MathDB

Let

n

be a positive integer. On a

2n\times 2n

board, the

2n^2

squares were painted white and the other

2n^2

squares were painted black. One operation is to choose a

2\times 2

subtable and mirror its

4

cells about the vertical or horizontal axis of symmetry of that subtable. For what values of

n

is it always possible to obtain a chess-like coloring from any initial coloring?

Problem Statement