then four 12×11 floor tiles can be used to pave a 23×23 square floor.

(2) We will use 23×23 floor tiles. Westbank > lines 1, 13, 16, 19 and 22 are dyed red, and the remaining 15 lines are all dyed white.

No matter how any small squares of 2×2 or 3×3 are placed (the edges coincide with the grid lines of the big square), each square of 2×2 or 3×3 will cover even white squares of 1×1. Then the total number of white 1×1 squares covered by them is even. < P > However, after 23×23 floor dyeing, there are 23×15 (odd) 1×1 white squares, which are contradictory. < P > Therefore, only 2×2 and 3×3 floor tiles can not cover the 23×23 square floor in any case.