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A diagonalized Sudoku torus.
0

%I #13 Apr 19 2013 10:28:36

%S 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,

%T 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,

%U 9,2,1,3,9,7,8,3,1,2,6,4,5

%N A diagonalized Sudoku torus.

%C This Sudoku contains 27 (internal and external) diagonals.

%C Conjecture: This is the maximum for a Xoox-free grid.

%C More are possible (45 in the example) if the grid is allowed to contain Xoox's (ambiguous Sudoku's).

%e 1 2 3 4 5 6 7 8 9

%e 6 5 4 9 8 7 3 2 1

%e 7 8 9 1 2 3 4 5 6

%e 2 3 1 5 6 4 8 9 7

%e 4 6 5 7 9 8 1 3 2

%e 8 9 7 2 3 1 5 6 4

%e 3 1 2 6 4 5 9 7 8

%e 5 4 6 8 7 9 2 1 3

%e 9 7 8 3 1 2 6 4 5

%e A Xoox is for example:

%e 14

%e 41

%e and is not necessarily adjacent.

%e This grid:

%e 1 8 3 4 2 6 7 5 9

%e 6 5 4 9 8 7 3 2 1

%e 7 2 9 1 5 3 4 8 6

%e 2 9 1 5 3 4 8 6 7

%e 4 6 5 7 9 8 1 3 2

%e 8 3 7 2 6 1 5 9 4

%e 3 7 2 6 1 5 9 4 8

%e 5 4 6 8 7 9 2 1 3

%e 9 1 8 3 4 2 6 7 5

%e contains 45 diagonals, but also 36 Xoox's, for example the 1 and 5 on rows 1 and 8.

%Y Cf. A211172.

%K nonn

%O 1,2

%A _Jon Perry_, Mar 12 2013