A rook begins at a corner of an $8 \times 8$ chessboard. Every minute, it makes a legal move, where each move has the same probability of being chosen. What is the expected number of minutes before the rook reaches the opposite corner?

Source: 2015 HMMT November Team Round, Problem 8.

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 7 million people

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Your answer seems reasonable.
Find out if you're right!