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A328283
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The maximum number m such that m white, m black and m red queens can coexist on an n X n chessboard without attacking each other.
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1
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0, 0, 0, 1, 1, 2, 3, 4, 5, 7, 8, 10, 12, 14
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OFFSET
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1,6
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COMMENTS
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This is the peaceable queens problem (A250000) for 3 players.
For n >= 11, it seems that a(n) is simply 2n - 14. However this turns out to be false as a(18) >= 23.
In the limit of large n, Arthur O'Dwyer (see links) showed that the optimal value is lower bounded by 0.0718*n^2. All currently known best solutions follow this formula (when rounded down). - M. A. Achterberg, Dec 01 2022
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LINKS
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EXAMPLE
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a(8) = 4, because 4 queens of each color can co-exist without attacking queens of another color. Note that in this case both red (6) and white (5) have more than 4 queens.
+ - - - - - - - - +
| R . R . R . . . |
| R . . . . . . . |
| . . . . . W . W |
| R . R . . . . . |
| . . . . . W . W |
| . B . B . . . . |
| . . . . . . . W |
| . B . B . . . . |
+ - - - - - - - - +
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CROSSREFS
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KEYWORD
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nonn,more,hard
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AUTHOR
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STATUS
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approved
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