有趣的象棋残局

sean9991

Red wins, first move, cannon 7 up 1. www.ddhw.com

sean9991

This problem is equivalent to removing matches from several stacks.  You can remove any positive number of matches from one stack at any time.  Whoever gets the last match wins the game.   www.ddhw.com

sean9991

if red pawn 1 up 1, black will cannon 3 up 2.  Remember the objective of this game is to have the last move so that four cannons are touched and have one spot between the pawns. www.ddhw.com

sean9991

This is a famous ending named "双炮禁双炮".  As I said before, it's equivalent to a game of removing matches (or stones) from several stackes.  The rule is that two players take turns removing any positive number of matches from a single stack and whoever gets the last match wins.  To win this game, represent the number of matches of each stack in binary format, and try to maintain even number of one's in every digit.  To be specific, as in this game, there are 4 and 6 spots between 2 cannons and 2 spot between the pawns.  Our objective is to have the last move so that the four cannons are touches, and have 1 spot left between the pawns.  So we can think of 3 stackes of matches with 1, 4, and 6 matches, respectively.  Represent them as binary number, we have 1, 100, and 110.  So the first move is reduce 6 to 5, and make it 101.  Now we have 1, 100, and 101.  Note here we have even number of 1's in every digit.  www.ddhw.com