

A216196


A diagonalized Sudoku torus.


0



1, 2, 3, 4, 5, 6, 7, 8, 9, 6, 5, 4, 9, 8, 7, 3, 2, 1, 7, 8, 9, 1, 2, 3, 4, 5, 6, 2, 3, 1, 5, 6, 4, 8, 9, 7, 4, 6, 5, 7, 9, 8, 1, 3, 2, 8, 9, 7, 2, 3, 1, 5, 6, 4, 3, 1, 2, 6, 4, 5, 9, 7, 8, 5, 4, 6, 8, 7, 9, 2, 1, 3, 9, 7, 8, 3, 1, 2, 6, 4, 5
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OFFSET

1,2


COMMENTS

This Sudoku contains 27 (internal and external) diagonals.
Conjecture: This is the maximum for a Xooxfree grid.
More are possible (45 in the example) if the grid is allowed to contain Xoox's (ambiguous Sudoku's).


LINKS

Table of n, a(n) for n=1..81.


EXAMPLE

1 2 3 4 5 6 7 8 9
6 5 4 9 8 7 3 2 1
7 8 9 1 2 3 4 5 6
2 3 1 5 6 4 8 9 7
4 6 5 7 9 8 1 3 2
8 9 7 2 3 1 5 6 4
3 1 2 6 4 5 9 7 8
5 4 6 8 7 9 2 1 3
9 7 8 3 1 2 6 4 5
A Xoox is for example:
14
41
and is not necessarily adjacent.
This grid:
1 8 3 4 2 6 7 5 9
6 5 4 9 8 7 3 2 1
7 2 9 1 5 3 4 8 6
2 9 1 5 3 4 8 6 7
4 6 5 7 9 8 1 3 2
8 3 7 2 6 1 5 9 4
3 7 2 6 1 5 9 4 8
5 4 6 8 7 9 2 1 3
9 1 8 3 4 2 6 7 5
contains 45 diagonals, but also 36 Xoox's, for example the 1 and 5 on rows 1 and 8.


CROSSREFS

Cf. A211172.
Sequence in context: A122425 A074044 A079827 * A028901 A081597 A245351
Adjacent sequences: A216193 A216194 A216195 * A216197 A216198 A216199


KEYWORD

nonn


AUTHOR

Jon Perry, Mar 12 2013


STATUS

approved



