2. For n ≥ 2, define the n-dimensional hypercube Qn to have vertex set V(Qn) = {(1, .,.£n) = R¹" : x¡ € {0,1},1 ≤ i ≤¹ {n} and two vertices are joined by an edge if and only if they agree in n - 1 coordinates. Prove that Qn has a Hamiltonian cycle for n > 2.

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