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?

A king put himself into check when it is next to a row that is covered by a rook.  The 3x3 box the king is in has to remain free of "rook paths".

Since a king has access to 4 possible sides, the rooks just have to make sure that with every move they make, no more than 1 "rook path" touches the *side* of this 3x3 box at any given time.

With 3 rooks, the "rook paths" can't touch more than 2 sides of a 5x5 box around the king.

Is it possible with 3 rooks? No.  Picture the first three rows of a chessboard on all sides.  Position one rook for each row such that if a rook is on row 3, it is only allowed to move to row 3 of another side. Same with a rook on rows 2 and 1.  This is the only setup in which any rook can completely avoid a king in the least moves (which is 2 - by moving to the same position on the opposite corner of the board). 

Keeping out of the way of the king is impossible because the board is only 8x8.  The king will always be able to force his 5x5 box into the path of a rook, because the 5x5 box is surrounded by the 3x3 "frame", and will always be able to make more than 2 sides of his box touch a rook's path before the rooks can make their 6 moves to get entirely out of its way.

Posted by BC on 2004-12-07 01:58:06