A rectangular M×N board is divided into 1× cells. There are also many domino pieces of size 1×2. These pieces are placed on a board so that each piece occupies two cells. The board is not entirely covered, but it is impossible to move the domino pieces (the board has a frame, so that the pieces cannot stick out of it). Prove that the number of uncovered cells is
(a) less than 41MN,(b) less than 51MN. combinatoricscombinatorial geometryTiling