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?

(In reply to re: Solution by Federico Kereki)

Yes, Federico, I agree, it was not a proof.  I just thougt that going from b2 to g7 was the most efficient strategy for the king and if even that didn't work...

Now what do you think of this:
Let rook 1 be at a1 and he only moves on the outer square (a1, a8, h1 and h8).
Rook 2 is on g7 and moves on the second outer square (b2, b7, g2 and g7)
Divide the chess field is 4 equal squares, (a1, d4), (a8,d5), (h1,e4) and (h8,e5)  .

Start with the king on d4.  This is in the (a1, d4) square.

If the king enters another square, move rook 2 to the side of the board where the square the king just left is situated.  E.g. if he goes to square (a8, d5), rook 2 goes to g2.
If the king continues going to the 8 line, there is nothing to fear, life gets easier.
If the king went deeper in the square (a1, d4), move rook 1 to the a8 position, if he continues, rook 1 goes to h8.

The above (I think) gives prove for 'horizontal/vertical' moves.
What for a diagonal move?
A) going to rook1:
If the king goes from d4 to c3, move rook 1 to a8, if the king continues to b2, rook 1 travels to h8.
B) going to rook 2:
If the king goes from d4 to e5, move rook 2 to g2, if the king continues to f6, rook 2 travels to b2.

It is a bit difficult to explain, but I think it works.

Posted by Hugo on 2004-11-19 20:14:47