MathDB

On a rectangular board with

m \times n

squares (

m, n \ge 3

) there are dominoes (

2 \times 1

1\times 2

tiles), which do not overlap and do not extend beyond the board. Every domino covers exactly two squares of the board. Assume that the dominos cover the has the property that no more dominos can be added to the board and that the four corner spaces of the board are not all empty. Prove that at least

2/3

of the squares of the board are covered with dominos.

Problem Statement