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1. 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? (i have already tired 12 and 11, and both don't work.)

2. Marvin the fly starts at (0,0) Each step, Marvin moves one unit right or one unit up. He is trying to get to the point (5,7). However, at  (4,4) there is a frog that will eat him if he goes through that point. In how many ways can Marvin reach (5,7)? (i already tried 782, but that wasn't it.)

 Oct 19, 2022
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1. The answer is 18.

 

2. The number of ways is 488.

 Oct 19, 2022

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