A king and a rook are on opposite corners of an 8x8 chessboard. The king is trying to avoid being checked by the rook. Normally the rook would check the king in one move but this rook is restricted - his moves are limited to up to two spaces, that also applies to his ability to make the check.
Can the king avoid check indefinitely? If not, how long can he last?
Still waiting for an answer as to whether the Rook can satisfy its mission by checking the King from an adjacent square.
Assuming that the Rook can check from an adjacent square, then the King cannot get close enough to attack the Rook, and in fact must move away from the rook, so the Rook can move with some impunity. It takes the Rook 4 moves to situate itself in one of the central 4 squares, and once there the King is "cornered", forever restricted to one quadrant of the board. If the King delays the game-ending check as long as possible, then the rook can further corner the king by moving towards the king without giving check one or two spaces at a time. Within 4 rook moves at worst, the rook has the king cornered in a 2X2 corner, and check is achieved on the Rook's 9th move.
The problem is harder if the Rook is not allowed to check the King from an adjacent square.
Open question
