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?

I solved this by going to ms paint and color coding the squares I thought were important.  I began to test to see if any squares would guarantee the knight's win, and I found one!--assuming the king's best strategy is to surround himself as fast as possible.

 _ _ _ _ _ _ _ _
|_|_|k|_|_|_|_|_|
|_|_|_|_|1|_|_|_|
|_|_|9|_|_|_|6|_|
|_|_|_|8|x|7|_|_|
|_|x|_|x|_|x|_|x|
|_|_|_|3|x|4|_|_|
|_|_|2|_|_|_|5|_|
|_|_|_|_|K|_|_|_|

The strategy:
Move to square 1.
If king moves 2, knight moves 6.
If king moves 3, knight moves 7.
If king moves 4, knight moves 8.
If king moves 5, knight moves 9.

Depending on the king's next move, the knight can move to the right square labeled x; these are the important squares.  No matter the king's next move, the knight will break through.

This solution assumes that the king only sows mines one knight's move away.  It seems to me safe to assume the king cannot win any other way.

Posted by Tristan on 2005-03-08 01:10:01