Fundamental Solutions to the N+3 Queens Problem for N=8,9 ... fileBoard of Order 8 Board of Order 9...

Board of Order 8 Board of Order 9 Board of Order 10

Fundamental Solutions to the N + 3 QueensProblem for N = 8, 9, and 10

Doug Chatham

March 9, 2007


Solution 1P: [1, 3], [3, 4], [4, 1]Q: [0, 3], [1, 1], [1, 6], [2, 4], [3, 2], [3, 7], [4, 0], [4, 5], [5, 3], [6, 1], [7, 4]

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Solution 1P: [2, 6], [3, 4], [4, 2]Q: [0, 1], [1, 6], [2, 4], [2, 8], [3, 2], [3, 6], [4, 0], [4, 4], [5, 2], [6, 7], [7, 5], [8, 3]

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Solution 2P: [1, 3], [2, 5], [4, 2]Q: [0, 3], [1, 0], [1, 5], [2, 2], [2, 7], [3, 4], [4, 1], [4, 6], [5, 8], [6, 2], [7, 5], [8, 3]

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Solution 3P: [3, 4], [3, 7], [5, 1]Q: [0, 7], [1, 2], [2, 4], [3, 1], [3, 6], [3, 8], [4, 3], [5, 0], [5, 5], [6, 7], [7, 1], [8, 4]

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Solution 4P: [3, 6], [4, 4], [5, 2]Q: [0, 3], [1, 1], [2, 6], [3, 4], [3, 8], [4, 2], [4, 6], [5, 0], [5, 4], [6, 2], [7, 7], [8, 5]

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Solution 5P: [3, 4], [4, 5], [5, 2]Q: [0, 7], [1, 4], [2, 2], [3, 0], [3, 5], [4, 3], [4, 8], [5, 1], [5, 6], [6, 4], [7, 2], [8, 5]

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Solution 6P: [2, 2], [4, 6], [5, 4]Q: [0, 2], [1, 8], [2, 1], [2, 6], [3, 4], [4, 2], [4, 7], [5, 0], [5, 5], [6, 3], [7, 6], [8, 4]

0ZqZ0Z0Z0Z0Z0Z0Z0l0lpZ0ZqZ0Z0Z0l0Z0Z0ZqZ0Zpl0l0Z0oqZ0Z0Z0l0Z0Z0Z0Z0Z0l0Z0Z0ZqZ0Z0


Solution 1P: [1, 4], [3, 7], [4, 2]Q: [0, 4], [1, 2], [1, 7], [2, 5], [3, 3], [3, 8], [4, 1], [4, 6], [5, 9], [6, 0], [7, 2], [8, 4], [9, 7]

0Z0ZqZ0Z0ZZ0l0o0ZqZ00Z0Z0l0Z0ZZ0ZqZ0Zpl00lpZ0ZqZ0ZZ0Z0Z0Z0ZqqZ0Z0Z0Z0ZZ0l0Z0Z0Z00Z0ZqZ0Z0ZZ0Z0Z0ZqZ0


Solution 2P: [2, 4], [3, 7], [4, 3]Q: [0, 7], [1, 4], [2, 1], [2, 6], [3, 3], [3, 8], [4, 0], [4, 5], [5, 2], [6, 4], [7, 9], [8, 7], [9, 3]

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Solution 3P: [1, 4], [2, 6], [4, 3]Q: [0, 4], [1, 0], [1, 6], [2, 3], [2, 9], [3, 6], [4, 2], [4, 4], [5, 7], [6, 1], [7, 3], [8, 5], [9, 8]

0Z0ZqZ0Z0Zl0Z0o0l0Z00Z0l0ZpZ0lZ0Z0Z0l0Z00ZqoqZ0Z0ZZ0Z0Z0ZqZ00l0Z0Z0Z0ZZ0ZqZ0Z0Z00Z0Z0l0Z0ZZ0Z0Z0Z0l0


Solution 4P: [1, 3], [3, 6], [4, 3]Q: [0, 3], [1, 0], [1, 6], [2, 3], [3, 5], [3, 9], [4, 2], [4, 7], [5, 4], [6, 1], [7, 3], [8, 8], [9, 6]

0Z0l0Z0Z0Zl0ZpZ0l0Z00Z0l0Z0Z0ZZ0Z0Zqo0Zq0Zqo0Z0l0ZZ0Z0l0Z0Z00l0Z0Z0Z0ZZ0ZqZ0Z0Z00Z0Z0Z0ZqZZ0Z0Z0l0Z0


Solution 5P: [1, 4], [3, 6], [4, 3]Q: [0, 4], [1, 0], [1, 6], [2, 3], [3, 5], [3, 9], [4, 2], [4, 7], [5, 4], [6, 1], [7, 3], [8, 8], [9, 6]

0Z0ZqZ0Z0Zl0Z0o0l0Z00Z0l0Z0Z0ZZ0Z0Zqo0Zq0Zqo0Z0l0ZZ0Z0l0Z0Z00l0Z0Z0Z0ZZ0ZqZ0Z0Z00Z0Z0Z0ZqZZ0Z0Z0l0Z0


Solution 6P: [1, 3], [3, 6], [4, 4]Q: [0, 3], [1, 1], [1, 6], [2, 4], [3, 2], [3, 9], [4, 0], [4, 5], [5, 8], [6, 4], [7, 7], [8, 3], [9, 6]

