Permutations of the powers of two
Source: Canada 1989 (couldn't find it with search)
September 30, 2007
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Problem Statement
Given the numbers 1,2,2^2, \ldots ,2^{n\minus{}1}, for a specific permutation \sigma \equal{} x_1,x_2, \ldots, x_n of these numbers we define S_1(\sigma) \equal{} x_1, S_2(\sigma)\equal{}x_1\plus{}x_2, and Q(\sigma)\equal{}S_1(\sigma)S_2(\sigma)\cdot \cdot \cdot S_n(\sigma). Evaluate , where the sum is taken over all possible permutations.