Suppose we have an ant travelling on edges of a cube, going from one vertex to another. The ant never stops and it takes him one minute to go along one edge. At every vertex, the ant randomly picks...

Extracted text: Suppose we have an ant travelling on edges of a cube, going from one vertex to another. The ant never stops and it takes him one minute to go along one edge. At every vertex, the ant randomly picks one of the three available edges and starts going along that edge. We pick a vertex of the cube and put the ant there. What is the expected number of minutes that it will take the ant to return to that same vertex?