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I run a coffee club with n people, not including myself. Every day, for 365 days, I invite four members in the club to have coffee with me. What is the smallest positive integer n so that I can avoid having the same group of four members over all 365 days?

 Jan 11, 2020
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Not counting yourself, in order to have a DISTINCT group of 4 people, you would have at least 12 people, because: 11 C 4 =330  Distinct combinations of 4 people. You need a minimum of 365. Therefore:

12 C 4 =495 Distinct combinations, which would be the minimum n.

 Jan 11, 2020

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