. A chess knight has injured his leg and is limping. He alternates between a normal move and a short move where he moves to any diagonally neighbouring cell.

![](https://cdn.mathpix.com/cropped/2024_04_17_6a5543a8a260575a56cdg-05.jpg?height=315&width=317&top_left_y=385&top_left_x=732)

Normal move

![](https://cdn.mathpix.com/cropped/2024_04_17_6a5543a8a260575a56cdg-05.jpg?height=199&width=195&top_left_y=503&top_left_x=1136)

Short move

The limping knight moves on a $5 \times 6$ cell chessboard starting with a normal move. What is the largest number of moves he can make if he is starting from a cell of his own choice and is not allowed to visit any cell (including the initial cell) more than once?

#
Answer: 25 moves.

Let us enumerate the rows of the chessboard with numbers 1 to 5 . We will consider only the short moves. Each short move connects two cells from rows of different parity and no two short moves has a common cell. Therefore there can be at most 12 short moves as there are just 12 cells in the rows of even parity (second and fourth). It means that the maximal number of moves is 12 short +13 normal $=25$ moves.

The figure shows that 25 moves indeed can be made.

| 19 | 5 | 7 | 9 | 11 |  |
| :---: | :---: | :---: | :---: | :---: | :---: |
| 4 | 18 | 20 | 6 | 8 | 10 |
|  | 2 |  | 21 | 26 | 12 |
| 17 | 3 | 24 | 15 | 13 | 22 |
| 2 | 16 | 14 | 25 | 23 |  |