0Z0l0Z0Z0ZZqZpZ0l0Z00Z0ZqZ0Z0ZZ0l0Z0o0ZqqZ0Zpl0Z0ZZ0Z0Z0Z0l00Z0ZqZ0Z0ZZ0Z0Z0ZqZ00Z0l0Z0Z0ZZ0Z0Z0l0Z0


Solution 7P: [1, 3], [3, 6], [4, 4]Q: [0, 3], [1, 1], [1, 6], [2, 4], [3, 2], [3, 9], [4, 0], [4, 7], [5, 5], [6, 3], [7, 8], [8, 6], [9, 4]

0Z0l0Z0Z0ZZqZpZ0l0Z00Z0ZqZ0Z0ZZ0l0Z0o0ZqqZ0ZpZ0l0ZZ0Z0ZqZ0Z00Z0l0Z0Z0ZZ0Z0Z0Z0l00Z0Z0ZqZ0ZZ0Z0l0Z0Z0


Solution 8P: [3, 3], [3, 6], [4, 4]Q: [0, 3], [1, 8], [2, 6], [3, 2], [3, 4], [3, 9], [4, 0], [4, 7], [5, 5], [6, 3], [7, 1], [8, 6], [9, 4]

0Z0l0Z0Z0ZZ0Z0Z0Z0l00Z0Z0ZqZ0ZZ0lpl0o0ZqqZ0ZpZ0l0ZZ0Z0ZqZ0Z00Z0l0Z0Z0ZZqZ0Z0Z0Z00Z0Z0ZqZ0ZZ0Z0l0Z0Z0


Solution 9P: [2, 5], [3, 1], [4, 4]Q: [0, 5], [1, 1], [2, 4], [2, 6], [3, 0], [3, 9], [4, 3], [4, 7], [5, 5], [6, 2], [7, 8], [8, 1], [9, 4]

0Z0Z0l0Z0ZZqZ0Z0Z0Z00Z0ZqoqZ0ZlpZ0Z0Z0Zq0Z0lpZ0l0ZZ0Z0ZqZ0Z00ZqZ0Z0Z0ZZ0Z0Z0Z0l00l0Z0Z0Z0ZZ0Z0l0Z0Z0


Solution 10P: [1, 6], [3, 2], [4, 4]Q: [0, 6], [1, 4], [1, 9], [2, 2], [3, 0], [3, 5], [4, 3], [4, 8], [5, 6], [6, 2], [7, 7], [8, 1], [9, 4]

0Z0Z0ZqZ0ZZ0Z0l0o0Zq0ZqZ0Z0Z0Zl0o0ZqZ0Z00Z0lpZ0ZqZZ0Z0Z0l0Z00ZqZ0Z0Z0ZZ0Z0Z0ZqZ00l0Z0Z0Z0ZZ0Z0l0Z0Z0


Solution 11P: [2, 5], [3, 6], [4, 4]Q: [0, 5], [1, 1], [2, 4], [2, 6], [3, 0], [3, 9], [4, 3], [4, 7], [5, 5], [6, 2], [7, 8], [8, 6], [9, 4]

0Z0Z0l0Z0ZZqZ0Z0Z0Z00Z0ZqoqZ0Zl0Z0Z0o0Zq0Z0lpZ0l0ZZ0Z0ZqZ0Z00ZqZ0Z0Z0ZZ0Z0Z0Z0l00Z0Z0ZqZ0ZZ0Z0l0Z0Z0


Solution 12P: [1, 4], [3, 8], [4, 4]Q: [0, 4], [1, 1], [1, 8], [2, 4], [3, 0], [3, 9], [4, 3], [4, 7], [5, 5], [6, 2], [7, 8], [8, 6], [9, 4]

0Z0ZqZ0Z0ZZqZ0o0Z0l00Z0ZqZ0Z0Zl0Z0Z0Z0oq0Z0lpZ0l0ZZ0Z0ZqZ0Z00ZqZ0Z0Z0ZZ0Z0Z0Z0l00Z0Z0ZqZ0ZZ0Z0l0Z0Z0


Solution 13P: [1, 5], [3, 8], [4, 4]Q: [0, 5], [1, 1], [1, 8], [2, 4], [3, 0], [3, 9], [4, 3], [4, 7], [5, 5], [6, 2], [7, 8], [8, 6], [9, 4]

0Z0Z0l0Z0ZZqZ0ZpZ0l00Z0ZqZ0Z0Zl0Z0Z0Z0oq0Z0lpZ0l0ZZ0Z0ZqZ0Z00ZqZ0Z0Z0ZZ0Z0Z0Z0l00Z0Z0ZqZ0ZZ0Z0l0Z0Z0


Solution 14P: [2, 5], [4, 2], [4, 7]Q: [0, 7], [1, 5], [2, 2], [2, 8], [3, 5], [4, 1], [4, 3], [4, 9], [5, 6], [6, 0], [7, 2], [8, 4], [9, 7]

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Solution 15P: [3, 6], [4, 2], [4, 7]Q: [0, 6], [1, 8], [2, 2], [3, 5], [3, 7], [4, 1], [4, 3], [4, 9], [5, 6], [6, 0], [7, 2], [8, 4], [9, 7]

