A216196 A diagonalized Sudoku torus.

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

Offset

1,2

Comments

This Sudoku contains 27 (internal and external) diagonals.

Conjecture: This is the maximum for a Xoox-free 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: A360073 A074044 A079827 * A028901 A081597 A351578

Adjacent sequences: A216193 A216194 A216195 * A216197 A216198 A216199

Keyword

nonn

Author

Jon Perry, Mar 12 2013

Status

approved