Question

Prove or disprove that you can use dominoes to tile a standard checkerboard with all four corners removed

Short answer

The given statement in the question is true regarding dominoes on the standard checkerboard.

Step-by-step solution

Introduction

A standard checkerboard is a board with 8 rows and 8 columns, forming squares of equal size.

A domino is a rectangle, equal to the size of two squares attached either horizontally or vertically.

A board is tiled by dominoes when all its squares are covered with no overlapping dominoes and no dominoes overhanging the board.

Analyzing and concluding

In view of the above information, suppose all the four corner squares have been removed from the standard checkerboard, leaving 60 squares on the board.

If the set of dominoes arranged in a vertical manner is started to cover the checkerboard vertically, it is easy to see that 3 dominoes cover all the 6 remaining squares on the left-most column of the checkerboard.

Four dominoes cover each of the next six columns completely.

Similar to the first column, three dominoes cover the 8^th column of the board.

This way, all the squares of the checkerboard can be tiled with all the four corners are removed from the standard checkerboard.