Solutions to puzzles - Revision history

Hexanna: typo

2024-08-25T14:12:50Z

typo

Selinger: table -> trapezoid

2024-02-14T23:41:51Z

table -> trapezoid

Demer: /* Puzzle 5 */ fixed wrong cells

2024-02-12T06:38:50Z

‎Puzzle 5: fixed wrong cells

Demer: /* Puzzle 5 */ changed phrasing to correspond to who's turn it is

2024-02-12T06:31:26Z

‎Puzzle 5: changed phrasing to correspond to who's turn it is

Demer: /* Puzzle 5 */ put up solution for puzzle 5

2024-02-06T06:38:18Z

‎Puzzle 5: put up solution for puzzle 5

Demer: Undo revision 8425 by Demer (talk)

2024-02-06T06:37:32Z

Undo revision 8425 by Demer (talk)

Demer: /* Puzzle 5 */ put up solution for puzzle 4

2024-02-06T06:33:41Z

‎Puzzle 5: put up solution for puzzle 4

Demer: /* Puzzle 4 */ fixed typo

2024-01-31T22:26:54Z

‎Puzzle 4: fixed typo

Demer: /* Puzzle 4 */ fixed wrong cell

2024-01-22T05:08:12Z

‎Puzzle 4: fixed wrong cell

Selinger: /* Puzzle 4 */ Fixed a link and a typo

2024-01-22T01:19:48Z

‎Puzzle 4: Fixed a link and a typo

@@ Line 106: / Line 106: @@
 The rest of this paragraph uses [[edge template III2a]] extensively, and so we do not mention it each time it's used.  If Red plays a5 or b4, then Blue plays b3, winning via d3 or e1.  If Red plays a4, then Blue plays c4, connecting left via a3 or a5.  a3 is Red's winning move.  If Red plays b3, then Blue plays c2, connecting left via a3 or b4.  If Red plays c2, then Blue plays c4, winning.
-Red's only remaining try is e4.  Blue responds with c4.  After that, consider [[edge template III2a]] to the left edge.
+Red's only remaining try is e2.  Blue responds with c4.  After that, consider [[edge template III2a]] to the left edge.
 <hexboard size="5x5"

@@ Line 507: / Line 507: @@
 If Blue plays in {a2,b1,b2,c1,d1}, then Red plays c2.  This connects to the top with d1 or c1 or b2, and connects down with a [[Interior template#The box|box]].
-If Blue plays c2, then Red plays d2.  This connects down with a [[Interior template#The mouth or trapezoid|table]], and connects to the top with d1 or a3, since a3 forms [[Edge template III2d]].
+If Blue plays c2, then Red plays d2.  This connects down with a [[trapezoid]], and connects to the top with d1 or a3, since a3 forms [[Edge template III2d]].
 If Blue plays d2, then Red plays c3.  This has a bridge down, and connects to the top for the same reason as without the a5-b4 exchange.

@@ Line 521: / Line 521: @@
 Against that, Red plays    5. c4  .
-This threatens c2, which would connect to the top via d1 or c1 or b2, so Blue must respond in {c2,c3,b3}.  If Blue plays c2 or c3, then Red plays a3, winning with [[Edge template III2d]].  Thus Blue plays b3 instead.  Red responds with d2, connecting down via c4 or e4, and connecting to the top because a1 escapes the ladder.
+This threatens c2, which would connect to the top via d1 or c1 or b2, so Blue must respond in {c2,c3,b3}.  If Blue plays c2 or c3, then Red plays a3, winning with [[Edge template III2d]].  Thus Blue plays b3 instead.  Red responds with d2, connecting down via c3 or e3, and connecting to the top because a1 escapes the ladder.
 Therefore  1. b4  does win for Red.

@@ Line 463: / Line 463: @@
    />
-Blue must continue with c3, and what's left of this case is checking that e2 connects down no matter which of the above shaded cells was Blue's first move.  If that move was neither d3 nor e3, then Red bridges to d4, and connects down with c4 or c5 or d5.  Otherwise, Red plays whichever of d3,e3 Blue didn't play.  Since Red has a5 and b4, b5 is [[Dead cell|dead]], so Red ladders to b4.
+Blue must continue with c3, and what's left of this case is checking that Red can connect e2 down no matter which of the above shaded cells was Blue's first move.  If that move was neither d3 nor e3, then Red bridges to d4, and connects down with c4 or c5 or d5.  Otherwise, Red plays whichever of d3,e3 Blue didn't play.  Since Red has a5 and b4, b5 is [[Dead cell|dead]], so Red ladders to b4.
 If Blue plays d4, then Red plays c4, capturing a5 and c5.  This threatens c2, which would connect to the top via d1 or c1 or b2, so Blue must respond in {c2,c3,b3}.  If Blue plays c2 or c3, then Red plays a3, winning with [[Edge template III2d]].  If Blue plays b3, then Red plays d2, bridging from c4 and laddering to a1.

