A white knight is at c1, and the black king is at its starting position. White moves first, and tries to reach the black king, who will remain at its square. At each turn, the black king can sow a mine in any empty square. White wins if the knight reaches the King, and loses if it runs out of moves.

Who wins this game?

To figure out this game, I made a map of the chessboard.  The proposed strategy then uses the principle of the "fork" move in chess, where one piece can attack two different squares.

Start with a chess board, mark the King's position with a 'K'.  Now mark the 4 squares that are one knight's move away from the 'K' with a small 'k'.  If the white Knight can reach any of the k squares, White wins.

Mark the kNight's position with 'N'.
Mark the 4 squares the knight can move to with a '1' (a2, b3, d3, e2)
Mark all squares a knight can move to from a '1' with a '2': (a5, b4, c3, c5, d4, e5, f2, f4, g3)
Mark all squares a knight can move to from a '2' with a '3': (a6, b5, b7, c4, c6, d5, d7, e4, e6, f3, f5, f7, g4, g6, h1, h3, h5)

Now, make any of the '3' squares boldface if that square can attack 2 different 'k' squares.  There are four bold '3's: (b5, e4, e6, h5)
Now make any of the '2' squares bold if they can attack two different bold '3' squares.  There are 5 boldface '2's:  (c3, c5, d4, f4, g3)

White's strategy would be to move to a bold '2' then to a bold '3' in order to have the optimum chance of defeating Black's fence method of defense.

Despite this graphic aid, however, I still have not found a plan of attack that guarantee's White a victory.

Posted by Larry on 2005-03-09 03:13:21