Cover time is the expected number of steps in a random walk required to visit all the vertices of a connected graph (a graph in which there is always a path, consisting of one or more edges, between any two vertices). Blom, Holst and Sandell (in Problems and Snapshots from the World of Probability, Springer, 1994) describe a similar problem: moving randomly from point to point on the corners of a cube, what is the expected number of visits required to visit each edge. The surprising answer is 48.5.
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