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%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
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