />
Move 10: I8?</div>
Halladba
https://www.hexwiki.net/index.php/NiallVsJamesACook_1252463
NiallVsJamesACook 1252463
2010-12-13T20:52:12Z
<p>Halladba: NiallVsJamesACook 1252463 moved to James A. Cook vs. Niall, December 2010: uniformisation</p>
<hr />
<div>#REDIRECT [[James A. Cook vs. Niall, December 2010]]</div>
Halladba
https://www.hexwiki.net/index.php/Nietsabes_vs._Niall,_November_2010
Nietsabes vs. Niall, November 2010
2010-12-13T20:49:14Z
<p>Halladba: templatization</p>
<hr />
<div>== Game information ==<br />
* Size: 13x13<br />
* Red: nietsabes<br />
* Blue: [[user:Niall | Niall]]<br />
* Result: 0-1 (Blue won)<br />
* Comments: Niall, [[user:Halladba | Halladba]]<br />
* Location: [[Little Golem]], game [http://www.littlegolem.net/jsp/game/game.jsp?gid=1241576 1241576] in championship 25.2.2<br />
<br />
== Comments ==<br />
<br />
Notes for nietsabes game (unfortunately he resigned before I expected and I lost some notes about the last few moves), I had gone through a few variations quite well :( If you have any questions about specific sequences I can probably still answer them.<br />
<br />
Move 24:<br />
I8 (L6) J9 (K9) - now what?<br />
<br />
Move 22: Problem with sequence from 16: C12 can be answered with C9!!<br />
I5 (H4) H3 (F5) F4 (D7) D6 (B7) C7 (B8) C8 (B9) C12 (C9) - now what?<br />
<br />
move 16:<br />
E5 (H4) H3 (F5) F4 (D7) D6 (B7) C7 (B8) C8 (B9) C12 (C10) E9 (D9) E8<br />
(D8) [connects to D7] F6 - connects and wins, as red has neither E6 or<br />
G5, so blue can use either. It then continues with the almost separate<br />
battle of:<br />
... (K3) L2 (K2) J4 (K4) I7 (J7) I9 (K8) (J10) - push through, and run<br />
up the right to L2 - red connects to the RHS.(can force the same after<br />
M2)<br />
<br />
<br />
<br />
If red exchanges (H4) H3 & (F5) F4, then blue D4 avoids the ladder to<br />
(L2) and I think almost connects for blue.<br />
E5 (D7) E7 (F5) F4 [doesn't threaten the connection to the top!] (F6)<br />
D6 - transposes to the below, a win for red?<br />
<br />
E5 (D7) D6 (B7) C7 (B8) C8 (B9)<br />
- D8 (D9)<br />
- C9/D9 - seem to suffer from being laddered by A12<br />
<br />
(F5) response to my moves is a problem. Connected to the main red<br />
chain and F4 doesn't threaten the (D4) connection to the top. Red may<br />
also force at (H4).<br />
F6 (E7) red can force the same sequence as before. the E8 peep seems<br />
to be of no use.<br />
<br />
D7 (F5) - blue is done for<br />
Seems like I might as well force at G9. [Overthinking... Unless I can<br />
see a win, or I think red just made a mistake? [Or red wanted to get:<br />
move on the left G9, and then force at F10...]]<br />
<br />
<br />
move 14:<br />
E10 (B9) C12 - good enough to retains the threat at E5 right?<br />
E10 (B9) C8 (D9) - could be problems for blue<br />
E10 (G9) E5<br />
E10 (G9) E5 (C8) D7 (C7) D8 - blue connects<br />
E6 (F5) F4 (E5)<br />
- D4 (H3) H4 (E4) F2 (F3) ... (L2) again! win for red?<br />
- E3 (D3) E1 (E2) F1 ... (L2) K2 (J4) red has connected (F8) to the<br />
top, and probably to the bottom. Red probably wins.<br />
<br />
Unfortunately C5 destroys the plan at move 12.<br />
E6 (D7) E7 (D8) E8 (D9) D6 (B7) C7 (B8) C8 (B9) C10 (C9) E10 (E9) G9.<br />
Instead of (B9) red can force at (J4) . If blue B9 red (K3) connects<br />
to the top and red can't stop The F8 end of this chain with the extra<br />
red support at (J4/K3). So instead blue must play K3. Red cannot<br />
further force at K4 as this can be locally ignored. Now red can play<br />
B9. Following as above to G9 blue red can now block blue with J7<br />
(connected to the top).<br />
From here: Blue J8 looks powerful. So maybe this is good for blue.<br />
<br />
<br />
Move 12:<br />
J3 (E6) F10 (G9) G10 (H9) H10 (E10) D12 (E11) E12 (F11) F12 (G11) G12<br />
(I11) H11 (J9) I9 (J8) I8 (K6) J7 (K7) J5 (L3) L2 (K3) K2 (J4). Now<br />
red has connected F8 to the bottom and blue has the task of blocking<br />
D5. However red has given blue J2 - so now E3 becomes a powerful move.<br />
- Would blue having H7 help here?<br />
F10, double-ladder creating RHS chain up to (L3) L2 (K3) K2 (E6) E3<br />
(F4) G2 (H3) I2...<br />
<br />
Move 8,<br />
h9 c11 - blue feels somewhat blocked from the left now?<br />
c11 g8 i3 - red cannot get to the bottom without a ladder the right.<br />
Which means that i3 stone has a forcing move to help it, unless red<br />
can get to the top by sliding left. E7 answered by E6? The c11 stone<br />
feeds blue back up to C1 for a connection... Lots of holes and<br />
problems...<br />
F9 E9 D11 C11 D10 C10 D9 C9 D7 D8 E7 - oops red is already connected<br />
d6?<br />
f6 f7 - now I need another move both to go right and to go left<br />
ck di fi ej ei dj eh dh... bleeurgh<br />
<br />
D10 area? But D10 doesn't act as a ladder breaker.<br />
dj ej ff gf ic jc id jd ie je if jf ii ig hg kh jj kj - hmm, how is this going?<br />
dj ej gg fg gf ee - red wins :(<br />
F4 looking good, alternatives? Lower left looks unpromising...<br />
F4 C5 E6 D7...<br />
F4 C5 E7 ?<br />
E3 F4 G2 G3 H2 H3 I2 J3 I3 I4 H4 G8 - and I've been crushed<br />
E4 has the same problem.<br />
However D5 needs to also connect to the central group or the bottom to<br />
be useful. So a more creative version of F4 might work.<br />
G4? Connects well to C1, so sets up the push at G7. if red blocks at<br />
G6 then blue can go make trouble in the top right.<br />
<br />
<br />
[[category:game record]]</div>
Halladba
https://www.hexwiki.net/index.php/Nietsabes_vs._Niall,_November_2010
Nietsabes vs. Niall, November 2010
2010-12-13T20:45:28Z
<p>Halladba: NiallVsNietsabes 1241576 moved to Nietsabes vs. Niall, November 2010: uniformisation</p>
<hr />
<div>Notes for nietsabes game (unfortunately he resigned before I expected and I lost some notes about the last few moves), I had gone through a few variations quite well :( If you have any questions about specific sequences I can probably still answer them.<br />
<br />
http://www.littlegolem.net/jsp/game/game.jsp?gid=1241576<br />
<br />
Move 24:<br />
I8 (L6) J9 (K9) - now what?<br />
<br />
Move 22: Problem with sequence from 16: C12 can be answered with C9!!<br />
I5 (H4) H3 (F5) F4 (D7) D6 (B7) C7 (B8) C8 (B9) C12 (C9) - now what?<br />
<br />
move 16:<br />
E5 (H4) H3 (F5) F4 (D7) D6 (B7) C7 (B8) C8 (B9) C12 (C10) E9 (D9) E8<br />
(D8) [connects to D7] F6 - connects and wins, as red has neither E6 or<br />
G5, so blue can use either. It then continues with the almost separate<br />
battle of:<br />
... (K3) L2 (K2) J4 (K4) I7 (J7) I9 (K8) (J10) - push through, and run<br />
up the right to L2 - red connects to the RHS.(can force the same after<br />
M2)<br />
<br />
<br />
<br />
If red exchanges (H4) H3 & (F5) F4, then blue D4 avoids the ladder to<br />
(L2) and I think almost connects for blue.<br />
E5 (D7) E7 (F5) F4 [doesn't threaten the connection to the top!] (F6)<br />
D6 - transposes to the below, a win for red?<br />
<br />
E5 (D7) D6 (B7) C7 (B8) C8 (B9)<br />
- D8 (D9)<br />
- C9/D9 - seem to suffer from being laddered by A12<br />
<br />
(F5) response to my moves is a problem. Connected to the main red<br />
chain and F4 doesn't threaten the (D4) connection to the top. Red may<br />
also force at (H4).<br />
F6 (E7) red can force the same sequence as before. the E8 peep seems<br />
to be of no use.<br />
<br />
D7 (F5) - blue is done for<br />
Seems like I might as well force at G9. [Overthinking... Unless I can<br />
see a win, or I think red just made a mistake? [Or red wanted to get:<br />
move on the left G9, and then force at F10...]]<br />
<br />
<br />
move 14:<br />
E10 (B9) C12 - good enough to retains the threat at E5 right?<br />
E10 (B9) C8 (D9) - could be problems for blue<br />
E10 (G9) E5<br />
E10 (G9) E5 (C8) D7 (C7) D8 - blue connects<br />
E6 (F5) F4 (E5)<br />
- D4 (H3) H4 (E4) F2 (F3) ... (L2) again! win for red?<br />
- E3 (D3) E1 (E2) F1 ... (L2) K2 (J4) red has connected (F8) to the<br />
