What is the largest square you can paint onto a chess board such that you can still place five queens all on unpainted squares where all 64 squares are attacked?

(In reply to Clarification and Solution by Juggler)

The problem doesn't say that the painted square must be parallel to the sides of the chessboard. Placing the queens as you suggest allows painting a 4√2 square at a 45 degrees angle.

Posted by Federico Kereki on 2004-09-20 10:11:05