2018 AIME I Problem 12


For every subset TT of U={1,2,3,,18}U = \{ 1,2,3,\ldots,18 \}, let s(T)s(T) be the sum of the elements of TT, with s()s(\emptyset) defined to be 00. If TT is chosen at random among all subsets of UU, the probability that s(T)s(T) is divisible by 33 is mn\frac{m}{n}, where mm and nn are relatively prime positive integers. Find mm.


Leading zeroes must be inputted, so if your answer is 34, then input 034. Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

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Category: AIME I
Points: 5
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