top, and probably to the bottom. Red probably wins.<br />
<br />
Unfortunately C5 destroys the plan at move 12.<br />
E6 (D7) E7 (D8) E8 (D9) D6 (B7) C7 (B8) C8 (B9) C10 (C9) E10 (E9) G9.<br />
Instead of (B9) red can force at (J4) . If blue B9 red (K3) connects<br />
to the top and red can't stop The F8 end of this chain with the extra<br />
red support at (J4/K3). So instead blue must play K3. Red cannot<br />
further force at K4 as this can be locally ignored. Now red can play<br />
B9. Following as above to G9 blue red can now block blue with J7<br />
(connected to the top).<br />
From here: Blue J8 looks powerful. So maybe this is good for blue.<br />
<br />
<br />
Move 12:<br />
J3 (E6) F10 (G9) G10 (H9) H10 (E10) D12 (E11) E12 (F11) F12 (G11) G12<br />
(I11) H11 (J9) I9 (J8) I8 (K6) J7 (K7) J5 (L3) L2 (K3) K2 (J4). Now<br />
red has connected F8 to the bottom and blue has the task of blocking<br />
D5. However red has given blue J2 - so now E3 becomes a powerful move.<br />
- Would blue having H7 help here?<br />
F10, double-ladder creating RHS chain up to (L3) L2 (K3) K2 (E6) E3<br />
(F4) G2 (H3) I2...<br />
<br />
Move 8,<br />
h9 c11 - blue feels somewhat blocked from the left now?<br />
c11 g8 i3 - red cannot get to the bottom without a ladder the right.<br />
Which means that i3 stone has a forcing move to help it, unless red<br />
can get to the top by sliding left. E7 answered by E6? The c11 stone<br />
feeds blue back up to C1 for a connection... Lots of holes and<br />
problems...<br />
F9 E9 D11 C11 D10 C10 D9 C9 D7 D8 E7 - oops red is already connected<br />
d6?<br />
f6 f7 - now I need another move both to go right and to go left<br />
ck di fi ej ei dj eh dh... bleeurgh<br />
<br />
D10 area? But D10 doesn't act as a ladder breaker.<br />
dj ej ff gf ic jc id jd ie je if jf ii ig hg kh jj kj - hmm, how is this going?<br />
dj ej gg fg gf ee - red wins :(<br />
F4 looking good, alternatives? Lower left looks unpromising...<br />
F4 C5 E6 D7...<br />
F4 C5 E7 ?<br />
E3 F4 G2 G3 H2 H3 I2 J3 I3 I4 H4 G8 - and I've been crushed<br />
E4 has the same problem.<br />
However D5 needs to also connect to the central group or the bottom to<br />
be useful. So a more creative version of F4 might work.<br />
G4? Connects well to C1, so sets up the push at G7. if red blocks at<br />
G6 then blue can go make trouble in the top right.</div>
Halladba
https://www.hexwiki.net/index.php/NiallVsNietsabes_1241576
NiallVsNietsabes 1241576
2010-12-13T20:45:28Z
<p>Halladba: NiallVsNietsabes 1241576 moved to Nietsabes vs. Niall, November 2010: uniformisation</p>
<hr />
<div>#REDIRECT [[Nietsabes vs. Niall, November 2010]]</div>
Halladba
https://www.hexwiki.net/index.php/Niall_vs._Halladba,_November_2010
Niall vs. Halladba, November 2010
2010-11-15T09:45:21Z
<p>Halladba: game info, board representations, presentation</p>
<hr />
<div>== Game information ==<br />
* Size: 13x13<br />
* Red: [[user:Halladba | Halladba]]<br />
* Blue: [[user:Niall | Niall]]<br />
* Result: 0-1 (Blue won)<br />
* Comments: Niall, Halladba<br />
* Location: [[Little Golem]], game [http://www.littlegolem.net/jsp/game/game.jsp?gid=1241590 1241590] in championship 25.2.2<br />
<br />
== Comments ==<br />
<br />
{| cellspacing="0" style="width: 500px"<br />
| 1. || a3 || || <br />
|-<br />
| 2. || ... || swap || <br />
|-<br />
| 3. || j9 || || <br />
|-<br />
| 4. || ... || i5 || <br />
|-<br />
| 5. || k3 || || <br />
|-<br />
| 6. || ... || j11 || <br />
|-<br />
| 7. || l11 || || <br />
|-<br />
| 8. || ... || k12 ||<br />
|}<br />
<br />
<hex> R13 C13 Q1<br />
B2c1 <br />
R5k3 <br />
B4i5 <br />
R3j9 <br />
B6j11 R7l11 <br />
B8k12 </hex><br />
<br />
{| cellspacing="0" style="width: 500px"<br />
| 9. || f8 || || <br />
|-<br />
| 10. || ... || d10 || <br />
|-<br />
| 11. || c11 || || <br />
|-<br />
| 12. || ... || f6 || followed by (g6) h4 (g5) g4 (e5) and f3 blocks red form the top<br />
|}<br />
<br />
<hex> R13 C13 Q1<br />
Bc1 <br />
Rk3 <br />
Bi5 <br />
B4f6<br />
R1f8<br />
Rj9 <br />
B2d10<br />
R3c11 Bj11 Rl11 <br />
Bk12 </hex><br />
<br />
{| cellspacing="0" style="width: 500px"<br />
| 13. || i6 || || <br />
|-<br />
| 14. || ... || j5 || <br />
|-<br />
| 15. || k6 || || <br />
|-<br />
| 16. || ... || l4 || <br />
|-<br />
| 17. || h5 || || <br />
|-<br />
| 18. || ... || f9 || followed by (g8) g9 (h8) h9 (i9) i8 (j7) j8 (l7) - blue wins [still, blue is making a lot of [[multiple threat|double threats]] here, so red may answer with [[double defence]]s] or f9 [I believe that d10 is currently connected to the left via f6/c1 2/3rd line [[ladder escape]]...] (g8 -as this is what red must do if blue started by pushing at h6) g9...<br />
|}<br />
<br />
<hex> R13 C13 Q1<br />
Bc1 <br />
Rk3 <br />
B6l4<br />
R7h5 Bi5 B4j5<br />
Bf6 R3i6 R5k6<br />
Rf8<br />
B8f9 Rj9 <br />
Bd10<br />
Rc11 Bj11 Rl11 <br />
Bk12 </hex><br />
<br />
{| cellspacing="0" style="width: 500px"<br />
| 19. || g8 || || g8: The trick, for red, is to play around d7 before forcing blue to connect to f6 or d10. Is there a move which threatens both which I cannot answer to save both?<br />
g8 (e7) f7 (e8) e6 (d7) d6 (c7) d2 (g7) f9 (c10) - blue loses ;<br />
g8 [(g7) f9?] (h7 - guards against both h6 and i7) h8 (k7) i10 (i9, red h9 answered by blue i8) h10 (h9) g10 (g9) e11 ;<br />
g8 (h10) h6 (g6) f9 - looking good for blue<br />
g8 (h10) h6 (<br />
|}<br />
<br />
<hex> R13 C13 Q1<br />
Bc1 <br />
Rk3 <br />
Bl4<br />
Rh5 Bi5 Bj5<br />
Bf6 Ri6 Rk6<br />
Rf8 R1g8<br />
Bf9 Rj9 <br />
Bd10<br />
Rc11 Bj11 Rl11 <br />
Bk12 </hex><br />
<br />
<br />
{| cellspacing="0" style="width: 500px"<br />
| 20. || ... || g9 || <br />
|-<br />
| 21. || h8 || || <br />
|-<br />
| 22. || ... || h9 || <br />
|-<br />
| 23. || e9 || || <br />
|-<br />
| 24. || ... || e10 || <br />
|}<br />
<br />
<hex> R13 C13 Q1<br />
Bc1 <br />
Rk3 <br />
Bl4<br />
Rh5 Bi5 Bj5<br />
Bf6 Ri6 Rk6<br />
Rf8 Rg8 R2h8<br />
R4e9 Bf9 B1g9 B3h9 Rj9 <br />
Bd10 B5e10<br />
Rc11 Bj11 Rl11 <br />
Bk12 </hex><br />
<br />
{| cellspacing="0" style="width: 500px"<br />
| 25. || l8 || || <br />
|-<br />
| 26. || ... || h6 ||<br />
|}<br />
<br />
<hex> R13 C13 Q1<br />
Bc1 <br />
Rk3 <br />
Bl4<br />
Rh5 Bi5 Bj5<br />
Bf6 Ri6 Rk6<br />
Rf8 Rg8 Rh8 R1l8<br />
Re9 Bf9 Bg9 Bh9 Rj9 <br />
Bd10 Be10<br />
Rc11 Bj11 Rl11 <br />
Bk12 </hex><br />
<br />
<hex> R13 C13 Q1<br />
Bc1 <br />
Rk3 <br />
Bl4<br />
Rh5 Bi5 Bj5<br />
Bf6 B2h6 Ri6 Rk6<br />
Rf8 Rg8 Rh8 R1l8<br />
Re9 Bf9 Bg9 Bh9 Rj9 <br />
Bd10 Be10<br />
Rc11 Bj11 Rl11 <br />
Bk12 </hex><br />
<br />
{| cellspacing="0" style="width: 500px"<br />
| 27. || d9 || || <br />
|-<br />
| 28. || ... || f7 || <br />
|-<br />
| 29. || b9 || || <br />
|-<br />
| 30. || ... || c7 || <br />
|-<br />
| 31. || d7 || || <br />
|-<br />
| 32. || ... || e5 || <br />
|-<br />
| 33. || d6 || || <br />
|-<br />
| 34. || ... || d5 || <br />
|-<br />
| 35. || resign || ||<br />
|}<br />
<br />
<hex> R13 C13 Q1<br />
Bc1 <br />
Rk3 <br />
Bl4<br />
B8d5 B6e5 Rh5 Bi5 Bj5<br />
R7d6 Bf6 Bh6 Ri6 Rk6<br />
B4c7 R5d7 B2f7<br />
Rf8 Rg8 Rh8 Rl8<br />
R3b9 R1d9 Re9 Bf9 Bg9 Bh9 Rj9 <br />
Bd10 Be10<br />
Rc11 Bj11 Rl11 <br />
Bk12 </hex><br />
<br />
[[category:game record]]</div>
Halladba
https://www.hexwiki.net/index.php/Niall_vs._Halladba,_November_2010
Niall vs. Halladba, November 2010
2010-11-15T09:43:07Z
<p>Halladba: NiallVsHalladba Nov2010 moved to Niall vs. Halladba, November 2010: uniformisation</p>
<hr />
<div>Notes concerning the game:<br />
http://www.littlegolem.net/jsp/game/game.jsp?gid=1241590<br />
<br />
Move 18: <br />
F9 (G8) G9 (H8) H9 (I9) I8 (J7) J8 (L7) - blue wins [still, blue is making a lot of double threats here, so red may answer with double defences]<br />
F9 [I believe that D10 is currently connected to the left via F6/C1 2/3rd line ladder escape...] (G8 -as this is what red must do if blue started by pushing at H6) G9...<br />
<br />
