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?

As Federico said, it depends almost entirely on initial position. If the king is within one move of check on both rooks, then the king can easily force itself into check. Similarly, if the rooks are as far away as possible from the king, then the king never really has an optimal move, and the rooks can avoid check indefinitely.

I believe that on the average case, the two rooks can avoid check indefinitely. Ideally, the rooks want to become as redundant as possible. So, for three rooks, you'd want them at opposite corners. Now, for three rooks, if the king is within two moves of check for two pieces (and set to move) then he can get to within one move of check on two pieces, and hence he can achieve his goal. With three rooks, I think the king can eventually get there since he closes the distance on at least one rook per move. Even if that rook moves, there will still be a closest pair of rooks, only one of which can escape.

I think the only way the king can achieve this goal with two rooks if it starts within reach. If the king starts in a safe zone, then it cannot never get into check. However, with three rooks, I think the king can eventually get into check.

Posted by Eric on 2004-11-16 10:19:06