Consider N×N grids of black-or-white stones (in any combination), like these for the case of N = 4:
We say the grid contains a rectangle if there is a pair of distinct rows (a and b) and a pair of distinct columns (x and y) which combine (ax, bx, ay, by) to give four stones of the same colour.
The grid on the left has several rectangles, of which three are shown. The two grids on the right are rectangle-free.
Question: does there exist a 5×5 rectangle-free grid?
(Puzzle by Laurent Rosaz, from the EATCS Bulletin, #97, Feb 2009.)