G8: The trick, for red, is to play around D7 before forcing blue to connect to F6 or D10. Is there a move which threatens both which I cannot answer to save both?<br />
G8 (E7) F7 (E8) E6 (D7) D6 (C7) D2 (G7) F9 (C10) - blue loses <br />
<br />
G8 [(G7) F9?] (H7 - guards against both H6 and I7) H8 (K7) I10 (I9, red H9 answered by blue I8) H10 (H9) G10 (G9) E11<br />
G8 (H10) H6 (<br />
G8 (H10) H6 (G6) F9 - looking good for blue<br />
<br />
Move 12:<br />
F6 (G6) H4 (G5) G4 (E5) F3 blocks red form the top</div>
Halladba
https://www.hexwiki.net/index.php/NiallVsHalladba_Nov2010
NiallVsHalladba Nov2010
2010-11-15T09:43:07Z
<p>Halladba: NiallVsHalladba Nov2010 moved to Niall vs. Halladba, November 2010: uniformisation</p>
<hr />
<div>#REDIRECT [[Niall vs. Halladba, November 2010]]</div>
Halladba
https://www.hexwiki.net/index.php/Proverbs
Proverbs
2010-06-30T10:11:53Z
<p>Halladba: cat. community</p>
<hr />
<div>== Proverbs about strategy ==<br />
In [[Go]], there are many proverbs about strategy. Since the strategic concepts are very related, one might check whether the proverbs also apply to [[Hex]].<br />
<br />
*[[Offense equals defense]], this is due to the no-[[draw]] property.<br />
*Consider playing in the "[[wrong direction]]", [[rope]]s make the board much easier to cross.<br />
*A player's position is only as good as its [[weakest link]].<br />
*Do not play an [[isolated piece]] with three or fewer liberties.<br />
<br />
== Quotations ==<br />
* According to Edward Lasker, a chess player,<br />
:''Chess is a game restricted to this world, Go has something extraterrestrial. If ever we find an extraterrestrial civilization that plays a game that we also play, it will be Go, without any doubt.''<br />
* [[Jack van Rijswijck]] goes beyond,<br />
: '''Hex has a Platonic existence, independent of human thought. If ever we find an extraterrestrial civilization at all, they will know Hex, without any doubt.''' (source [[Set Colouring Games]], 2006. Page 163)<br />
<br />
== External links ==<br />
* http://senseis.xmp.net/?GoProverbs<br />
* The [[Twixt]] [http://twixt.wetpaint.com/page/Maxims+for+moves proverbs] are also often relevant to Hex.<br />
<br />
[[category:strategy]]<br />
[[category:Hex community]]</div>
Halladba
https://www.hexwiki.net/index.php/Template
Template
2010-06-20T12:41:40Z
<p>Halladba: added link to second order template</p>
<hr />
<div>A '''template''' is a [[pattern]] which guarantees some kind of [[connection]]. There are several different (and sometimes overlapping) types:<br />
<br />
* [[:Category:Edge templates |Edge templates]]<br />
* [[Ladder template]]s<br />
* [[Unnamed interior templates|Interior template]]s<br />
* [[Second order template]]s<br />
<br />
== See also ==<br />
<br />
* [[Naming of templates]]<br />
<br />
== Reference ==<br />
<br />
* [http://www.drking.plus.com/hexagons/hex/templates.html David King's Hex template page]<br />
* [http://www.f.kth.se/~rydh/Hex/templates.html Jonatan Rydh's Hex edge templates page]<br />
<br />
[[category:templates]]<br />
[[category:connection types]]</div>
Halladba
https://www.hexwiki.net/index.php/Second_order_template
Second order template
2010-06-20T12:40:47Z
<p>Halladba: concept + examples + usage</p>
<hr />
<div>A '''second order [[template]]''', is a pattern which guarantees a connection even if the opponent is given a free move at the beginning. Put another way, a second order template is a pattern in which an intrusion is not a [[forcing move]]. A pattern can be proved to be a second order template by showing that every possible intrusion preserves at least one [[edge template|first order template]].<br />
<br />
== Examples ==<br />
<hex> R2 C3<br />
Sa1 Vb1 Vc1<br />
</hex><br />
=== Third row ===<br />
<hex> R3 C6<br />
Sa1 Sb1 Vd1 Ve1<br />
Sa2</hex><br />
<br />
This pattern can be reduced to [[ziggurat]]s:<br />
<br />
<hex> R3 C6<br />
Sa1 Sb1 Pc1 Vd1 Ve1<br />
Sa2 Pb2 Pc2<br />
Pa3 Pb3<br />
</hex><br />
<br />
<hex> R3 C6<br />
Sa1 Sb1 Vd1 Ve1 Pf1<br />
Sa2 Pe2 Pf2<br />
Pe3 Pf3<br />
</hex><br />
<br />
Therefore the only forcing moves must lie in the overlapping area. However, the overlapping is alson non-forcing thanks to Vertical's (1) moves.<br />
<hex> R3 C6<br />
Sa1 Sb1 Vd1 Ve1<br />
Sa2 V1b2 Pd2 V1f2<br />
Pc3 Pd3<br />
</hex><br />
<br />
== Usage ==<br />
<br />
A first order edge template prove that a group is connected to the edge provided the player answer threats made to the connection. If the player wants to preserve the connection, the opponent can throw stones in the carrier that will later serve as [[ladder escape]]s, such moves belong to the category of [[double threat]]s. Recognizing second order edge templates helps to know whether an area is safe or might be subject to such double threats.<br />
<br />
<br />
[[category:templates]]<br />
[[category:connection types]]<br />
[[category:advanced Strategy]]</div>
Halladba
https://www.hexwiki.net/index.php/Small_boards
Small boards
2010-04-21T10:59:25Z
<p>Halladba: /* Winner depending on the first move */ size 9</p>
<hr />
<div>Playing [[Hex]] on [[board]]s of size smaller than 10 &times; 10 is not very interesting, since many players will be able to play almost perfectly. However it may still be intersting for theoretical studies, and for making [[Puzzles|problems]].<br />
<br />
The boards of size up to five can be solved by hand. Hex on 6 &times; 6 has been solved by [[Queenbee]].<br />
<br />
Here are the winning first moves on the small boards. [[Red (player)|Red]] is vertical and plays first. The [[Hex (board element)|cells]] containing a red [[Piece|stone]] are winning moves for red, while those containing a blue stone are losing. For more details, visit Queenbee's own [http://www.cs.ualberta.ca/~queenbee/openings.html opening page].<br />
<br />
''Update:'' The 7 &times; 7 board has been solved by [[Ryan Hayward|R. Hayward]], et.al. For more details, visit http://www.cs.ualberta.ca/~hayward/hex7trees/<br />
<br />
== Winner depending on the first move ==<br />
The following boards can help you decide where you should [[swap]] when playing on small boards, and it might give you ideas of patterns for bigger boards.<br />
<hex>R2 C2 Q1 Vb1 Va2 Ha1 Hb2</hex><br />
<br />
<hex>R3 C3 Q1 Va2 Va3 Hb1 Vb2 Hb3 Vc1 Vc2 Ha1 Hc3</hex><br />
<br />
<hex>R4 C4 Q1 Va4 Vb3 Vc2 Vd1 Ha1 Ha2 Ha3 Hb1 Hb2 Hb4 Hc1 Hc3 Hc4 Hd2 Hd3 Hd4</hex><br />
<br />
<hex>R5 C5 Q1 Ve1 Vb2 Vc2 Vd2 Ve2 Vb3 Vc3 Vd3 Va4 Vb4 Vc4 Vd4 Va5 Ha1 Ha2 Ha3 Hb1 Hc1 Hd1 Hb5 Hc5 Hd5 He5 He4 He3</hex><br />
<br />
<hex>R6 C6 Q1 Ve1 Vb2 Vc2 Vd2 Ve2 Vb3 Vc3 Vd3 Va4 Vb4 Vc4 Vd4 Va5 Ha1 Ha2 Va3 Hb1 Hc1 Hd1 He1 Vb5 Vc5 Vd5 Ve5 Ve4 Ve3 Vf1 Vf2 Vf3 Vf4 Hf5 Hf6 He6 Hd6 Hc6 Hb6 Va6</hex><br />
<br />
=== Size 7 ===<br />
<br />
Size 7 was first solved by [[Ryan Hayward]] using [[domination]].<br />
<br />
<hex>R7 C7 Q1 Ha1 Hb1 Hc1 Hd1 He1 Hf1 Vg1 Ha2 Hb2 Vc2 Hd2 Ve2 Vf2 Vg2 Ha3 Vb3 Vc3 Vd3 Ve3 Vf3 Hg3 Va4 Vb4 Vc4 Vd4 Ve4 Vf4 Vg4 Ha5 Vb5 Vc5 Vd5 Ve5 Vf5 Hg5 Va6 Vb6 Vc6 Hd6 Ve6 Hf6 Hg6 Va7 Hb7 Hc7 Hd7 He7 Hf7 Hg7</hex><br />
<br />
=== Size 8 ===<br />
<br />
The outcomes for size 8 were computer generated by [[Javerberg]]. The solution was independantly computer generated by Hayward et al. and appeared in [[INJCAI|IJCAI09]].<br />
<br />
<hex><br />
R8 C8 Q1<br />
Ha1 Hb1 Hc1 Hd1 He1 Hf1 Hg1 Vh1<br />
Ha2 Hb2 Hc2 Hd2 He2 Hf2 Vg2 Vh2<br />
Ha3 Vb3 Vc3 Vd3 Ve3 Vf3 Vg3 Hh3<br />
Ha4 Vb4 Vc4 Vd4 Ve4 Vf4 Vg4 Vh4<br />
Va5 Vb5 Vc5 Vd5 Ve5 Vf5 Vg5 Hh5<br />
Ha6 Vb6 Vc6 Vd6 Ve6 Vf6 Vg6 Hh6<br />
Va7 Vb7 Hc7 Hd7 He7 Hf7 Hg7 Hh7<br />
Va8 Hb8 Hc8 Hd8 He8 Hf8 Hg8 Hh8<br />
</hex><br />
<br />
=== Size 9 ===<br />
<br />
The outcomes for size 9 are computer generated by [[University of Alberta]]'s Hex group.<br />
<br />
<hex><br />
R9 C9 Q1<br />
Ha1 Hb1 Hc1 Hd1 He1 Hf1 Hg1 Hh1 Pi1<br />
Pa2 Pb2 Pc2 Hd2 He2 Hf2 Hg2 Vh2 Pi2<br />
Pa3 Vb3 Vc3 Vd3 Ve3 Vf3 Vg3 Ph3 Pi3<br />
Pa4 Pb4 Vc4 Vd4 Ve4 Vf4 Vg4 Ph4 Pi4<br />
Pa5 Vb5 Vc5 Vd5 Ve5 Vf5 Vg5 Vh5 Pi5<br />
Pa6 Pb6 Vc6 Vd6 Ve6 Vf6 Vg6 Ph6 Pi6<br />
