Proofs without Words 63

6.11 Tiling with dominoes

Take a square grid with two opposite corners missing. Can you tile it with 2 ×1 dominoes?

Place the dominoes, without overlapping, so as to completely cover the board.

I have placed two red dominoes already, but please feel free to move them, if this would

help you to find a way to tile the whole figure. Give it a try!

Interlude. . .

Did you find a tiling? Let me give you a hint. One way to argue begins by placing a

chessboard pattern on the grid, as pictured here.

Can you see how to mount an argument with this chessboard pattern?