There are two black rooks on the chessboard and a white chess king that tries to violate the chess rules, that is tries to move into a position which it would be in check. Can the king force itself into check or can the two rooks avoid check indefinitely?
What if there are three rooks?
I'm thinking that to solve this we have to forget what we normally think about chess. In this puzzle, a King captures a Rook by placing itself in a Rook's path. The only way the King can be sure to capture a rook is if it is one space away from both of that Rook's paths, ie. it must be one diagonal space away from the Rook. Is it possible for the King to push its way to be in that situation?
The worst position for a Rook to be in is somewhere in the middle of the board (b-g, 2-7), in that position, there are four places the King can make a winning strike. For the Rooks to fend the king off indefinately they must occupy the outside rows and columns of the board (a, h, and 1, 8). I think it can be shown that for two Rooks, it is possible to fend the King off indifinately by choosing to move the Rooks so that there is always at least one empty row and one empty column between the Rooks' paths and the Kings position.
I think it is possible for the King to capture a Rook if there are three Rooks on the board, but I'm still working that one out.
Posted by Erik O.
on 2004-11-16 11:27:35