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A365437
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Number of ways of placing n non-attacking queens on an n X n board, with no three queens in a straight line.
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0
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1, 1, 0, 0, 2, 0, 0, 0, 8, 32, 40, 96, 410, 1392, 4416, 18752, 71486, 235056, 1001972, 4285920, 21887710, 94619480, 422557444, 2101021824, 11943690634, 61113195600
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OFFSET
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0,5
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REFERENCES
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Donald E. Knuth, Constraint Satisfaction (volume 4, fascicle 7a of The Art of Computer Programming, in preparation).
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LINKS
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Sam Loyd, A Crow Puzzle, in Brooklyn Daily Eagle, 20 December 1896, for the case n=8.
Wikipedia, Eight Queens Puzzle, [Of the twelve fundamental solutions on the 8x8 chessboard, only "Solution 10" satisfies no three in a line. In "Solution 9" the queens on a5, e3 and g2 are in one line. - Vaclav Kotesovec, Nov 08 2023]
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EXAMPLE
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For n=8, place queens for rows 1..8 into columns 3,6,8,2,4,1,7,5, i.e.,
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+-----------------+
| . . Q . . . . . |
| . . . . . Q . . |
| . . . . . . . Q |
| . Q . . . . . . |
| . . . Q . . . . |
| Q . . . . . . . |
| . . . . . . Q . |
| . . . . Q . . . |
+-----------------+
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and rotate and/or reflect to get the other seven ways.
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(Note that solutions such as
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+-----------------+
| . . Q . . . . . |
| . . . . . Q . . |
| . . . Q . . . . |
| Q . . . . . . . |
| . . . . . . . Q |
| . . . . Q . . . |
| . . . . . . Q . |
| . Q . . . . . . |
+-----------------+
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do not count as the queens on rows 4, 6, and 7 are in a straight line.)
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CROSSREFS
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KEYWORD
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nonn,more,changed
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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