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249:, a pawn may be moved in two different ways: it may be moved one square vertically forward, or it may capture a pawn one square diagonally ahead of it. A pawn may not be moved forward if there is a pawn in the next square. Unlike chess, the first move of a pawn may not advance it by two spaces. A player loses if they have no legal moves or one of the other player's pawns reaches the end of the board.
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Whenever a player advances a pawn to the penultimate rank and attacks an opposing pawn, there is a threat to proceed to the final rank by capture. The opponent's only sensible responses, therefore, are to either capture the advanced pawn or advance the threatened one, the latter only being sensible
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in the row closest to them. The goal of each player is to either advance a pawn to the opposite end of the board or leave the other player with no legal moves, either by
200:; with perfect play, White will always lose in 3 moves (1.b2 axb2 2.cxb2 c2 3.a2 c1#). Indeed, Gardner specifically constructed it as a game with a small
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33011302110453748 1120311033224455933011302110453748 1120311033224455933011302110453748 1120311033224455933011302110453748 ...,
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when removing three objects from a heap of five or more, the player may also split the remainder into two heaps.
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where bold entries indicate the values that differ from the eventual periodic behavior of the sequence.
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removing just one object is a legal move only if the removed object is the only object in the heap, and
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166:. It is played on a rectangular board of variable size, for example on a 3×3 board or on a regular
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hexapawn with the additional rule that capturing is always compulsory, the result is the game
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230:, which is played on a 4×4 board with 4 pawns on each side. It is a forced win for White.
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in the case that there is one threatened pawn rather than two. If one restricts 3×
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on a turn, the player may remove one to three objects from a heap,
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Only 24 matchboxes are required for a hexapawn version of
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The
Unexpected Hanging and Other Mathematical Diversions
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in order to demonstrate how it could be played by a
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303:The initial position is a single heap of size
235:Matchbox Educable Noughts and Crosses Engine
221:Matchbox Educable Noughts and Crosses Engine
193:or by having all of their pieces captured.
16:Two-player game invented by Martin Gardner
285:. This means that it is equivalent to a
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196:Hexapawn on the 3×3 board is a
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273:Dawson's chess reduces to the
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398:- an article by Robert Price.
385:, by Martin Gardner, pp. 93ff
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381:, March 1962, reprinted in
266:. The game was invented by
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356:"A Note on Dawson's Chess"
226:A variant of this game is
178:, each player begins with
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404:- source code included.
408:Hexapawn game for IOS
289:-like game in which:
170:. On a board of size
402:Hexapawn java applet
375:Mathematical Games,
354:Ferguson, Thomas S.
268:Thomas Rayner Dawson
378:Scientific American
213:mechanical computer
146:3x3 Hexapawn setup
429:Mathematical games
311:for this game is
283:Conway's notation
211:implemented by a
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330:1120311033224455
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185:, one for each
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390:External links
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275:impartial game
264:Dawson's chess
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253:Dawson's chess
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164:Martin Gardner
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439:1962 in chess
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415:- Play Online
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413:Play Hexapawn
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449:Solved games
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309:nim-sequence
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162:invented by
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223:(MENACE).
198:solved game
158:two-player
423:Categories
341:References
168:chessboard
270:in 1935.
215:based on
206:heuristic
202:game tree
191:stalemate
396:Hexapawn
277:denoted
228:octopawn
152:Hexapawn
370:Sources
307:. The
245:As in
187:square
359:(PDF)
247:chess
241:Rules
183:pawns
154:is a
279:.137
160:game
287:Nim
281:in
219:'s
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320:22
237:.
209:AI
361:.
332:2
328:0
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318:5
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305:N
260:N
180:m
176:m
174:×
172:n
136:c
133:b
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