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Given the set of S natural numbers S = {1, 2, 3, . . . , 200} select one hundred and one numbers from S. Prove that at least one of the numbers you chose is a multiple of another number that you chose.

I know that you are supposed to use the Pigeon Hole Principle, but I don't know how to set up the equation to solve it.

Minji Park
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  • The way this problem is stated is not how it is intended, I think. As currently stated, I can solve it by stating “I choose the numbers 1 through 101. 2 is a multiple of 1, so we’re done.” I know what you mean, and I’m not trying to be nitpicky; I just found it rather funny... – Franklin Pezzuti Dyer Nov 13 '19 at 21:58

1 Answers1

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Consider integers equivalent if their ratio is a power of $2$. There are $100$ equivalence classes, one per odd number.

J.G.
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