1. Suppose you take a chessboard.

X	X
		Y

Then you delete two squares of the opposite color, for example the two squares marked X and Y above. Can you cover the remaining 62 squares with 1x2 dominoes? Can you prove your answer?

2. A “tetromino” consists of four squares glued together along edges. There are five of them:

Can you cover a 5x4 rectangle using these? Can you prove your answer.

Another group of shapes are the 12 pentominoes.

You can try this game: Place any pentomino. Then opponent takes a remaining pentomino and places it without overlapping. Last player to move wins! Try this using pencils and these diagrams.