MathDB

For

n>2

, an

n\times n

grid of squares is coloured black and white like a chessboard, with its upper left corner coloured black. Then we can recolour some of the white squares black in the following way: choose a

2\times 3

(or

3\times 2

) rectangle which has exactly

3

white squares and then colour all these

3

white squares black. Find all

n

such that after a series of such operations all squares will be black.

Problem Statement