The hypothesis that the determinant is zero can be checked, and possibly refuted, by an explicit calculation for small n. -- Gene On Friday, December 7, 2018, 12:24:43 PM PST, Dan Asimov <dasimov@earthlink.net> wrote: I never got a few things right in the statement of this problem, even on the second try. But now it's right: ----- A2 Let S_1, S_2, ..., S_(2^n−1) be the nonempty subsets of {1,2,...,n} in some order, and let M be the (2^n−1)×(2^n−1) matrix whose (i,j)th entry m(i,j) = 0 if S_i ∩ S_j is empty; m(i,j) = 1 otherwise. Calculate the determinant of this matrix. ----- Allan's point that if the order doesn't matter, the determinant must be 0 also occurred to me. But maybe they're looking for an answer of the form ±[expression] ??? In any case, if the answer doesn't turn out to be too trivial, this is a very cool problem. —Dan