February 2001 solution

Solution to February 2001 Problem

This solution is a combination of solutions sent in by Alexander Potapenko (Russia) and Juan Mir Pieras (Spain).

No, it is not possible.

A 10 by 10 chessboard with squares colored alternately black and white has 50 white squares and 50 black. A tetromino covers either 3 white and 1 black or 3 black and 1 white. Since we must have an equal number of each type, we need an even number of tetrominoes to cover the squares . Each tetromino covers 4 squares so that 25 would be needed to cover the chessboard. Because 25 is not an even number, the 10 by 10 board cannot be covered.

Comments. Matthew Wright included with his solution a simple explanation of how to cover the 4 by 4 board with 4 tetrominoes:

+	*	*	*
+	+	*	0
+	~	0	0
~	~	~	0

This pattern can be repeated to cover a 4n by 4n board for any n. In the given problem, one can cover all but 4 of the 100 squares using 24 tetrominoes.