On an 8x8 board, a knight is on the second square of the last row. Only moving upwards, how many routes to the top?

Question

In chess, a knight moves in L-shaped jumps consisting of two squares along a row or column plus one square at a right angle. If it can only move up the board, how many routes can it take to reach any square on the top row of the board?

Gareth McCaughan · Answer

The easiest way to do this, I think, is

The answer is

and here are the calculations:

On an 8x8 board, a knight is on the second square of the last row. Only moving upwards, how many routes to the top?

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