Problem 4

Suppose we have a 3x9 grid of 27 squares, where each square is either orange or black. That is, the

grid has 9 columns, each with 3 rows.

For example, it's possible that all 27 squares are orange, that all 27 square are black, or any

combination of orange or black.

Use the Pigeonhole Principle to prove that there are two columns that have the same colour pattern

(e.g. if one is orange, orange, black, then the other is also orange, orange, black, in the same order.)