2012 OIM Problems/Problem 3

Problem

Let $n$ be a positive integer. Given a set $\left\{a_1, a_2, \cdots , a_n\right\}$ of integers between 0 and $2^n-1$ inclusive, to each of its $2^n$ subsets we assign the sum of their elements; in particular, the empty subset has sum 0. If these $2^n$ sums leave different remainders when divided by $2^n$ , the subset $\left\{a_1, a_2, \cdots , a_n\right\}$ is said to be $n$ -complete. Find, for each $n$ , the number of $n$ -complete sets.

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

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2012 OIM Problems/Problem 3

Problem

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