0Z0Z0ZqZ0ZZ0Z0Z0Z0l00ZqZ0Z0Z0ZZ0Z0ZqoqZ00lpl0Z0o0lZ0Z0Z0l0Z0qZ0Z0Z0Z0ZZ0l0Z0Z0Z00Z0ZqZ0Z0ZZ0Z0Z0ZqZ0


Solution 16P: [2, 3], [3, 5], [5, 1]Q: [0, 5], [1, 3], [2, 1], [2, 6], [3, 3], [3, 9], [4, 7], [5, 0], [5, 2], [6, 4], [7, 8], [8, 1], [9, 5]

0Z0Z0l0Z0ZZ0ZqZ0Z0Z00l0o0ZqZ0ZZ0ZqZpZ0Zq0Z0Z0Z0l0Zlpl0Z0Z0Z00Z0ZqZ0Z0ZZ0Z0Z0Z0l00l0Z0Z0Z0ZZ0Z0ZqZ0Z0


Solution 17P: [1, 6], [4, 5], [5, 1]Q: [0, 6], [1, 2], [1, 8], [2, 5], [3, 1], [4, 4], [4, 9], [5, 0], [5, 7], [6, 5], [7, 3], [8, 1], [9, 6]

0Z0Z0ZqZ0ZZ0l0Z0o0l00Z0Z0l0Z0ZZqZ0Z0Z0Z00Z0Zqo0Z0llpZ0Z0ZqZ00Z0Z0l0Z0ZZ0ZqZ0Z0Z00l0Z0Z0Z0ZZ0Z0Z0l0Z0


Solution 18P: [2, 6], [4, 5], [5, 1]Q: [0, 6], [1, 2], [2, 5], [2, 7], [3, 1], [4, 4], [4, 6], [5, 0], [5, 9], [6, 5], [7, 8], [8, 1], [9, 3]

0Z0Z0ZqZ0ZZ0l0Z0Z0Z00Z0Z0lpl0ZZqZ0Z0Z0Z00Z0ZqoqZ0ZlpZ0Z0Z0Zq0Z0Z0l0Z0ZZ0Z0Z0Z0l00l0Z0Z0Z0ZZ0ZqZ0Z0Z0


Solution 19P: [3, 4], [4, 6], [5, 1]Q: [0, 7], [1, 2], [2, 4], [3, 1], [3, 6], [4, 3], [4, 9], [5, 0], [5, 5], [6, 8], [7, 1], [8, 4], [9, 6]

0Z0Z0Z0l0ZZ0l0Z0Z0Z00Z0ZqZ0Z0ZZqZ0o0l0Z00Z0l0ZpZ0llpZ0ZqZ0Z00Z0Z0Z0ZqZZqZ0Z0Z0Z00Z0ZqZ0Z0ZZ0Z0Z0l0Z0


Solution 20P: [3, 2], [4, 6], [5, 1]Q: [0, 2], [1, 9], [2, 6], [3, 1], [3, 3], [4, 5], [4, 7], [5, 0], [5, 2], [6, 8], [7, 6], [8, 4], [9, 1]

0ZqZ0Z0Z0ZZ0Z0Z0Z0Zq0Z0Z0ZqZ0ZZqoqZ0Z0Z00Z0Z0lpl0Zlpl0Z0Z0Z00Z0Z0Z0ZqZZ0Z0Z0l0Z00Z0ZqZ0Z0ZZqZ0Z0Z0Z0


Solution 21P: [3, 6], [4, 4], [5, 2]Q: [0, 9], [1, 1], [2, 6], [3, 4], [3, 8], [4, 2], [4, 6], [5, 0], [5, 4], [6, 2], [7, 7], [8, 5], [9, 3]

0Z0Z0Z0Z0lZqZ0Z0Z0Z00Z0Z0ZqZ0ZZ0Z0l0o0l00ZqZpZqZ0Zl0o0l0Z0Z00ZqZ0Z0Z0ZZ0Z0Z0ZqZ00Z0Z0l0Z0ZZ0ZqZ0Z0Z0


Solution 22P: [2, 6], [4, 5], [5, 2]Q: [0, 6], [1, 2], [2, 5], [2, 7], [3, 1], [4, 4], [4, 8], [5, 0], [5, 6], [6, 3], [7, 9], [8, 2], [9, 5]

0Z0Z0ZqZ0ZZ0l0Z0Z0Z00Z0Z0lpl0ZZqZ0Z0Z0Z00Z0Zqo0ZqZl0o0Z0l0Z00Z0l0Z0Z0ZZ0Z0Z0Z0Zq0ZqZ0Z0Z0ZZ0Z0ZqZ0Z0


Solution 23P: [1, 6], [3, 2], [5, 3]Q: [0, 6], [1, 2], [1, 9], [2, 7], [3, 1], [3, 5], [4, 3], [5, 0], [5, 8], [6, 2], [7, 4], [8, 6], [9, 3]

0Z0Z0ZqZ0ZZ0l0Z0o0Zq0Z0Z0Z0l0ZZqo0ZqZ0Z00Z0l0Z0Z0Zl0ZpZ0Z0l00ZqZ0Z0Z0ZZ0Z0l0Z0Z00Z0Z0ZqZ0ZZ0ZqZ0Z0Z0


