MathDB

Colouring of a 9 x 9 square

Source: Dutch NMO 1999

October 22, 2005

geometryrectanglemodular arithmetic

Problem Statement

9 \times 9

square consists of

81

unit squares. Some of these unit squares are painted black, and the others are painted white, such that each

2 \times 3

rectangle and each

3 \times 2

rectangle contain exactly 2 black unit squares and 4 white unit squares. Determine the number of black unit squares.