Max Black proposed this problem in
1945. He was a British philosopher and
mathematician.

Suppose you had a chess or checker board (8
x 8 = 64 squares), but you cut off a corner square from two opposite corners. You would get a board that looked like the
picture above, with just 62 squares.

Now suppose that you had 31 dominoes. Each domino was just the right size to cover
two squares on the board. 31 dominoes,
each covering 2 squares would cover a total of 62 squares (31 x 2 = 62).

Can the 31 dominoes be arranged on the board
to cover all 62 squares?

When I first saw this problem I felt that
the answer was probably “Yes, it is possible.”
I thought I could just make two copies of the 62 square board, and cut
one of them into two square “dominoes” and arrange them on the second copy of
the board.

Try it.
If you try it you will probably learn what I learned.

I’ll post a follow up in a few days to see
how you did.

David

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