Solution 24P: [2, 7], [3, 2], [5, 3]Q: [0, 7], [1, 2], [2, 6], [2, 8], [3, 1], [3, 3], [4, 7], [5, 0], [5, 4], [6, 2], [7, 9], [8, 5], [9, 3]

0Z0Z0Z0l0ZZ0l0Z0Z0Z00Z0Z0ZqoqZZqoqZ0Z0Z00Z0Z0Z0l0Zl0Zpl0Z0Z00ZqZ0Z0Z0ZZ0Z0Z0Z0Zq0Z0Z0l0Z0ZZ0ZqZ0Z0Z0


Solution 25P: [1, 4], [3, 7], [5, 3]Q: [0, 4], [1, 2], [1, 7], [2, 5], [3, 3], [3, 8], [4, 6], [5, 0], [5, 9], [6, 3], [7, 1], [8, 4], [9, 7]

0Z0ZqZ0Z0ZZ0l0o0ZqZ00Z0Z0l0Z0ZZ0ZqZ0Zpl00Z0Z0ZqZ0Zl0ZpZ0Z0Zq0Z0l0Z0Z0ZZqZ0Z0Z0Z00Z0ZqZ0Z0ZZ0Z0Z0ZqZ0


Solution 26P: [3, 6], [4, 4], [5, 3]Q: [0, 3], [1, 1], [2, 6], [3, 4], [3, 8], [4, 2], [4, 6], [5, 0], [5, 4], [6, 9], [7, 7], [8, 5], [9, 3]

0Z0l0Z0Z0ZZqZ0Z0Z0Z00Z0Z0ZqZ0ZZ0Z0l0o0l00ZqZpZqZ0Zl0Zpl0Z0Z00Z0Z0Z0Z0lZ0Z0Z0ZqZ00Z0Z0l0Z0ZZ0ZqZ0Z0Z0


Solution 27P: [2, 5], [4, 7], [5, 3]Q: [0, 7], [1, 5], [2, 2], [2, 8], [3, 5], [4, 3], [4, 9], [5, 0], [5, 6], [6, 3], [7, 1], [8, 4], [9, 7]

0Z0Z0Z0l0ZZ0Z0ZqZ0Z00ZqZ0o0ZqZZ0Z0ZqZ0Z00Z0l0Z0o0ll0ZpZ0l0Z00Z0l0Z0Z0ZZqZ0Z0Z0Z00Z0ZqZ0Z0ZZ0Z0Z0ZqZ0


Solution 28P: [3, 6], [4, 7], [5, 3]Q: [0, 6], [1, 8], [2, 2], [3, 5], [3, 7], [4, 3], [4, 9], [5, 0], [5, 6], [6, 3], [7, 1], [8, 4], [9, 7]

0Z0Z0ZqZ0ZZ0Z0Z0Z0l00ZqZ0Z0Z0ZZ0Z0ZqoqZ00Z0l0Z0o0ll0ZpZ0l0Z00Z0l0Z0Z0ZZqZ0Z0Z0Z00Z0ZqZ0Z0ZZ0Z0Z0ZqZ0


Solution 29P: [2, 4], [3, 7], [5, 3]Q: [0, 4], [1, 2], [2, 0], [2, 7], [3, 5], [3, 9], [4, 3], [5, 1], [5, 8], [6, 4], [7, 7], [8, 3], [9, 6]

0Z0ZqZ0Z0ZZ0l0Z0Z0Z0qZ0ZpZ0l0ZZ0Z0ZqZpZq0Z0l0Z0Z0ZZqZpZ0Z0l00Z0ZqZ0Z0ZZ0Z0Z0ZqZ00Z0l0Z0Z0ZZ0Z0Z0l0Z0


Solution 30P: [1, 4], [3, 8], [5, 3]Q: [0, 4], [1, 2], [1, 8], [2, 0], [3, 5], [3, 9], [4, 3], [5, 1], [5, 8], [6, 4], [7, 7], [8, 3], [9, 6]

0Z0ZqZ0Z0ZZ0l0o0Z0l0qZ0Z0Z0Z0ZZ0Z0ZqZ0oq0Z0l0Z0Z0ZZqZpZ0Z0l00Z0ZqZ0Z0ZZ0Z0Z0ZqZ00Z0l0Z0Z0ZZ0Z0Z0l0Z0


Solution 31P: [1, 5], [3, 8], [5, 3]Q: [0, 5], [1, 2], [1, 8], [2, 0], [3, 5], [3, 9], [4, 3], [5, 1], [5, 8], [6, 4], [7, 7], [8, 3], [9, 6]

0Z0Z0l0Z0ZZ0l0ZpZ0l0qZ0Z0Z0Z0ZZ0Z0ZqZ0oq0Z0l0Z0Z0ZZqZpZ0Z0l00Z0ZqZ0Z0ZZ0Z0Z0ZqZ00Z0l0Z0Z0ZZ0Z0Z0l0Z0


Solution 32P: [1, 6], [2, 4], [5, 3]Q: [0, 6], [1, 4], [1, 8], [2, 0], [2, 6], [3, 3], [4, 9], [5, 2], [5, 7], [6, 4], [7, 1], [8, 3], [9, 5]

0Z0Z0ZqZ0ZZ0Z0l0o0l0qZ0ZpZqZ0ZZ0ZqZ0Z0Z00Z0Z0Z0Z0lZ0lpZ0ZqZ00Z0ZqZ0Z0ZZqZ0Z0Z0Z00Z0l0Z0Z0ZZ0Z0ZqZ0Z0


