Question

Prove or disprove that you can use dominoes to tile a 5 X 5 checkerboard with three corners removed.

Short answer

It is not possible to use dominoes to tile a 5 X 5 checkerboard with three corners removed.

Step-by-step solution

To prove

You can or cannot use dominoes to tile a 5 X 5 checkerboard with three corners removed.

Proof

There are alternate white and black squares in a 5 X 5 checkerboard.

It can be seen in a 5 X 5 checkerboard that it contains 13 black squares and 12 white squares.

Now, three corners are removed. There are 10 black squares and 12 white squares left since all the corners are black tiles.

Thus, each domino contains exactly one black square and one white square since each domino tile have to cover two adjacent squares.

Hence, there are not equal amount of black and white squares left as 10≠12.

Thus, it is not possible to use dominoes to tile a 5 X 5 checkerboard with three corners removed.