Pa7 Pb7 Vc7 Vd7 Ve7 Vf7 Vg7 Vh7 Pi7<br />
Pa8 Vb8 Hc8 Hd8 He8 Hf8 Pg8 Ph8 Pi8<br />
Pa9 Hb9 Hc9 Hd9 He9 Hf9 Hg9 Hh9 Hi9<br />
</hex><br />
<br />
== Reference ==<br />
* [[Queenbee]]'s opening [http://www.cs.ualberta.ca/~queenbee/openings.html page] is a reference for sizes under 6x6.<br />
* This [http://www.ru.is/faculty/yngvi/pdf/HaywardBJKPR05.pdf article] by Ryan Hayward ''et al.'' is a reference for 7x7.<br />
* This [[Little Golem]]'s forum [http://www.littlegolem.net/jsp/forum/topic2.jsp?forum=50&topic=338 thread] is a reference for size 8x8.<br />
<br />
== See also ==<br />
<br />
* [[Board size]]<br />
* [[Jing Yang]] designed a [[decomposition method]] to find winning strategy in Hex. [http://www.ee.umanitoba.ca/~jingyang/index.html Home Page].<br />
<br />
[[Category: Theory]]</div>
Halladba
https://www.hexwiki.net/index.php/User_talk:Shalevbd
User talk:Shalevbd
2010-03-25T08:44:19Z
<p>Halladba: a9 ?</p>
<hr />
<div>Hi!<br />
<br />
I don't see the point of Red a9 in the intermediate strategy guide, could you give a few more details ?<br />
<br />
[[User:Halladba|Halladba]] 09:44, 25 March 2010 (CET)</div>
Halladba
https://www.hexwiki.net/index.php/User_talk:HappyHippo
User talk:HappyHippo
2009-06-12T00:57:04Z
<p>Halladba: Thanks !</p>
<hr />
<div>Good job on template VI2 ! [[User:Halladba|Halladba]] 02:57, 12 June 2009 (CEST)</div>
Halladba
https://www.hexwiki.net/index.php/Draw
Draw
2009-03-22T17:33:34Z
<p>Halladba: another equivalence</p>
<hr />
<div>One of the beautiful properties of Hex is that the game can never end in a '''draw''', i.e., there is always a winner.<br />
<br />
There are various ways of proving this, for example:<br />
<br />
* A [http://www.cs.ualberta.ca/~javhar/hex/hex-galeproof.html proof] by [[David Gale]] that used the fact that exactly three hexes meet at every vertex.<br />
* An [http://www.cs.ualberta.ca/~javhar/hex/hex-yproof.html elegant proof] using the [[Y|game of Y]]. <br />
* Another [[Y#No draws|proof]] using the game of Y.<br />
<br />
In fact, David Gale showed that the no-draw property is equivalent to the 2-dimensional case of [http://en.wikipedia.org/wiki/Brouwer_fixed_point_theorem Brouwer's fixed point theorem] (a non-trivial theorem from topology saying that any continuous map from the unit square into itself must have a fixed point).<br />
<br />
In 2006, [[Yasuhito Tanaka]] proved another equivalence involving Hex. The no-draw property is equivalent to the [[Arrow impossibility theorem]].<br />
<br />
[[category:Theory]]</div>
Halladba
https://www.hexwiki.net/index.php/Hex_theory
Hex theory
2009-03-22T17:27:01Z
<p>Halladba: </p>
<hr />
<div>Unlike many other games, it is possible to say certain things about '''[[Hex]]''', with absolute certainty. Whether this makes Hex a [[why did you start playing Hex|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 />
== Winning Strategy ==<br />
<br />
* When the [[Swap rule|swap option]] is not used, the [[Red (player)|first player]] has a winning strategy.<br />
* When playing with the swap option, the second player has a winning strategy.<br />
<br />
These two statements come from the fact that without swap, Blue has no winning strategy and from the fact that draws are impossible in Hex.<br />
<br />
=== No winning strategy for Blue ===<br />
<br />
While 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 [[strategy-stealing argument|argument]] can show that the [[Blue (player)|second player]] certainly does not have a '''[[winning strategy]]''' from the [[starting position]]: <br />
<br />
=== No draw ===<br />
<br />
If a Hex board is full then there is one and only one player connecting their edges. See [[draw]].<br />
<br />
== [[Complexity]] ==<br />
<br />
* The decision problem associated to generalised Hex is '''PSPACE-complete'''.<br />
* The detection of [[dominated cell]]s is NP-complete. ('''To be checked''' then sourced)<br />
* The detection of the [[virtual connection]]s is PSPACE-complete. Reference [http://www.fmi.uni-stuttgart.de/szs/publications/info/kiefersn.Kie03.shtml here]<br />
<br />
== Solving Hex ==<br />
<br />
* Hex has been solved on [[small boards]].<br />
* The game can not end in a [[draw]]. ([http://javhar1.googlepages.com/hexcannotendinadraw Proofs] on [[Jack van Rijswijck|Javhar]]'s page)<br />
<br />
== See also ==<br />
<br />
[[Open problems]]<br />
<br />
== External links ==<br />
<br />
* [[Thomas Maarup]] masters [http://maarup.net/thomas/hex/ thesis]<br />
<br />
[[category:Theory]]</div>
Halladba
https://www.hexwiki.net/index.php/IgGameCenter
IgGameCenter
2009-03-16T07:30:40Z
<p>Halladba: wikification</p>
<hr />
<div>'''igGameCenter''' is a special on-line game gadget that allows playing abstract board games with other opponents in real-time directly from the site or from the Google Personalized Homepage.<br />
<br />
There are [http://www.iggamecenter.com/rules.html 76 games] available at igGameCenter at the moment and the number is growing all the time. Among the games there are 14 different [[Connection_game|connection games]] that can be played on igGameCenter in real-time:<br />
<br />
* [[Atoll]]<br />
* [[CrossWay]]<br />
* [[Gonnect]]<br />
* [[Havannah]]<br />
* [[Hex]]<br />
* [[Master Y]]<br />
* [[Metamorphosis]]<br />
* [[Mind Ninja]]<br />
* [[Quax]]<br />
* [[Pex]]<br />
* [[Twixt]]<br />
* [[Unlur]]<br />
* [[Y]]<br />
<br />
== Hex ==<br />
<br />
Hex can be played with various size and using the [[swap]] rule.<br />
<br />
== See also ==<br />
<br />
The creator of igg: [[user:Artyomch | Arty]].<br />
<br />
== External links ==<br />
<br />
* [http://www.iggamecenter.com/ igGameCenter]<br />
<br />
[[category:Hex community]]</div>
Halladba
https://www.hexwiki.net/index.php/Proverbs
Proverbs
2009-03-14T14:54:46Z
<p>Halladba: added a quotation</p>
<hr />
<div>== Proverbs about strategy ==<br />
In [[Go]], there are many proverbs about strategy. Since the strategic concepts are very related, one might check whether the proverbs also apply to [[Hex]].<br />
<br />
*[[Offense equals defense]], this is due to the no-[[draw]] property.<br />
*Consider playing in the "[[wrong direction]]", [[rope]]s make the board much easier to cross.<br />
*A player's position is only as good as its [[weakest link]].<br />
*Do not play an [[isolated piece]] with three or fewer liberties.<br />
<br />
== Quotations ==<br />
* According to Edward Lasker, a chess player,<br />
:''Chess is a game restricted to this world, Go has something extraterrestrial. If ever we find an extraterrestrial civilization that plays a game that we also play, it will be Go, without any doubt.''<br />
* [[Jack van Rijswijck]] goes beyond,<br />
: '''Hex has a Platonic existence, independent of human thought. If ever we find an extraterrestrial civilization at all, they will know Hex, without any doubt.''' (source [[Set Colouring Games]], 2006. Page 163)<br />
<br />
== External links ==<br />
* http://senseis.xmp.net/?GoProverbs<br />
* The [[Twixt]] [http://twixt.wetpaint.com/page/Maxims+for+moves proverbs] are also often relevant to Hex.<br />
<br />
[[category:strategy]]</div>
Halladba
https://www.hexwiki.net/index.php/Hex_Strategy_Making_the_Right_Connections
Hex Strategy Making the Right Connections
2009-03-13T11:28:09Z
<p>Halladba: basic info</p>
<hr />
<div>'''Hex Strategy: Making the Right Connections''' is book written by [[Cameron Browne]], published in 2000.<br />
<br />
The book is devoted to Hex and it covers with several aspects of the game. [[Theory]], [[Computer Hex]], [[Strategy]] among others.<br />
<br />
Although the [[opening]] chapter is not completely up to date as it deals mainly with non-swap Hex, the rest of the strategy advice is totally relevant. Cameron Browne used [[Richard Rognlie]]'s server and forum to sum up the advice of dozens of expert players.<br />
<br />
== External links==<br />
<br />
* Cameron Browne's [http://www.cameronius.com/ website]<br />
<br />
{{stub}}<br />
[[category:strategy]]<br />
