Suppose you have 15 single tiles, 15 double tiles, and 15 triple tiles and you want to fill an 8 x 8 square with as few of the 45 tiles as possible such that tiles of the same size never touch. The cover shows one solution with 35 tiles (14 x 1 + 13 x 2 + 8 x 3 = 64). Can you do better than that?