MathDB

n\times n

board is coloured in

n

colours such that the main diagonal (from top-left to bottom-right) is coloured in the first colour; the two adjacent diagonals are coloured in the second colour; the two next diagonals (one from above and one from below) are coloured in the third colour, etc; the two corners (top-right and bottom-left) are coloured in the

n

-th colour. It happens that it is possible to place on the board

n

rooks, no two attacking each other and such that no two rooks stand on cells of the same colour. Prove that

n=0\pmod{4}

n=1\pmod{4}

Problem Statement