  The graph obtained from the integer grid Z x Z by the removal of all
horizontal edges that do not belong to the x-axis is called a comb. In a random
walk on a graph, whenever a walker is at a vertex v, in the next step it will
visit one of the neighbors of v, each with probability 1/d(v), where d(v)
denotes the degree of v. We answer a question of Cs\'aki, Cs\"org\"o, F\"oldes,
R\'ev\'esz, and Tusn\'ady by showing that the expected number of vertices
visited by a random walk on the comb after n steps is
(1/(2\sqrt{2\pi})+o(1))\sqrt n\log n. This contradicts a claim of Weiss and
Havlin.
