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I run a book club with n people, not including myself. Every day, for 100 days, I invite 14 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 14 members over all 100 days?
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In my solution, I will assume that the person "I" does not participate in any group of 14 persons.
The problem is silent about it, so I can make such assumption.
The number of all possible different groups of 14 members is .
The problem asks you to find the minimal n such that
<= 100, but > 100.
Obviously, n should be not less than 14.
The table below represnts several values of n >= 14 and relevant values of
n
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14 1
15 15
16 120
From the table, you may see that the minimal n is 16.
ANSWER to the problem's question is this: the smallest positive integer number n satisfying the problem's requirement is 16.
Solved.