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?

Please read Tristan's solution (The next one up).  Mine is incorrect.

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I just realized that the knight and the king start off in different colored squares.  Since the knight cannot reach him in the first three moves (it's too far), he must use five moves, in which time, the king will have made his fence.  Is this right?

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What I originally had:
I agree with Sam that If the king can block off C7, D6, F6, and G7 in time, the knight loses.

E6 is the place where the knight can go to either C7 or G7.
E4 is the place where the knight can go to either D6 or F6.

The knight's strategy is to get to the king as quickly as possible, while keeping the king guessing as to how he will get there.  So in his first two moves, the knight should go D3 and C5.  From C5, he can get to the two desired places, E6 and E4.

However, the king will probably suspect this, and cover one of the 7-rank squares after the knight's first move, and one of the 6-rank squares after his second move, and then, no matter whether the knight goes to E6 or E4, the king can block him.

I am fairly certain the king will win, but I'm not sure if this proof is adequate enough yet.

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Edited on March 7, 2005, 8:06 pm

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Edited on March 8, 2005, 1:50 am

Posted by Dustin on 2005-03-07 20:00:29