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 simple answer would be that, since the rules are being violated, the game can go on indefinitely. This is because if the King deliberately comes in the Rook's path, the Rook has an option of avoiding to capture the King by going out of the way. I am assuming here that the King, even though violating the rules, moves just one space at a time. This gives the Rooks ample room for manoeuvring.

 

The puzzle becomes interesting when the king cannot move into a cell on the Rooks path. In such a case, one Rook can remain in a corner on the board and the other Rook can keep on avoiding the King. Since the King has limited mobility, the Rook can wander around the entire board without obstructing the Kings path. The King can then only try to come closer to the Rooks, but cannot force itself to be checked. The only way the King can force this is by making sure that the 2 Rooks are blocking 2 complete rows/columns, AND the King is on the edge of the Board. The Rooks can avoid this by placing themselves on opposite ends of the board leaving 36 cells Safe for the King to move into.

 

The same goes for 3 Rooks, as now 2 Rooks can be placed adjacent to each other, still leaving ample room for manoeuvre. The King would still have 30 Safe spaces.

 

Am I making any sense ? ... Or have I missed something crucial here !!!

Edited on November 16, 2004, 9:19 am

Posted by Syzygy on 2004-11-16 09:18:31