Solution 33P: [2, 3], [3, 6], [5, 3]Q: [0, 3], [1, 8], [2, 0], [2, 6], [3, 3], [3, 9], [4, 6], [5, 2], [5, 4], [6, 7], [7, 1], [8, 3], [9, 5]

0Z0l0Z0Z0ZZ0Z0Z0Z0l0qZ0o0ZqZ0ZZ0ZqZ0o0Zq0Z0Z0ZqZ0ZZ0lpl0Z0Z00Z0Z0Z0l0ZZqZ0Z0Z0Z00Z0l0Z0Z0ZZ0Z0ZqZ0Z0


Solution 34P: [2, 5], [3, 6], [5, 3]Q: [0, 5], [1, 8], [2, 0], [2, 6], [3, 3], [3, 9], [4, 6], [5, 2], [5, 4], [6, 7], [7, 1], [8, 3], [9, 5]

0Z0Z0l0Z0ZZ0Z0Z0Z0l0qZ0Z0oqZ0ZZ0ZqZ0o0Zq0Z0Z0ZqZ0ZZ0lpl0Z0Z00Z0Z0Z0l0ZZqZ0Z0Z0Z00Z0l0Z0Z0ZZ0Z0ZqZ0Z0


Solution 35P: [2, 5], [4, 7], [5, 3]Q: [0, 7], [1, 5], [2, 3], [2, 8], [3, 5], [4, 0], [4, 9], [5, 2], [5, 4], [6, 6], [7, 1], [8, 3], [9, 7]

0Z0Z0Z0l0ZZ0Z0ZqZ0Z00Z0l0o0ZqZZ0Z0ZqZ0Z0qZ0Z0Z0o0lZ0lpl0Z0Z00Z0Z0ZqZ0ZZqZ0Z0Z0Z00Z0l0Z0Z0ZZ0Z0Z0ZqZ0


Solution 36P: [3, 6], [4, 7], [5, 3]Q: [0, 6], [1, 8], [2, 3], [3, 5], [3, 7], [4, 0], [4, 9], [5, 2], [5, 4], [6, 6], [7, 1], [8, 3], [9, 7]

0Z0Z0ZqZ0ZZ0Z0Z0Z0l00Z0l0Z0Z0ZZ0Z0ZqoqZ0qZ0Z0Z0o0lZ0lpl0Z0Z00Z0Z0ZqZ0ZZqZ0Z0Z0Z00Z0l0Z0Z0ZZ0Z0Z0ZqZ0


Solution 37P: [2, 3], [4, 7], [5, 3]Q: [0, 3], [1, 7], [2, 0], [2, 9], [3, 3], [4, 6], [4, 8], [5, 2], [5, 4], [6, 7], [7, 1], [8, 3], [9, 5]

0Z0l0Z0Z0ZZ0Z0Z0ZqZ0qZ0o0Z0Z0lZ0ZqZ0Z0Z00Z0Z0ZqoqZZ0lpl0Z0Z00Z0Z0Z0l0ZZqZ0Z0Z0Z00Z0l0Z0Z0ZZ0Z0ZqZ0Z0


Solution 38P: [2, 5], [4, 7], [5, 3]Q: [0, 5], [1, 7], [2, 0], [2, 9], [3, 3], [4, 6], [4, 8], [5, 2], [5, 4], [6, 7], [7, 1], [8, 3], [9, 5]

0Z0Z0l0Z0ZZ0Z0Z0ZqZ0qZ0Z0o0Z0lZ0ZqZ0Z0Z00Z0Z0ZqoqZZ0lpl0Z0Z00Z0Z0Z0l0ZZqZ0Z0Z0Z00Z0l0Z0Z0ZZ0Z0ZqZ0Z0


Solution 39P: [1, 4], [2, 6], [5, 4]Q: [0, 4], [1, 0], [1, 6], [2, 3], [2, 9], [3, 6], [4, 4], [5, 1], [5, 7], [6, 4], [7, 2], [8, 5], [9, 8]

0Z0ZqZ0Z0Zl0Z0o0l0Z00Z0l0ZpZ0lZ0Z0Z0l0Z00Z0ZqZ0Z0ZZqZ0o0ZqZ00Z0ZqZ0Z0ZZ0l0Z0Z0Z00Z0Z0l0Z0ZZ0Z0Z0Z0l0


Solution 40P: [1, 3], [3, 7], [5, 4]Q: [0, 3], [1, 0], [1, 7], [2, 2], [3, 4], [3, 8], [4, 6], [5, 1], [5, 9], [6, 3], [7, 5], [8, 7], [9, 4]

0Z0l0Z0Z0Zl0ZpZ0ZqZ00ZqZ0Z0Z0ZZ0Z0l0Zpl00Z0Z0ZqZ0ZZqZ0o0Z0Zq0Z0l0Z0Z0ZZ0Z0ZqZ0Z00Z0Z0Z0l0ZZ0Z0l0Z0Z0


Solution 41P: [3, 3], [3, 7], [5, 4]Q: [0, 7], [1, 5], [2, 3], [3, 0], [3, 6], [3, 8], [4, 4], [5, 1], [5, 9], [6, 4], [7, 2], [8, 7], [9, 3]

