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I run a book club with n people, not including myself. Every day, for 365 days, I invite three 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 three members over all 365 days?
 

 Jul 4, 2022

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We have the equation \({n +1\choose 3} \geq 365\)

 

Note that \({14 \choose 3} = 364\), so there are 15 members in the group, making for \(\color{brown}\boxed{14}\) people. 

 Jul 4, 2022
 #1
avatar+2448 
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Best Answer

We have the equation \({n +1\choose 3} \geq 365\)

 

Note that \({14 \choose 3} = 364\), so there are 15 members in the group, making for \(\color{brown}\boxed{14}\) people. 

BuilderBoi Jul 4, 2022

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