Math CentralQuandaries & Queries


Question from Hammed, a student:

Prove that if each of the 50 states in the USA is assigned one of the colors red, white, or blue, then some pair of adjacent states must have the same color. (If you think that Arizona and Colorado are adjacent, then you may not consider New Mexico and Utah to be adjacent, too. You can't have it both ways!)

Hi Hammed,

Try colouring the states that share a share a border with West Virginia (or Missouri) with three colours so that adjacent states get different colours. What happens?


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