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

catswift Apr 13, 2022

#1**+2 **

Can you please write who many days... I don't think the latex is showing....

Vinculum Apr 13, 2022

#2**+2 **

A question similar to this has been answered:

https://web2.0calc.com/questions/help-please_8381

If you can write the latex, or tell me what numbers are in the problem, I can help you if needed.

Vinculum Apr 13, 2022

#3**+1 **

oh sorry D:

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?

Guest Apr 13, 2022

#4**+2 **

You need \({n \choose 3} \ge 365\)

The smallest number that satisfies this is \(\color{brown}\boxed{15}\)

BuilderBoi
Apr 13, 2022