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?
+2666 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.
+2666 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.