[[category:Hex community]]</div>
Halladba
https://www.hexwiki.net/index.php/Edge_template_VI1a
Edge template VI1a
2009-03-10T23:35:53Z
<p>Halladba: /* Remaining possibilities for Blue */ cell links (new feature !)</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 />
[[#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>
Halladba
https://www.hexwiki.net/index.php/Template_VI1/Intrusion_on_the_3rd_row
Template VI1/Intrusion on the 3rd row
2009-03-10T23:25:53Z
<p>Halladba: back link to previous page</p>
<hr />
<div>This article deals with a special case in [[defending against intrusions in template VI1]], namely the intrusion on the 3rd that is not eliminated by [[sub-templates threat]]s.<br />
<br />
== Basic situation ==<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 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 [[#Third-row_followup:_i4|Pi4]] [[#Third-row_followup:_j3_(stub)|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 />
Pj4 Pl4<br />
Pj5<br />
</hex><br />
<br />
=== Figuring out the [[Must-play region]]===<br />
Red threatens to play at "+" points above, with these 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 />
Pk5<br />
Ph6 Pj6 Pk6 <br />
Pg7 Ph7 Pj7 Pk7<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 />
Bh5 Ri5 Bi4 Rk3 <br />
Rj5<br />
Pk4 Pj4<br />
Ph6 Pi6 Pj6 <br />
Pg7 Ph7 Pi7<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 />
Bh5 Ri5 Bi4 Rk3 <br />
Rj4<br />
Pj5<br />
Ph6 Pi6 Pj6 <br />
Pg7 Ph7 Pi7 Pj7<br />
</hex><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 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 />
Pj6<br />
Ph7<br />
</hex><br />
<br />
=== 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 />
=== 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 />
=== 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: 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 />
{{stub}}<br />
[[category:edge templates]]</div>
Halladba
https://www.hexwiki.net/index.php/Template_VI1
Template VI1
2009-03-10T23:20:45Z
<p>Halladba: redirect</p>
<hr />
<div>#REDIRECT [[Defending against intrusions in template VI1]]</div>
Halladba
https://www.hexwiki.net/index.php/Proverbs
Proverbs
2009-03-07T20:03:30Z
<p>Halladba: added a link to twixt</p>
<hr />
<div>In [[Go]], there are many proverbs about strategy. Since the strategic concepts are very related, one might check whether the proverbs also apply to [[Hex]].<br />
<br />
*[[Offense equals defense]], this is due to the no-[[draw]] property.<br />
*Consider playing in the "[[wrong direction]]", [[rope]]s make the board much easier to cross.<br />
*A player's position is only as good as its [[weakest link]].<br />
*Do not play an [[isolated piece]] with three or fewer liberties.<br />
== External links ==<br />
* http://senseis.xmp.net/?GoProverbs<br />
* The [[Twixt]] [http://twixt.wetpaint.com/page/Maxims+for+moves proverbs] are also often relevant to Hex.<br />
<br />
[[category:strategy]]</div>
Halladba
https://www.hexwiki.net/index.php/Template_VI1/Intrusion_on_the_3rd_row
Template VI1/Intrusion on the 3rd row
2009-03-07T07:08:33Z
<p>Halladba: /* Third-row followup: i4 */ reorganized a little bit</p>
<hr />
<div><hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 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 />
Pj4 Pl4<br />
Pj5<br />
</hex><br />
<br />
=== Figuring out the [[Must-play region]]===<br />
Red threatens to play at "+" points above, with these 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 />
Pk5<br />
Ph6 Pj6 Pk6 <br />
Pg7 Ph7 Pj7 Pk7<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 />
Bh5 Ri5 Bi4 Rk3 <br />
Rj5<br />
Pk4 Pj4<br />
Ph6 Pi6 Pj6 <br />
Pg7 Ph7 Pi7<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 />
Bh5 Ri5 Bi4 Rk3 <br />
Rj4<br />
Pj5<br />
Ph6 Pi6 Pj6 <br />
Pg7 Ph7 Pi7 Pj7<br />
</hex><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 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 />
Pj6<br />
Ph7<br />
</hex><br />
<br />
=== 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 />
=== 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 />
=== 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: 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 />
{{stub}}<br />
[[category:edge templates]]</div>
Halladba
https://www.hexwiki.net/index.php/Edge_template_VI1a
Edge template VI1a
2009-03-07T06:48:15Z
<p>Halladba: /* The remaining intrusion on the third row (stub) */ moved contents</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<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>
Halladba
https://www.hexwiki.net/index.php/Template_VI1/Intrusion_on_the_3rd_row
Template VI1/Intrusion on the 3rd row
2009-03-07T06:47:28Z
<p>Halladba: moved contents</p>
<hr />
<div><hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 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 />
{{stub}}<br />
[[category:edge templates]]</div>
Halladba
https://www.hexwiki.net/index.php/Hexgui
Hexgui
2009-03-04T14:42:20Z
<p>Halladba: redirect</p>
<hr />
<div>#REDIRECT [[HexGui]]</div>
Halladba
https://www.hexwiki.net/index.php/Claude_Berge%27s_puzzles
Claude Berge's puzzles
2009-03-04T10:50:59Z
<p>Halladba: /* Puzzle 4 */ corrected the puzzle (the former was a win for blue)</p>
<hr />
<div>Here are presented a couple of puzzles designed by [[Claude Berge]]. Their respective solutions can be found [[Solutions to Claude Berge's puzzles|here]]. <br />
<br />
== Puzzles ==<br />
=== Puzzle 1 ===<br />
[[Blue]] to move and win.<br />
<hex>R5 C5<br />
Ha1<br />
Vb2 Hd2 Ve2<br />
Vc3 Hd3 Ve3<br />
Hc4<br />
Va5 Hb5<br />
</hex><br />
<br />
=== Puzzle 2 ===<br />
Blue to move and win.<br />
<hex>R5 C5<br />
Va2<br />
Ha3 Vb3 Hc3<br />
Vb4<br />
Ha5<br />
</hex><br />
<br />
=== Puzzle 3 ===<br />
Not posted yet...<br />
=== Puzzle 4 ===<br />
Red to move and win.<br />
<br />
<hex>R14 C14 Q1<br />
Hh1 Hk1<br />
Vf2 Vg2 Hh2 Hj2 Vl2<br />
Vg3 Hh3 Hk3 Vl3<br />
Vg4 Hi4 Vl4<br />
Vg5 Hj5 Vl5<br />
Vg6 Hh6 Hk6 Vl6<br />
Vg7 Hi7 Vl7<br />
Vg8 Hj8 Vl8<br />
Vg9 Hh9 Hk9 Vl9<br />
Vg10 Hi10 Vl10<br />
Vg11 Hj11 Vm11<br />
Hg12 Hh12 Vi12 Hk12 Vn12<br />
He13 Hi13 Hl13 <br />
Ha14 Hb14 Hc14 Hd14 Hg14 Hi14 Hl14 Hm14 Hn14</hex><br />
<br />
=== Puzzle 5 ===<br />
Not posted yet...<br />
<br />
== References ==<br />
The puzzles are taken from:<br />
<br />
* Claude Berge. L'Art Subtil du Hex. Manuscript, 1977.<br />
<br />
via<br />
<br />
* [[Jack van Rijswijck]]. Set Colouring Games, 2006.<br />
== See also ==<br />
<br />
* Main article: [[Puzzles]]<br />
* [[Solutions to Claude Berge's Puzzles|Solutions]]<br />
<br />
[[category:Puzzle]]</div>
Halladba
https://www.hexwiki.net/index.php/Hex_Bibliography
Hex Bibliography
2009-03-03T23:29:10Z
<p>Halladba: thomas maarup's thesis +categories</p>
<hr />
<div>Depending on the topic, you may find useful the following books and articles.<br />
<br />
== General ==<br />
*[[Thomas Maarup]]'s Master Thesis: [http://maarup.net/thomas/hex/ Everything You Ever Wanted to Know About Hex But Were Afraid to Ask]. University of Southern Denmark, 2005.<br />
== Theory ==<br />
== Strategy ==<br />
<br />
[[Cameron Browne]]. [[Hex Strategy Making the Right Connections]]. AK Peters; 1st edition (May 30, 2000). ISBN-13: 978-1568811178<br />
<br />
== Computer Hex ==<br />
== Other ==<br />
<br />
{{stub}}<br />
[[category:Hex community]]<br />
[[category:Computer Hex]]</div>
Halladba
https://www.hexwiki.net/index.php/User_talk:Halladba
User talk:Halladba
2009-03-03T21:19:42Z
<p>Halladba: </p>
<hr />
<div>Hi Halladba, I see you asked Gregorio about the hex tournament. Here it is the link:<br />
<br />
http://spainhex.blogspot.com/<br />
<br />
you can find participants and classifications. Gregorio will add more sometime :)<br />
<br />
I really liked your page on Y corner templates. &mdash; [[User:Turing|turing]]<br />
<br />
oh, yes, sorry :-) --[[User:Gregorio|Gregorio]] 20:00, 4 January 2009 (CET)<br />
<br />
<br />
