 Solution

ID: past-exam-of-the-probability-statistics-and-options-i-course-of-the-university-of-oxford/2009/r/1/iv/solution

The hypercube is connected: successive coordinate flips reach any target bit string. Every vertex has degree

k

. A finite connected graph has an Euler circuit exactly when all vertex degrees are even. Therefore

Q_{k} is Eulerian exactly when k is even .

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