Counting Solutions
The following table gives the number of solutions for placing n queens on an n × n board, both unique (sequence A002562 in OEIS) and distinct (sequence A000170 in OEIS), for n=1–14, 24–26.
| n: | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | .. | 24 | 25 | 26 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| unique: | 1 | 0 | 0 | 1 | 2 | 1 | 6 | 12 | 46 | 92 | 341 | 1,787 | 9,233 | 45,752 | .. | 28,439,272,956,934 | 275,986,683,743,434 | 2,789,712,466,510,289 |
| distinct: | 1 | 0 | 0 | 2 | 10 | 4 | 40 | 92 | 352 | 724 | 2,680 | 14,200 | 73,712 | 365,596 | .. | 227,514,171,973,736 | 2,207,893,435,808,352 | 22,317,699,616,364,044 |
Note that the six queens puzzle has fewer solutions than the five queens puzzle.
There is currently no known formula for the exact number of solutions.
Read more about this topic: Eight Queens Puzzle
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