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A374013
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n-queens completion threshold. The maximum number such that placing a(n) or fewer mutually non-attacking queens on an n X n chessboard is always completeable to a full n-queen configuration.
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0
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0, 1, 0, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4
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OFFSET
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4,7
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COMMENTS
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For n large enough, n/60 <= a(n) <= 0.241*n [Glock et al.].
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LINKS
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EXAMPLE
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There are 2 solutions to the 4-queens problem:
. Q . .
. . . Q
Q . . .
. . Q .
and
. . Q .
Q . . .
. . . Q
. Q . .
Neither of these has a queen in the upper left corner, so placing a queen here will definitely make the configuration non-completable, while placing no queens is completable, see the two examples.
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PROG
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(C) \\ see github link
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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