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avatar+1053 

I run a book club with $n$ people, not including myself.  Every day, for $400$ days, I invite $2$ 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 $2$ members over all $400$ days?

 Dec 15, 2023
 #1
avatar+126978 
+1

We need to solve this :

 

C (n , 2)  >  400

 

     n!

_______  >  400

(n -2)! 2!

 

 

    n!

_____    >   400 * 2!   

(n -2)!

 

 

n ( n - 1) >  800

 

Note that  28^2 =  784

 

So

29 (29 -1)  =  29 * 28  = 812

 

Smallest n = 29   

 

cool cool cool

 Dec 16, 2023

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