0Z0Z0Z0l0ZZ0Z0ZqZ0Z00Z0l0Z0Z0Zl0ZpZ0lpl00Z0ZqZ0Z0ZZqZ0o0Z0Zq0Z0ZqZ0Z0ZZ0l0Z0Z0Z00Z0Z0Z0l0ZZ0ZqZ0Z0Z0


Solution 42P: [1, 3], [3, 7], [5, 4]Q: [0, 3], [1, 0], [1, 5], [2, 7], [3, 1], [3, 9], [4, 4], [5, 2], [5, 6], [6, 8], [7, 3], [8, 7], [9, 4]

0Z0l0Z0Z0Zl0ZpZqZ0Z00Z0Z0Z0l0ZZqZ0Z0ZpZq0Z0ZqZ0Z0ZZ0l0o0l0Z00Z0Z0Z0ZqZZ0ZqZ0Z0Z00Z0Z0Z0l0ZZ0Z0l0Z0Z0


Solution 43P: [1, 3], [3, 7], [5, 4]Q: [0, 3], [1, 0], [1, 7], [2, 4], [3, 1], [3, 8], [4, 5], [5, 2], [5, 9], [6, 6], [7, 3], [8, 7], [9, 4]

0Z0l0Z0Z0Zl0ZpZ0ZqZ00Z0ZqZ0Z0ZZqZ0Z0Zpl00Z0Z0l0Z0ZZ0l0o0Z0Zq0Z0Z0ZqZ0ZZ0ZqZ0Z0Z00Z0Z0Z0l0ZZ0Z0l0Z0Z0


Solution 44P: [1, 6], [4, 1], [5, 4]Q: [0, 6], [1, 4], [1, 8], [2, 1], [3, 5], [4, 0], [4, 9], [5, 2], [5, 6], [6, 4], [7, 7], [8, 1], [9, 3]

0Z0Z0ZqZ0ZZ0Z0l0o0l00l0Z0Z0Z0ZZ0Z0ZqZ0Z0qo0Z0Z0Z0lZ0l0o0l0Z00Z0ZqZ0Z0ZZ0Z0Z0ZqZ00l0Z0Z0Z0ZZ0ZqZ0Z0Z0


Solution 45P: [1, 4], [2, 6], [5, 4]Q: [0, 4], [1, 0], [1, 6], [2, 4], [2, 9], [3, 6], [4, 1], [5, 3], [5, 5], [6, 7], [7, 2], [8, 4], [9, 8]

0Z0ZqZ0Z0Zl0Z0o0l0Z00Z0ZqZpZ0lZ0Z0Z0l0Z00l0Z0Z0Z0ZZ0ZqoqZ0Z00Z0Z0Z0l0ZZ0l0Z0Z0Z00Z0ZqZ0Z0ZZ0Z0Z0Z0l0


Solution 46P: [3, 7], [5, 1], [5, 6]Q: [0, 7], [1, 3], [2, 1], [3, 6], [3, 8], [4, 2], [5, 0], [5, 5], [5, 9], [6, 7], [7, 1], [8, 4], [9, 6]

0Z0Z0Z0l0ZZ0ZqZ0Z0Z00l0Z0Z0Z0ZZ0Z0Z0lpl00ZqZ0Z0Z0ZlpZ0Zqo0Zq0Z0Z0Z0l0ZZqZ0Z0Z0Z00Z0ZqZ0Z0ZZ0Z0Z0l0Z0


Solution 47P: [3, 4], [5, 1], [5, 7]Q: [0, 7], [1, 2], [2, 4], [3, 1], [3, 8], [4, 3], [5, 0], [5, 5], [5, 9], [6, 7], [7, 1], [8, 4], [9, 6]

0Z0Z0Z0l0ZZ0l0Z0Z0Z00Z0ZqZ0Z0ZZqZ0o0Z0l00Z0l0Z0Z0ZlpZ0ZqZpZq0Z0Z0Z0l0ZZqZ0Z0Z0Z00Z0ZqZ0Z0ZZ0Z0Z0l0Z0


Solution 48P: [3, 6], [5, 5], [6, 1]Q: [0, 3], [1, 6], [2, 2], [3, 5], [3, 7], [4, 1], [5, 4], [5, 6], [6, 0], [6, 9], [7, 5], [8, 8], [9, 1]

0Z0l0Z0Z0ZZ0Z0Z0l0Z00ZqZ0Z0Z0ZZ0Z0ZqoqZ00l0Z0Z0Z0ZZ0Z0lpl0Z0qo0Z0Z0Z0lZ0Z0ZqZ0Z00Z0Z0Z0ZqZZqZ0Z0Z0Z0


Solution 49P: [1, 5], [4, 6], [6, 2]Q: [0, 5], [1, 2], [1, 9], [2, 6], [3, 1], [4, 3], [4, 7], [5, 5], [6, 0], [6, 8], [7, 2], [8, 4], [9, 6]

0Z0Z0l0Z0ZZ0l0ZpZ0Zq0Z0Z0ZqZ0ZZqZ0Z0Z0Z00Z0l0Zpl0ZZ0Z0ZqZ0Z0qZpZ0Z0ZqZZ0l0Z0Z0Z00Z0ZqZ0Z0ZZ0Z0Z0l0Z0


