For n>2, an n×n grid of squares is coloured black and white like a chessboard, with its upper left corner coloured black. Then we can recolour some of the white squares black in the following way: choose a 2×3 (or 3×2) rectangle which has exactly 3 white squares and then colour all these 3 white squares black. Find all n such that after a series of such operations all squares will be black. geometryrectanglecombinatorics proposedcombinatorics