Help I have spent a long time on this
I run a book club with n people, not including myself. Every day, for 100 days, I invite 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 members over all 100 days?
If I understand your question:
You should have specified that of the "n" people, how many of them do you intend to use to review a book!
1 - If you intend to use 2 people, then minimum n = 15. Because 15 C 2 =105 unique combinations
2 - ................................3.......................................n = 10. .............. 10 C 3 = 120 ................................
3 - ................................ 4 .................................... n = 9 ................. 9 C 4 = 126 .................................
4 - ................................ 5 .................................... n = 9 .................. 9 C 5 = 126 .................................
5 - ............................... 6 ................................... n = 10 ................ 10 C 6 = 210 ...............................
And so on...............!
