

A353060


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


3




OFFSET

1,3


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.


LINKS



EXAMPLE

++++++
  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.


CROSSREFS



KEYWORD

nonn,more


AUTHOR



STATUS

approved



