4

Part of 2006 India National Olympiad

Problems(1)

46 squares are colored in red

Source: Indian National Maths Olympiad, Problem 4

Some 46 squares are randomly chosen from a

9 \times 9

chess board and colored in red. Show that there exists a

2\times 2

block of 4 squares of which at least three are colored in red.

geometryrectanglecombinatorics proposedcombinatorics