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Challenge 340: A Colouring Challenge

Are there two points at a distance of 1 unit that are the same colour? Prove it!

Each point on the x-y plane is assigned one of three colours, either red, blue or green. So, if you pick any point (x, y), it will have one of these three colours.

Prove that it must be possible to find two points on the plane which are 1 unit apart and have the same colour.