CMO 1989 Problem 5

Given the numbers $1,2,2^2, \ldots ,2^{n-1}$ , for a specific permutation $\sigma = x_1,x_2, \ldots, x_n$ of these numbers we define $S_1(\sigma) = x_1$ , $S_2(\sigma)=x_1+x_2$ , $\ldots$ and $Q(\sigma)=S_1(\sigma)S_2(\sigma)\cdot \cdot \cdot S_n(\sigma)$ . Evaluate $\sum 1/Q(\sigma)$ , where the sum is taken over all possible permutations.