Answer to the 62 square Chess Board Problem:
If you tried to cut out the two square “dominos” you found out that you could not cut 31 dominos –just 30. Each of the dominos you could cut out were made of one back square and one white square. And you also found out that there were to squares left over – and both of them were black. That may have puzzled you a little bit.
If you look at the copy of the board that you did not cut up. You will notice that both of the squares that were removed were white squares. So the board has 30 white squares and 32 black squares.
Sometimes in mathematics it is important to be able to explain why a problem does not have a solution.
There is no way to cut out a domino that has two black squares. There is no pair of black squares that are adjacent to each other. Each time you lay a domino on the board it covers two squares – one has to be white and the other has to be black.
So the problem has no possible solution.