  A particle moves among the vertices of an $(m+1)$-gon which are labeled
clockwise as $0,1,...,m$. The particle starts at 0 and thereafter at each step
it moves to the adjacent vertex, going clockwise with a known probability $p$,
or counterclockwise with probability $1-p$. The directions of successive
movements are independent. What is the expected number of moves needed to visit
all vertices? This and other related questions are answered using recursive
relations.