@@ Line 443: / Line 443: @@
    />
-This leaves b4 as the only possible move for Red. Indeed b4 is winning. We leave the verification of this to be done later.
+This leaves b4 as the only possible move for Red.
 === Puzzle 6 ===

@@ Line 443: / Line 443: @@
    />
-This leaves b4 as the only possible move for Red.
+This leaves b4 as the only possible move for Red. Indeed b4 is winning. We leave the verification of this to be done later.
-−
-Showing that b4 wins for Red:
-−
-<hexboard size="5x5"
-  contents="R e2 a1 1:b4 B b5 e1"
-  />
-−
-If Blue plays to the upper-left of the [[short diagonal]] ''other than'' in {c2,b3}, then Red responds with c2 and defends the bridge.  c2 connects to the top via d1 or c1 or b2, and connects to the bottom with a very short [[switchback]].
-−
-<hexboard size="5x5"
-  contents="R e2 a1 1:b4 3:c2 5:b3 7:d4 9:d2 B b5 e1 2:a3 4:c3 6:a5 8:c4"
-  />
-−
-If Blue plays to the lower-right of the [[short diagonal]] ''other than'' at d4, then Red plays a5.  This threatens c2, which would connect to the top via d1 or c1 or b2, so Blue must respond in {c2,c3,b3}.  If Blue plays c2 or c3, then Red plays a3, winning with [[Edge template III2d]].  Thus Blue plays b3 instead.  Red responds with d2, and a1 escapes that ladder.
-−
-<hexboard size="5x5"
-  contents="R e2 a1 1:b4 3:a5 B b5 e1 S blue:(d3 e3 e4 e5 d5 c5 c4)"
-  />
-−
-Blue must continue with c3, and what's left of this case is checking that e2 connects down no matter which of the above shaded cells was Blue's first move.  If that move was neither d3 nor e3, then Red bridges to d4, and connects down with c4 or c5 or d5.  Otherwise, Red plays whichever of d3,e3 Blue didn't play.  Since Red has a5 and b4, b5 is [[Dead cell|dead]], so Red ladders to b4.
-−
-If Blue plays d4, then Red plays c4, capturing a5 and c5.  This threatens c2, which would connect to the top via d1 or c1 or b2, so Blue must respond in {c2,c3,b3}.  If Blue plays c2 or c3, then Red plays a3, winning with [[Edge template III2d]].  If Blue plays b3, then Red plays d2, bridging from c4 and laddering to a1.
-−
-This leaves the following tries for Blue.
-−
-<hexboard size="5x5"
-  contents="R e2 a1 1:b4 B b5 e1 S d2 c2 c3 b3 a5"
-  />
-−
-c2 loses to a3, using [[Edge template III2d]]
-−
-<hexboard size="5x5"
-  contents="R e2 a1 1:b4 3:a3 5:d4 7:d2 B b5 e1 2:c2 4:a5 6:c4"
-  />
-−
-and a [[switchback]], as shown above.
-−
-If Blue plays b3, then Red plays d2, and a1 escapes that ladder.  Towards the bottom, if Blue plays outside of {c4,c3,d3}, then Red can play c4 and defend the bridge from d2, and if Blue plays outside of {d4,d5,c5}, then Red can play d4 and defend the c5+d5 [[Captured cell|capture]].
-−
-<hexboard size="5x5"
-  contents="R e2 a1 1:b4 3:d2 B b5 e1 2:b3"
-  />
-−
-In the former case, Red connects down with a5 or c5 or e4.  In the latter case, Red connects down with e3 or d3 or c3, since c3 threatens c4 and a5.  The sets {c4,c3,d3} and {d4,d5,c5} are disjoint, so Red gets at least one of those, and thereby connects down for a win.
-−
-If Blue plays c3, then Red plays d4, capturing e2 and b4 to the bottom.  Blue must respond in {d2,c2,b3}, since otherwise Red plays c2, connecting down with d2 or b3 and connecting to the top with d1 or c1 or b2.  If Blue plays d2 or c2, then Red plays a3, winning with [[Edge template III2d]].  If Blue plays b3, then Red plays d2, and wins by laddering to a1.
-−
-If Blue plays d2, then Red plays c3, connecting down with a5 or d4.  Towards the top, blue c2 loses to a3, forming [[Edge template III2d]], and Blue's other moves all lose to red c2, connecting with d1 or c1 or b2.
-−
-Blue's only remaining try is a5.  Red responds to that with d4, [[Captured cell|capturing]] c5 and d5.
-−
-<hexboard size="5x5"
-  contents="R e2 a1 1:b4 3:d4 c5 d5 B b5 e1 2:a5"
-  />
-−
-Red's main threat is d4, laddering to a1.
-−
-<hexboard size="5x5"
-  contents="R e2 a1 1:b4 3:d4 c5 d5 5:d2 B b5 e1 2:a5 S a2 b1 b2 c1 c2 d1 d2 d3 e3"
-  />
-−
-If Blue plays in {a2,b1,b2,c1,d1}, then Red plays c2.  This connects to the top with d1 or c1 or b2, and connects down with a [[Interior template#The box|box]].
-−
-If Blue plays c2, then Red plays d2.  This connects down with a [[Interior template#The mouth or trapezoid|table]], and connects to the top with d1 or a3, since a3 forms [[Edge template III2d]].
-−
-If Blue plays d2, then Red plays c3.  This has a bridge down, and connects to the top for the same reason as without the a5-b4 exchange.
-−
-The e2-d4 bridge is [[Bolstered template|bolstered]] at e3 ([[Equivalent patterns#Edge equivalence|by Blue's edge]]), so e3 is no better for Blue than d3.
-−
-Thus, the only remaining case is    4. d3  .
-−
-<hexboard size="5x5"
-  contents="R e2 a1 1:b4 3:d4 5:c4 c5 d5 B b5 e1 2:a5 4:d3"
-  />
-−
-Against that, Red plays    5. c4  .
-−
-This threatens c2, which would connect to the top via d1 or c1 or b2, so Blue must respond in {c2,c3,b3}.  If Blue plays c2 or c3, then Red plays a3, winning with [[Edge template III2d]].  Thus Blue plays b3 instead.  Red responds with d2, connecting down via c4 or e4, and connecting to the top because a1 escapes the ladder.
-−
-Therefore  1. b4  does win for Red.
 === Puzzle 6 ===

