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

Author

Jon Perry, Mar 12 2013

Keywords

• nonn

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).

Examples

			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.