5

Part of 1982 Swedish Mathematical Competition

Problems(1)

4 points of same color forming a rectangle in a 12x12 array, in 3 colours

Source: 1982 Swedish Mathematical Competition p5

Each point in a

12 \times 12

array is colored red, white or blue. Show that it is always possible to find

4

points of the same color forming a rectangle with sides parallel to the sides of the array.

Coloringcombinatorial geometrycombinatorics