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avatar+1420 

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?

 Jun 22, 2024
 #1
avatar+129725 
+1

n! / [ (n - 2)! *2] > 400

 

n! / (n -2)! > 800

 

n * ( n -1)  > 800

 

n^2 - n >  800

 

n^2 - n - 800 = 0

 

n =  [1 + sqrt [1 + 3200 ] ]  / 2   ≈  28.79

 

n = 29

 

Proof 

C(28, 2) = 378

C (29, 2)  =  406

 

 

cool cool cool

 Jun 22, 2024

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