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I had three boxes of cookies from my friends as a holiday gift. Unfortunately, I dropped all three boxes, and I don't know how many came from each friend. The cookies across the boxes were identical.

Let there be N N cookies. The probability of correctly putting the cookies back in the boxes, as they arrived, is 1 91 \frac{1}{91} . Find N N .


The answer is 12.

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1 solution

Alexander Sludds
Jan 2, 2014

Note can solve this problem by lining all of the cookies up and playing two "separators" between the cookies. To the left of the first separator is the cookies for box one, in the middle of the two of them is the cookies for box two, and on the right of the second separator are the cookies for box three. Thus, our answer is the same thing as solving for n in this equation ( ( n + 2 ) 2 ) (n+2) \choose 2 = 91 = 91 .

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