2017-2018 Spring OMO Problem 5
Source:
April 3, 2018
Problem Statement
A mouse has a wheel of cheese which is cut into slices. The mouse also has a -sided die, with faces labeled , and with each face equally likely to come up. Every second, the mouse rolls the dice. If the dice lands on , and the mouse has at least slices of cheese remaining, then the mouse eats slices of cheese; otherwise, the mouse does nothing. What is the expected number of seconds until all the cheese is gone?Proposed by Brandon Wang