|
|
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
|
|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|