@@ Line 314: / Line 314: @@
 Uniqueness:
-Blue's main threat is c2, briding to [[edge template III2a]].
+Blue's main threat is c2, bridging to [[edge template III2a]].
 <hexboard size="5x5"

@@ Line 376: / Line 376: @@
    />
-Before the d1,b2 exchange, Red responds to c3 with d1.  After the d1,b2 exchange, Red can respond to c3 with c2.  In each case, Red will have b2 and d2 [[Captured cell|captured]] to the top edge, so Blue must defend against both e3 - forming [[edge template III2d]] - and the [[ladder escape fork]] at c4.
+Before the d1,b2 exchange, Red responds to c3 with b2.  After the d1,b2 exchange, Red can respond to c3 with c2.  In each case, Red will have b2 and d2 [[Captured cell|captured]] to the top edge, so Blue must defend against both e3 - forming [[edge template III2d]] - and the [[ladder escape fork]] at c4.
 <hexboard size="5x5"

@@ Line 336: / Line 336: @@
 Showing that d2 wins for Red:
-This part is quite similar to showing that d2 wins for Blue in [[Solutions to puzzles#Puzzle 2|puzzle 2]].
+This part is quite similar to showing that d2 wins for Blue in [[Solutions to puzzles#Puzzle 2_2|puzzle 2]].
 <hexboard size="5x5"
@@ Line 387: / Line 387: @@
 The overlap between those threats is {d3,c5}.  Against d3, Red plays a4 and ladders to e5.  Against c5, Red plays b5, followed by a4 or d3.  (d3 connects with c4 or either of d4,e4).
-Thus, both before and immediately after the e2,d4 exchange, none of Blue's intrusions into
+Thus, both before and immediately after the d1,b2 exchange, none of Blue's intrusions into
 <hexboard size="5x5"