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The $n$ dimensional hypercube $Q_n$ is a graph that has a vertex $v_s$ for each string $s \in \{0, 1\}^n$ and an edge between two vertices $v_s$ and $v_t$ if and only if the Hamming distance between $s$ and $t$ is $1$. I would like to find directed hamiltonian cycles in this graph that satisfy a...