Chess and dominoes

pulern
Posers and Puzzles 03 May '10 14:27
1. 03 May '10 14:27
Just found this part of the forum, so I'm not sure if this one has been posted before.

If a domino piece is exactly the size of two squares of the chessboard, it would take 32 domino pieces to cover the 64 squares.

Now, if you take chessboard and cut of the a1 and h8 square, you are left with 62 squares.
Why is not possible to cover the rest of the board with 31 domino pieces?

Looking for a simple and intuitive answer.
2. 03 May '10 15:00
Originally posted by pulern
Just found this part of the forum, so I'm not sure if this one has been posted before.

If a domino piece is exactly the size of two squares of the chessboard, it would take 32 domino pieces to cover the 64 squares.

Now, if you take chessboard and cut of the a1 and h8 square, you are left with 62 squares.
Why is not possible to cover the rest of the board with 31 domino pieces?

Looking for a simple and intuitive answer.
Each domino must cover one white square and one black square. Since you cut out two black squares, there will be still 32 white squares remaining, and therefore you need 32 dominoes to cover the board.
3. 03 May '10 15:08
nice one!
4. AThousandYoung
All My Soldiers...
03 May '10 23:131 edit
Never mind, move on.