QUESTION 10 ("* and a half) For all positive integers n, the hypercube Qn is a graph given as follows. The vertex set of Qn is the set of all subsets of [n]. We join two sets A and B by an edge if B can be formed from A by either adding or removing a single element. For example, when n = 6, (2, 3, 5) is adjacent to (2, 3) and (2, 3, 5, 6), but not to (3) or (1, 2, 3, 5, 6). When does Qn contain an Euler walk? When n is even or n=1. When n is odd. Always. Never.