Solution 50P: [2, 4], [4, 7], [6, 2]Q: [0, 2], [1, 4], [2, 1], [2, 7], [3, 4], [4, 6], [4, 8], [5, 3], [6, 0], [6, 9], [7, 7], [8, 5], [9, 2]

0ZqZ0Z0Z0ZZ0Z0l0Z0Z00l0ZpZ0l0ZZ0Z0l0Z0Z00Z0Z0ZqoqZZ0ZqZ0Z0Z0qZpZ0Z0Z0lZ0Z0Z0ZqZ00Z0Z0l0Z0ZZ0l0Z0Z0Z0


Solution 51P: [3, 3], [4, 7], [6, 2]Q: [0, 3], [1, 1], [2, 7], [3, 2], [3, 4], [4, 6], [4, 8], [5, 3], [6, 0], [6, 9], [7, 7], [8, 5], [9, 2]

0Z0l0Z0Z0ZZqZ0Z0Z0Z00Z0Z0Z0l0ZZ0lpl0Z0Z00Z0Z0ZqoqZZ0ZqZ0Z0Z0qZpZ0Z0Z0lZ0Z0Z0ZqZ00Z0Z0l0Z0ZZ0l0Z0Z0Z0


Solution 52P: [2, 4], [5, 6], [6, 2]Q: [0, 2], [1, 4], [2, 1], [2, 7], [3, 4], [4, 6], [5, 3], [5, 9], [6, 0], [6, 6], [7, 8], [8, 5], [9, 2]

0ZqZ0Z0Z0ZZ0Z0l0Z0Z00l0ZpZ0l0ZZ0Z0l0Z0Z00Z0Z0ZqZ0ZZ0ZqZ0o0ZqqZpZ0ZqZ0ZZ0Z0Z0Z0l00Z0Z0l0Z0ZZ0l0Z0Z0Z0


Solution 53P: [3, 3], [5, 6], [6, 2]Q: [0, 3], [1, 1], [2, 7], [3, 2], [3, 4], [4, 6], [5, 3], [5, 9], [6, 0], [6, 6], [7, 8], [8, 5], [9, 2]

0Z0l0Z0Z0ZZqZ0Z0Z0Z00Z0Z0Z0l0ZZ0lpl0Z0Z00Z0Z0ZqZ0ZZ0ZqZ0o0ZqqZpZ0ZqZ0ZZ0Z0Z0Z0l00Z0Z0l0Z0ZZ0l0Z0Z0Z0


Solution 54P: [2, 4], [5, 6], [6, 2]Q: [0, 2], [1, 4], [2, 1], [2, 6], [3, 4], [4, 9], [5, 5], [5, 7], [6, 0], [6, 3], [7, 8], [8, 6], [9, 2]

0ZqZ0Z0Z0ZZ0Z0l0Z0Z00l0ZpZqZ0ZZ0Z0l0Z0Z00Z0Z0Z0Z0lZ0Z0ZqoqZ0qZpl0Z0Z0ZZ0Z0Z0Z0l00Z0Z0ZqZ0ZZ0l0Z0Z0Z0


Solution 55P: [3, 3], [5, 6], [6, 2]Q: [0, 3], [1, 1], [2, 6], [3, 2], [3, 4], [4, 9], [5, 5], [5, 7], [6, 0], [6, 3], [7, 8], [8, 6], [9, 2]

0Z0l0Z0Z0ZZqZ0Z0Z0Z00Z0Z0ZqZ0ZZ0lpl0Z0Z00Z0Z0Z0Z0lZ0Z0ZqoqZ0qZpl0Z0Z0ZZ0Z0Z0Z0l00Z0Z0ZqZ0ZZ0l0Z0Z0Z0


Solution 56P: [3, 6], [4, 3], [6, 2]Q: [0, 3], [1, 6], [2, 4], [3, 2], [3, 7], [4, 0], [4, 5], [5, 3], [6, 1], [6, 9], [7, 6], [8, 8], [9, 2]

0Z0l0Z0Z0ZZ0Z0Z0l0Z00Z0ZqZ0Z0ZZ0l0Z0oqZ0qZ0o0l0Z0ZZ0ZqZ0Z0Z00lpZ0Z0Z0lZ0Z0Z0l0Z00Z0Z0Z0ZqZZ0l0Z0Z0Z0


Solution 57P: [1, 5], [4, 6], [6, 2]Q: [0, 5], [1, 2], [1, 9], [2, 4], [3, 6], [4, 0], [4, 8], [5, 3], [6, 1], [6, 5], [7, 7], [8, 2], [9, 6]

0Z0Z0l0Z0ZZ0l0ZpZ0Zq0Z0ZqZ0Z0ZZ0Z0Z0l0Z0qZ0Z0ZpZqZZ0ZqZ0Z0Z00lpZ0l0Z0ZZ0Z0Z0ZqZ00ZqZ0Z0Z0ZZ0Z0Z0l0Z0


Solution 58P: [1, 5], [4, 6], [6, 2]Q: [0, 5], [1, 2], [1, 9], [2, 6], [3, 3], [4, 0], [4, 7], [5, 4], [6, 1], [6, 8], [7, 5], [8, 2], [9, 6]

0Z0Z0l0Z0ZZ0l0ZpZ0Zq0Z0Z0ZqZ0ZZ0ZqZ0Z0Z0qZ0Z0Zpl0ZZ0Z0l0Z0Z00lpZ0Z0ZqZZ0Z0ZqZ0Z00ZqZ0Z0Z0ZZ0Z0Z0l0Z0


