3

Part of 1999 Chile National Olympiad

Problems(1)

1000 red squares in 1999x1999 board (Chile NMO 1999 P3)

Source:

It is possible to paint with the colors red and blue the squares of a grid board

1999\times 1999

, so that in each of the

1999

rows, in each of the

1999

columns and each of the the

2

diagonals are exactly

1000

squares painted red?

combinatoricsColoring