Chessboard Tiling


There is a famous problem about a chess board that has been damaged...

Start with a chessboard: 

Cut off two opposite corners: 

Dominoes can cover two adjacent squares. Can you cover the remaining 62 squares using dominoes?

Once you've thought about it, click below to see some questions you might like to consider:

  • How many black and how many white squares are there on the original chessboard?
  • What colour squares were cut off?
  • When you place a domino on the board, what colour(s) does it cover up?

Can you explain why it is impossible to tile the chessboard once the opposite corners have been cut off?


I don't think you can, as there will always be 2 squares left over.

Can you explain why you think there will always be 2 squares left over?