Cheese in the Center
A mouse lives in a 3 × 3 grid of rooms; doors connect rooms that share a wall. Each minute the mouse leaves its room through a door chosen uniformly at random. It starts in a corner room, and there is cheese in the center room. What is the expected number of moves until the mouse first enters the center room? Give an exact number.
Related problems & prerequisites
Worth solving first
- First Heads Wins 3.0/10
- Seven Before Eight 2.0/10
Source: Classic exercise in wide circulation; no traceable original source. Statement written for AxiomIQ.