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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 (list; graph; refs; listen; history; text; internal format)
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: A122425 A074044 A079827 * A028901 A081597 A245351

Adjacent sequences:  A216193 A216194 A216195 * A216197 A216198 A216199

KEYWORD

nonn

AUTHOR

Jon Perry, Mar 12 2013

STATUS

approved

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Last modified October 18 20:10 EDT 2018. Contains 316325 sequences. (Running on oeis4.)