Hi, Halladba, I just read your article "Utilisation d’UCT au Hex". Very nice and enlightening, by the way. I have one question regarding the layout... how did you typeset the diagrams and symbols inside? Was it "handmade" or using some script or program? --[[User:Gregorio|Gregorio]] 13:19, 3 March 2009 (CET)<br />
: Hi, thanks for the comment. Unfortunately I handmade the diagrams using xfig, it was fairly quick once I had the primitives (cells, board), but still handmade... [[User:Halladba|Halladba]] 22:19, 3 March 2009 (CET)</div>
Halladba
https://www.hexwiki.net/index.php/Talk:Edge_template_VI1a
Talk:Edge template VI1a
2009-03-02T15:02:31Z
<p>Halladba: </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)</div>
Halladba
https://www.hexwiki.net/index.php/Edge_template_VI1a
Edge template VI1a
2009-03-01T21:51:48Z
<p>Halladba: moved contents</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 />
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>
Halladba
https://www.hexwiki.net/index.php/Template_VI1/Intrusion_on_the_4th_row
Template VI1/Intrusion on the 4th row
2009-03-01T21:50:54Z
<p>Halladba: moved from template VI</p>
<hr />
<div>This page is devoted to details on how to [[Defending against intrusions in template VI1|defend against intrusions in template VI]]. This page explores what are the possibilities for Red to defend the template when Blue intrude on the 4th row.<br />
<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 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 />
<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 />
[[category:edge templates]]</div>
Halladba
https://www.hexwiki.net/index.php/Hex_theory
Hex theory
2009-02-26T22:15:03Z
<p>Halladba: /* Complexity */ added about the virtual connections being PSPACE complete</p>
<hr />
<div>Unlike many other games, it is possible to say certain things about '''[[Hex]]''', with absolute certainty. Whether this makes Hex a [[why did you start playing Hex|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 />
== Winning Strategy ==<br />
<br />
While 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 [[strategy-stealing argument|argument]] can show that the [[Blue (player)|second player]] certainly does not have a '''[[winning strategy]]''' from the [[starting position]]: <br />
<br />
* When the [[Swap rule|swap option]] is not used, the [[Red (player)|first player]] has a winning strategy.<br />
* When playing with the swap option, the second player has a winning strategy.<br />
<br />
== [[Complexity]] ==<br />
<br />
* The decision problem associated to generalised Hex is '''PSPACE-complete'''.<br />
* The detection of [[dominated cell]]s is NP-complete. ('''To be checked''' then sourced)<br />
* The detection of the [[virtual connection]]s is PSPACE-complete. Reference [http://www.fmi.uni-stuttgart.de/szs/publications/info/kiefersn.Kie03.shtml here]<br />
<br />
== Solving Hex ==<br />
<br />
* Hex has been solved on [[small boards]].<br />
* The game can not end in a [[draw]]. ([http://javhar1.googlepages.com/hexcannotendinadraw Proofs] on [[Jack van Rijswijck|Javhar]]'s page)<br />
<br />
== See also ==<br />
<br />
[[Open problems]]<br />
<br />
== External links ==<br />
<br />
* [[Thomas Maarup]] masters [http://maarup.net/thomas/hex/ thesis]<br />
<br />
[[category:Theory]]</div>
Halladba
https://www.hexwiki.net/index.php/Opening
Opening
2009-02-05T08:54:39Z
<p>Halladba: /* Swapping */</p>
<hr />
<div>The '''opening''' is the first few moves of a [[Hex]] game. Exactly how many moves are considered part of the opening varies depending on the type of opening, and also on whom you ask. Typically, however, the two first moves are always considered part of the opening.<br />
<br />
== Opening Theory ==<br />
<br />
The two most basic questions in the opening theory of Hex are:<br />
<br />
* Where should I play my first move?<br />
* Should I [[swap]]?<br />
<br />
The two questions are closely related. The situation is probably most difficult for the [[first player]] &mdash; his move should not be too strong, since the [[second player]] then will [[swap]], but it should not be too weak either, as the second player then will decline the swap and have [[Advantage|a better situation]]. So the first player has to find a move which gives about equal chances to both players.<br />
<br />
=== The first move ===<br />
<br />
Fortunately strong players have thought thoroughly through this, and there are certain moves that are considered to be about equal, which one can safely play. For example are a2, a3 and b2 quite common opening moves.<br />
<br />
But these moves are only suggestions, and there are many other moves that may be tried such as a4, a8, a6 or a10 (on a 10 &times; 10 board).<br />
<br />
=== Swapping ===<br />
<br />
When to swap? One commonly used rule of thumb is to swap any opening, except if the first move was played on the [[first row]], adjacent to a [[friendly edge]], and not in the [[obtuse corner]]. You may also check out winning opening moves for [[small boards]].<br />
<br />
[[Swap|Detailled article : Swap]]<br />
<br />
== External link==<br />
<br />
[http://www.f.kth.se/~rydh/Hex/openings.html Jonatan Rydh's page on openings]<br />
<br />
== Openings deserving their own articles ==<br />
<br />
* [[A2 opening]]<br />
* [[A3 opening]]<br />
* [[B2 opening]]<br />
* [[Center opening]]<br />
* [[A1 opening]]<br />
* [[Obtuse corner opening]]<br />
* [[The Hungarian (opening)]]<br />
<br />
[[category:opening]]</div>
Halladba
https://www.hexwiki.net/index.php/Tournaments
Tournaments
2009-02-02T10:54:50Z
<p>Halladba: added about 2009</p>
<hr />
<div>==International Tournament 2009 in Granollers (Spain) 2009==<br />
<br />
More info [http://www.littlegolem.net/jsp/forum/topic2.jsp?forum=50&topic=353 here].<br />
<br />
==Second Spanish Hex 13x13 Online Championship in Little Golem==<br />
<br />
The Second Spanish Championship will start February 2008, the 15th. More info at [http://spainhex.blogspot.com/ its blog].<br />
<br />
== 8th Mind Sports Olympiad in Prague ==<br />
<br />
The event will be held from September 27th to October 5th in Prague. <br />
[http://www.deskohrani.cz/cgi/mso/index.pl?telo=propozice.pl&text=uvod.htm&turnaj=oly&hra=hxx&jazyk=en&rok=2008 Hex] might be played depending on the number of participants:<br />
<br />
==Spanish Hex 13x13 Online Championship in Little Golem==<br />
<br />
The first Spanish Championship started in January 2008, and it was played in [[Little Golem]] in a Round Robin (divided in groups). The winner was [[José María Grau Ribas]], [[user:Gregorio|Gregorio Morales]] finished second while José Ignacio Úbeda ended third. More info at [http://spainhex.blogspot.com/ its blog].<br />
<br />
==International Tournament 2006 in Oslo==<br />
<br />
Took place on August 11th - 13th 2006. Photos and results can be found on [http://www.littlegolem.net/jsp/forum/topic2.jsp?forum=50&topic=244 littlegolem].<br />
<br />
==International Tournament 2005 in Wrocław==<br />
<br />
The first international Hex tournament was held in May 2005 in Wrocław, [[Poland]].<br />
<br />
Here is some information:<br />
* a [http://masak.org/carl/wroclaw/ blog with results]<br />
* a page with [http://www.photos-wroclaw.prv.pl/ photos from the event]<br />
<br />
==Online Team Tournament in 2003==<br />
<br />
[[Team Tournament 1]]<br />
<br />
==See also==<br />
[[ICGA]]<br />
<br />
[[category: hex community]]<br />
[[category: History]]</div>
Halladba
https://www.hexwiki.net/index.php/Talk:Edge_template_VI1a
Talk:Edge template VI1a
2009-01-14T14:10:04Z
<p>Halladba: question to everybody</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)</div>
Halladba
https://www.hexwiki.net/index.php/Edge_template_VI1a
Edge template VI1a
2009-01-14T14:02:06Z
<p>Halladba: /* Specific defence */ one sub-defence less</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 discared 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 />
[[category:edge templates]]<br />
