April 24, 2012
Problem of the Week
for Tuesday, April 24, 2012
Proposed by Drew's Third Grade Class
A water-bug finds himself inside the octagon marked WB on a bathroom floor. He decides to go on a random walk. Inside an octagon, he rolls the octahedral or eight-sided die and moves to a neighboring polygon in one of eight directions. Inside a square, he rolls the tetrahedral or four-sided die and moves in one of the four cardinal directions to a neighboring octagon. If he does this process three times, what is the probability that he ends up in a square?
