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N-Queens number for large boards.

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Truman Collins

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Jan 30, 1997, 3:00:00 AM1/30/97

Several weeks ago Jouni Tolonen posted a question about what the
largest nxn board was where the number of ways of placing n queens so
the don't attack each other had been calculated. I got out a program
I had written some time ago, did some optimization on it and managed
to calculate the number for boards up to 19x19. I thought I might as
well post them in case anyone was interested. Has anyone found the
number for a 20x20 board?

Total solutions for a 1x1 board: 1
Total solutions for a 2x2 board: 0
Total solutions for a 3x3 board: 0
Total solutions for a 4x4 board: 2
Total solutions for a 5x5 board: 10
Total solutions for a 6x6 board: 4
Total solutions for a 7x7 board: 40
Total solutions for a 8x8 board: 92
Total solutions for a 9x9 board: 352
Total solutions for a 10x10 board: 724
Total solutions for a 11x11 board: 2680
Total solutions for a 12x12 board: 14200
Total solutions for a 13x13 board: 73712
Total solutions for a 14x14 board: 365596
Total solutions for a 15x15 board: 2279184
Total solutions for a 16x16 board: 14772512
Total solutions for a 17x17 board: 95815104
Total solutions for a 18x18 board: 666090624
Total solutions for a 19x19 board: 4968057848

-Truman

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