[[category:theory]]</div>
Halladba
https://www.hexwiki.net/index.php/Edge_template_VI1a
Edge template VI1a
2009-01-14T13:09:38Z
<p>Halladba: /* The remaining intrusion on the fourth row */ eliminated two blue answers (one explicitly, the other with template III1b)</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 discared 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 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 />
===== 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 />
[[category:edge templates]]<br />
[[category:theory]]</div>
Halladba
https://www.hexwiki.net/index.php/Edge_template_VI1a
Edge template VI1a
2009-01-13T10:50:15Z
<p>Halladba: moved the part, and rewritten a few of things</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 discared 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 />
===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 />
[[category:edge templates]]<br />
[[category:theory]]</div>
Halladba
https://www.hexwiki.net/index.php/Sixth_row_template_problem
Sixth row template problem
2009-01-13T10:24:49Z
<p>Halladba: moved some part of the article to another one</p>
<hr />
<div>As of January 2009 the following problem, initially stated by javerberg and wccanard in the LG forum, is still [[open problems|open]]:<br />
<br />
Is there a one stone sixth row [[template]] that uses no stones higher than the sixth row?<br />
<br />
More generally, it is still unknown whether one stone edge templates that use no cell higher than the initial stone) can be found for all heights. Such [[Edge templates with one stone|templates]] have been found for sizes up to 5 but none above. Answering with "No" to the former question answers the latter.<br />
<br />
== Description ==<br />
<br />
Is there a number m such that the game on the board of width m designed as follows, with Blue's turn to play, is won by Red ?<br />
<br />
<hex> R7 C11<br />
1:HHHHHVHHHHH<br />
2:_____V_____<br />
</hex><br />
<br />
== Generalisation ==<br />
<br />
The general problem of knowing if there is n such that there is no one stone edge template on the n^th row<math>n^th</math> is also referred to as the n-th row template problem.<br />
<br />
== Possible paths to answer ==<br />
===By "hand"...===<br />
====...answering "Yes" ====<br />
This would involve placing a stone on the 6th row of a sufficiently wide board, and showing how to always connect to the bottom. (Note this does not necessarily identify the minimal template needed.) <br />
<br />
See [[defending against intrusions in template VI1]] for complete proof.<br />
====6th row template====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 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 />
====...answering "No" ====<br />
This would involve showing how to connect (in the diagram above) the Blue stones to the right (plus Blue stones on the far right edge) to Blue stones on the left (plus Blue stones on the far left edge), no matter how wide the board is.<br />
<br />
=== Computer Aided demonstration ... ===<br />
==== ... answering "Yes" ====<br />
Such a proof would use the computer to find the template and it's [[carrier]]. Afterwards it should be easy to manually check that every Blue intrusion does not prevent Red from connecting to bottom.<br />
<br />
==== ... answering "No" ====<br />
TODO<br />
<br />
== See Also ==<br />
* [[Theory]]<br />
* [[User:Wccanard|Wccanard]]<br />
<br />
== External link ==<br />
<br />
* The [http://www.littlegolem.net/jsp/forum/topic2.jsp?forum=50&topic=339 thread] were the names were associated.<br />
<br />
[[category:theory]]<br />
[[category:templates]]</div>
Halladba
https://www.hexwiki.net/index.php/Edge_template_VI2a
Edge template VI2a
2009-01-13T10:13:10Z
<p>Halladba: stubbed</p>
<hr />
<div>== The edge template template VI2 ==<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3</hex><br />
<br />
Let us first see what possibilities [[Red (player)|Red]] has if he moves first.<br />
<br />
There are two obvious options:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Vf3 Pa6 Pb5 Pb6 Pc4 Pc5 Pc6 Pd4 Pd5 Pd6 Pe3 Pe4 Pe5 Pe6 Pf2 Pf4 Pf5 Pf6 Pg2 Pg4 Pg5 Pg6</hex><br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Vg3 Pc6 Pd5 Pd6 Pe4 Pe5 Pe6 Pf4 Pf5 Pf6 Pg4 Pg5 Pg6 Ph3 Ph4 Ph5 Ph6 Pi4 Pi5 Pi6 Pg2 Ph2</hex><br />
<br />
In both diagrams the possible [[Template intrusion|intrusion]] points are marked by (+). So we only have to consider the [[Overlapping templates|intersection of the intrusion points]]. They are:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Pc6 Pd5 Pd6 Pe4 Pe5 Pe6 Pf4 Pf5 Pf6 Pg4 Pg5 Pg6 Pg2</hex><br />
<br />
''More on this later...''<br />
<br />
[[Category:Edge templates]]<br />
{{stub}}</div>
Halladba
https://www.hexwiki.net/index.php/Sixth_row_template_problem
Sixth row template problem
2009-01-12T21:33:40Z
<p>Halladba: "</hex> " was written twice, removed it once</p>
<hr />
<div>As of January 2009 the following problem, initially stated by javerberg and wccanard in the LG forum, is still [[open problems|open]]:<br />
<br />
Is there a one stone sixth row [[template]] that uses no stones higher than the sixth row?<br />
<br />
More generally, it is still unknown whether one stone edge templates that use no cell higher than the initial stone) can be found for all heights. Such [[Edge templates with one stone|templates]] have been found for sizes up to 5 but none above. Answering with "No" to the former question answers the latter.<br />
<br />
== Description ==<br />
<br />
Is there a number m such that the game on the board of width m designed as follows, with Blue's turn to play, is won by Red ?<br />
<br />
<hex> R7 C11<br />
1:HHHHHVHHHHH<br />
2:_____V_____<br />
</hex><br />
<br />
== Generalisation ==<br />
<br />
The general problem of knowing if there is n such that there is no one stone edge template on the n^th row<math>n^th</math> is also referred to as the n-th row template problem.<br />
<br />
== Possible paths to answer ==<br />
===By "hand"...===<br />
====...answering "Yes" ====<br />
This would involve placing a stone on the 6th row of a sufficiently wide board, and showing how to always connect to the bottom. (Note this does not necessarily identify the minimal template needed.) <br />
<br />
Here is a start. Just from [[edge template IV1a]] and [[edge template IV1b]], Blue's first move must be one of the following:<br />
<hex><br />
R7 C19 Q0<br />
1:BBBBBBBBBRBBBBBBBBB<br />
Rj2<br />
Si3 Sj3<br />
Si4<br />
Sg5 Sh5 Si5 Sj5 <br />
Sf6 Sg6 Si6 Sj6<br />
Se7 Sf7 Sg7 Sh7 Si7 Sj7<br />
</hex><br />
Many of these moves will be easy to dismiss. Others will benefit from 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 C19 Q0<br />
1:BBBBBBBBBRBBBBBBBBB<br />
Rj2<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 C19 Q0<br />
1:BBBBBBBBBRBBBBBBBBB<br />
Rj2<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 />
====6th row template====<br />
<hex><br />
R7 C14 Q0<br />
1:BBBBBBBBBRBBBBB<br />
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 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 />
====...answering "No" ====<br />
This would involve showing how to connect (in the diagram above) the Blue stones to the right (plus Blue stones on the far right edge) to Blue stones on the left (plus Blue stones on the far left edge), no matter how wide the board is.<br />
<br />
=== Computer Aided demonstration ... ===<br />
==== ... answering "Yes" ====<br />
Such a proof would use the computer to find the template and it's [[carrier]]. Afterwards it should be easy to manually check that every Blue intrusion does not prevent Red from connecting to bottom.<br />
<br />
==== ... answering "No" ====<br />
TODO<br />
<br />
== See Also ==<br />
* [[Theory]]<br />
* [[User:Wccanard|Wccanard]]<br />
<br />
== External link ==<br />
<br />
* The [http://www.littlegolem.net/jsp/forum/topic2.jsp?forum=50&topic=339 thread] were the names were associated.<br />
<br />
