Missives from a fly bottle
barang dot sg
Last revised 19 August 2018
37. Dominoes on a chessboard

A chessboard has two diagonally-opposite corners removed. A domino placed upon the board can cover two adjacent squares of the board. (Two such dominoes are shown.)

You have as many dominoes as you like. Prove that there is no way to place them on the board so that the board is completely and exactly covered.

(The dominoes must be placed flat on the board without overlapping.)