MathDB

2

Part of 1999 Dutch Mathematical Olympiad

Problems(1)

Colouring of a 9 x 9 square

Source: Dutch NMO 1999

10/22/2005
A 9×99 \times 9 square consists of 8181 unit squares. Some of these unit squares are painted black, and the others are painted white, such that each 2×32 \times 3 rectangle and each 3×23 \times 2 rectangle contain exactly 2 black unit squares and 4 white unit squares. Determine the number of black unit squares.
geometryrectanglemodular arithmetic