A knight from corner to opposite corner

Question

A knight starts on a1 of an empty chessboard.

What is the smallest number of moves it needs to reach h8, the opposite corner? Give a route, prove no shorter route exists, and explain why an odd number of moves is impossible.

Accepted Answer

Six moves. Lower bound. Going from a1 to h8 requires moving 7 columns to the right and 7 rows up, a total of 14 squares of displacement. A knight move covers at most 3 squares of displacement (2 + 1). So at least 14/3, that is at least 5 moves. But 5 is odd, and a1 and h8 are the same colour; since a knight changes colour with every move, the number of moves must be even. So at least 6. A six-move route. a1, c2, d4, e6, g5, f7, h8. Check: a1 to c2 (two right, one up), c2 to d4 (one right, two up), d4 to e6 (one right, two up), e6 to g5 (two right, one down), g5 to f7 (one left, two up), f7 to…

A knight from corner to opposite corner

Your answer

Discussion

Learn the concepts

Related questions