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Question: use the pigeonhole principle to prove the following can you...

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Use the pigeonhole principle to prove the following:

Let S = {ai , . . . , ao) be any set of 9 points such that each ai = (Xi,Vi, z) where xi, yi, Zg are integers. Prove that, for some i and j, i f j, the midpoint of the segment joining ai and a, has integer coordinates.

Can you explain what the pigeon and what the pigeonholes would be in this case as well.

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