[[category:theory]]<br />
[[category:templates]]<br />
{{stub}}</div>
Halladba
https://www.hexwiki.net/index.php/Sixth_row_template_problem
Sixth row template problem
2009-01-10T19:17:03Z
<p>Halladba: added a sentence regarding upper cells in intro.</p>
<hr />
<div>As of January 2009 the following problem, initially stated by javerberg and wccanard in the LG forum, is still [[open problems|open]]:<br />
<br />
Is there any one stone sixth row [[template]] ?<br />
<br />
More generally, it is still unknown whether one stone edge templates (which carrier has not cell upper than the stone) can be found for every heights. Such [[Edge templates with one stone|templates]] have been found for sizes up to 5 but none above. Answering with "No" to the former question answers the latter.<br />
<br />
== Description ==<br />
<br />
Is there a number m such that the game on the board of width m designed as follows, with Blue's turn to play, is won by Red ?<br />
<br />
<hex> R7 C11<br />
1:HHHHHVHHHHH<br />
2:_____V_____<br />
</hex><br />
<br />
== Generalisation ==<br />
<br />
The general problem of knowing if there is n such that there is no one stone edge template on the n^th row<math>n^th</math> is also referred to as the n-th row template problem.<br />
<br />
== Possible paths to answer ==<br />
===By "hand"...===<br />
====...answering "Yes" ====<br />
This would involve placing a stone on the 6th row of a sufficiently wide board, and showing how to always connect to the bottom. (Note this does not necessarily identify the minimal template needed.) <br />
<br />
Here is a start. Just from [[edge template IV1a]] and [[edge template IV1b]], Blue's first move must be one of the following:<br />
<hex><br />
R7 C19 Q0<br />
1:BBBBBBBBBRBBBBBBBBB<br />
Rj2<br />
Si3 Sj3<br />
Si4<br />
Sg5 Sh5 Si5 Sj5 <br />
Sf6 Sg6 Si6 Sj6<br />
Se7 Sf7 Sg7 Sh7 Si7 Sj7<br />
</hex><br />
Many of these moves will be easy to dismiss. Others will benefit from 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 C19 Q0<br />
1:BBBBBBBBBRBBBBBBBBB<br />
Rj2<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 C19 Q0<br />
1:BBBBBBBBBRBBBBBBBBB<br />
Rj2<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 />
====...answering "No" ====<br />
This would involve showing how to connect (in the diagram above) the Blue stones to the right (plus Blue stones on the far right edge) to Blue stones on the left (plus Blue stones on the far left edge), no matter how wide the board is.<br />
<br />
=== Computer Aided demonstration ... ===<br />
==== ... answering "Yes" ====<br />
Such a proof would use the computer to find the template and it's [[carrier]]. Afterwards it should be easy to manually check that every Blue intrusion does not prevent Red from connecting to bottom.<br />
<br />
==== ... answering "No" ====<br />
TODO<br />
<br />
== See Also ==<br />
* [[Theory]]<br />
* [[User:Wccanard|Wccanard]]<br />
<br />
== External link ==<br />
<br />
* The [http://www.littlegolem.net/jsp/forum/topic2.jsp?forum=50&topic=339 thread] were the names were associated.<br />
<br />
[[category:theory]]<br />
[[category:templates]]<br />
{{stub}}</div>
Halladba
https://www.hexwiki.net/index.php/Sixth_row_template_problem
Sixth row template problem
2009-01-10T07:54:29Z
<p>Halladba: /* ...answering "Yes" */ edge template IV1b removes one cell</p>
<hr />
<div>As of January 2009 the following problem is still [[open problems|open]]. '''Javerberg-Wccanard Problem''' is simply put as follow.<br />
<br />
Is there any one stone sixth row [[template]] ?<br />
<br />
It is still unknown whether one stone edge templates can be found for every heights. Such [[Edge templates with one stone|templates]] have been found for sizes up to 5 but none above. Answering with "No" to the former question answers the latter.<br />
<br />
== Description ==<br />
<br />
Is there a width n such that the game on the board of width n designed as follow with turn to Blue is won by Red ?<br />
<br />
<hex> R7 C11<br />
1:HHHHHVHHHHH<br />
2:_____V_____<br />
</hex><br />
<br />
== Generalisation ==<br />
<br />
The general problem of knowing if there is n such that there is no one stone edge template on the n^th row<math>n^th</math> is also referred to as '''Javerberg-Wccanard Problem'''.<br />
<br />
== Possible paths to answer ==<br />
===By "hand"...===<br />
====...answering "Yes" ====<br />
This would involve placing a stone on the 6th row of a sufficiently wide board, and showing how to always connect to the bottom. (Note this does not necessarily identify the minimal template needed.) <br />
<br />
Here is a start. Just from [[edge template IV1a]] and [[edge template IV1b]], Blue's first move must be one of the following:<br />
<hex><br />
R7 C19 Q0<br />
1:BBBBBBBBBRBBBBBBBBB<br />
Rj2<br />
Si3 Sj3<br />
Si4<br />
Sg5 Sh5 Si5 Sj5 <br />
Sf6 Sg6 Si6 Sj6<br />
Se7 Sf7 Sg7 Sh7 Si7 Sj7<br />
</hex><br />
Many of these moves will be easy to dismiss. Others will benefit from the [[Parallel ladder]] trick. Of course, symmetry will cut our work in half!<br />
<br />
====...answering "No" ====<br />
This would involve showing how to connect (in the diagram above) the Blue stones to the right (plus Blue stones on the far right edge) to Blue stones on the left (plus Blue stones on the far left edge), no matter how wide the board is.<br />
<br />
=== Computer Aided demonstration ... ===<br />
==== ... answering "Yes" ====<br />
Such a proof would use the computer to find the template and it's [[carrier]]. Afterwards it should be easy to manually check that every Blue intrusion does not prevent Red from connecting to bottom.<br />
<br />
==== ... answering "No" ====<br />
TODO<br />
<br />
== See Also ==<br />
* [[Theory]]<br />
* [[User:Wccanard|Wccanard]]<br />
<br />
== External link ==<br />
<br />
* The [http://www.littlegolem.net/jsp/forum/topic2.jsp?forum=50&topic=339 thread] were the names were associated.<br />
<br />
[[category:theory]]<br />
[[category:templates]]<br />
{{stub}}</div>
Halladba
https://www.hexwiki.net/index.php/Bill_LeBoeuf_vs._Universidad_de_Oviedo
Bill LeBoeuf vs. Universidad de Oviedo
2009-01-07T19:52:03Z
<p>Halladba: headings and source, too lazy to add the game</p>
<hr />
<div>== Game information ==<br />
* Size: 13x13<br />
* Red: Bill LeBoeuf<br />
* Blue: Universidad de Oviedo<br />
* Date: from 09-10-2003 to 30-11-2003<br />
* Result: 1-0 (Red won)<br />
* Comments: Bill LeBoeuf<br />
* Note: [[Turn-based]] game<br />
<br />
== Moves and comments ==<br />
<br />
TODO<br />
<br />
== Source ==<br />
<br />
* Comments : this [[Little Golem]] forum [http://www.littlegolem.net/jsp/forum/topic2.jsp?forum=50&topic=53 thread].<br />
<br />
* Game : this [http://www.littlegolem.net/jsp/game/game.jsp?gid=90921 game] on LG.<br />
<br />
{{stub}}<br />
[[category:Game record]]</div>
Halladba
https://www.hexwiki.net/index.php/Commented_games
Commented games
2009-01-07T19:41:29Z
<p>Halladba: added link to a game by Bill LeBoeuf</p>
<hr />
<div>The best ways for getting better at Hex are to learn strategies, solve problems and to replay games of stronger players. The following collection of games are intended to help you get stronger.<br />
<br />
{| class="wikitable" border="1" cellpadding="2" cellspacing="0"<br />
|-<br />
! Game !! Commented by !! Intended audience<br />
|-<br />
| [[Roland Illig vs. Six 0.5.3, 2007-09-28]] || Nobody yet || ---<br />
|-<br />
| [[Glenn C. Rhoads vs. unknown]] || [[Glenn C. Rhoads]] || advanced<br />
|-<br />
| [[V vs. H game 1|Vertical vs. Horizontal]] || David Boll || ---<br />
|-<br />
| [[Bill LeBoeuf vs. Universidad de Oviedo]] || Bill LeBoeuf || ---<br />
|}<br />
<br />
Remarks:<br />
* The '''Game''' should be a link to the commented game.<br />
* The '''Commented by''' field should contain the name of the person who did the commentary.<br />
* The '''Intended audience''' can be ''beginners'', ''advanced'', ''experts'', whatever.<br />
<br />
[[category:Game record]]</div>
Halladba