2022 LMT Spring Accuracy Problem 9
Source:
September 29, 2023
combinatorics
Problem Statement
A rook is randomly placed on an otherwise empty chessboard. Owen makes moves with the rook by randomly choosing of the possible moves. Find the expected value of the number of moves it takes Owen to move the rook to the top left square. Note that a rook can move any number of squares either in the horizontal or vertical direction each move.