A353060 Solution to Snake Numbers Problems from 1 to n for an n X n square grid with chess knight moves (see Comments).

1, 1, 3, 13, 15, 36, 39, 64

Offset: 1

Author

Rodolfo Kurchan, Apr 20 2022

Keywords

• nonn
• more

Comments

On an n X n square board we draw a path with squares that we number 1, 2, ..., n, 1, 2, ..., n, 1, ... of the greatest length, which will be a(n). The path advances from one number to the next with a knight move; after n it goes back to number 1. There cannot be repeated numbers in the same row or column.

Examples

			a(5) = 15 by _Rodolfo Kurchan_:
  +---+---+---+---+---+
  |   | 04| 12|   |   |
  +---+---+---+---+---+
  |   |   |   | 05| 13|
  +---+---+---+---+---+
  | 03| 11| 14| 22| 25|
  +---+---+---+---+---+
  | 15| 23|   | 01|   |
  +---+---+---+---+---+
  |   | 02| 21| 24|   |
  +---+---+---+---+---+
First digit of the 2 digits number indicates the order of the path, second digit indicates the number of the "snake" path that cannot be repeated in same row or column.
In case of a(5) it is 01, 02, 03, 04, 05, 11, 12, 13, 14, 15, 21, 22, 23, 24, 25 and then it is impossible go to 31 because number 1 will be repeated in the row or column.
a(6), a(7) and a(8) solutions found by computer from Giorgio Vecchi.
		

Links

• Rodolfo Kurchan, Puzzle Fun, Snake Number Problem

Crossrefs

Cf. A353259.