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

 Jul 2, 2020
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This is a combination problem. Every day you invite 5 people out of the n people, so it would be c(n,5). c(n,5) has to be more than 365. c(10,5) is 252, so that is too little. c(11,5) is 462, so the correct answer is 11.

 Jul 25, 2020

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