Question 13
A tourist arrives in Moscow by train and wanders randomly through the streets on foot. After supper he decides to return to the station along sections of street that he has traversed an odd number of times. Prove that this is always possible. [In other words, given a path over a graph from $A$ to $B$, find a path from $B$ to $A$ consisting of edges that are used an odd number of times in the first path.]