MathDB

John and Mary each have a white

8 \times 8

square divided into

1 \times 1

cells. They have painted an equal number of cells on their respective squares in blue. Prove that one can cut up each of the two squares into

2 \times 1

dominoes so that it is possible to reassemble John's dominoes into a new square and Mary's dominoes into another square with the same pattern of blue cells.
(A Shapovalov)

Problem Statement