Solution 59P: [1, 5], [4, 6], [6, 2]Q: [0, 5], [1, 3], [1, 9], [2, 6], [3, 0], [4, 2], [4, 7], [5, 4], [6, 1], [6, 6], [7, 8], [8, 2], [9, 5]

0Z0Z0l0Z0ZZ0ZqZpZ0Zq0Z0Z0ZqZ0Zl0Z0Z0Z0Z00ZqZ0Zpl0ZZ0Z0l0Z0Z00lpZ0ZqZ0ZZ0Z0Z0Z0l00ZqZ0Z0Z0ZZ0Z0ZqZ0Z0


Solution 60P: [3, 6], [5, 5], [6, 2]Q: [0, 6], [1, 4], [2, 2], [3, 0], [3, 7], [4, 5], [5, 3], [5, 8], [6, 1], [6, 6], [7, 9], [8, 2], [9, 5]

0Z0Z0ZqZ0ZZ0Z0l0Z0Z00ZqZ0Z0Z0Zl0Z0Z0oqZ00Z0Z0l0Z0ZZ0ZqZpZ0l00lpZ0ZqZ0ZZ0Z0Z0Z0Zq0ZqZ0Z0Z0ZZ0Z0ZqZ0Z0


Solution 61P: [3, 6], [5, 5], [6, 2]Q: [0, 6], [1, 4], [2, 2], [3, 0], [3, 8], [4, 5], [5, 3], [5, 7], [6, 1], [6, 9], [7, 6], [8, 2], [9, 5]

0Z0Z0ZqZ0ZZ0Z0l0Z0Z00ZqZ0Z0Z0Zl0Z0Z0o0l00Z0Z0l0Z0ZZ0ZqZpZqZ00lpZ0Z0Z0lZ0Z0Z0l0Z00ZqZ0Z0Z0ZZ0Z0ZqZ0Z0


Solution 62P: [2, 5], [5, 6], [6, 3]Q: [0, 5], [1, 3], [2, 1], [2, 6], [3, 9], [4, 5], [5, 2], [5, 8], [6, 0], [6, 4], [7, 7], [8, 3], [9, 6]

0Z0Z0l0Z0ZZ0ZqZ0Z0Z00l0Z0oqZ0ZZ0Z0Z0Z0Zq0Z0Z0l0Z0ZZ0l0Z0o0l0qZ0oqZ0Z0ZZ0Z0Z0ZqZ00Z0l0Z0Z0ZZ0Z0Z0l0Z0


Solution 63P: [2, 5], [5, 6], [6, 3]Q: [0, 5], [1, 3], [2, 1], [2, 8], [3, 6], [4, 4], [5, 2], [5, 9], [6, 0], [6, 7], [7, 5], [8, 3], [9, 6]

0Z0Z0l0Z0ZZ0ZqZ0Z0Z00l0Z0o0ZqZZ0Z0Z0l0Z00Z0ZqZ0Z0ZZ0l0Z0o0ZqqZ0o0Z0l0ZZ0Z0ZqZ0Z00Z0l0Z0Z0ZZ0Z0Z0l0Z0


Solution 64P: [3, 4], [3, 6], [6, 3]Q: [0, 4], [1, 6], [2, 3], [3, 0], [3, 5], [3, 9], [4, 2], [5, 4], [6, 1], [6, 7], [7, 3], [8, 8], [9, 6]

0Z0ZqZ0Z0ZZ0Z0Z0l0Z00Z0l0Z0Z0Zl0Z0oqo0Zq0ZqZ0Z0Z0ZZ0Z0l0Z0Z00l0o0Z0l0ZZ0ZqZ0Z0Z00Z0Z0Z0ZqZZ0Z0Z0l0Z0


Solution 65P: [3, 4], [4, 6], [6, 3]Q: [0, 4], [1, 6], [2, 3], [3, 0], [3, 5], [4, 2], [4, 7], [5, 4], [6, 1], [6, 8], [7, 3], [8, 9], [9, 6]

0Z0ZqZ0Z0ZZ0Z0Z0l0Z00Z0l0Z0Z0Zl0Z0oqZ0Z00ZqZ0Zpl0ZZ0Z0l0Z0Z00l0o0Z0ZqZZ0ZqZ0Z0Z00Z0Z0Z0Z0lZ0Z0Z0l0Z0


Solution 66P: [2, 5], [4, 6], [6, 3]Q: [0, 2], [1, 5], [2, 3], [2, 8], [3, 6], [4, 4], [4, 9], [5, 7], [6, 1], [6, 5], [7, 3], [8, 6], [9, 0]

0ZqZ0Z0Z0ZZ0Z0ZqZ0Z00Z0l0o0ZqZZ0Z0Z0l0Z00Z0ZqZpZ0lZ0Z0Z0ZqZ00l0o0l0Z0ZZ0ZqZ0Z0Z00Z0Z0ZqZ0Zl0Z0Z0Z0Z0

Fundamental Solutions to the N+3 Queens Problem for N=8,9 ... fileBoard of Order 8 Board of Order 9...

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Transcript of Fundamental Solutions to the N+3 Queens Problem for N=8,9 ... fileBoard of Order 8 Board of Order 9...