A python script that allows you to have all formations of n-queens puzzle!
The n-queens puzzle is the problem of placing n chess queens on an n×n chessboard so that no two queens threaten each other; thus, a solution requires that no two queens share the same row, column, or diagonal. Solutions exist for all natural numbers n with the exception of n=2 and n=3.
fig.1: A sample iterations for finding a correct formation of 8 queens.
The following tables give the number of solutions for placing n queens on an n × n board, both fundamental (sequence A002562 in the OEIS) and all (sequence A000170 in the OEIS).
n |
fundamental |
all |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 0 | 0 |
| 3 | 0 | 0 |
| 4 | 1 | 2 |
| 5 | 2 | 10 |
| 6 | 1 | 4 |
| 7 | 6 | 40 |
| 8 | 12 | 92 |
| 9 | 46 | 352 |
| 10 | 92 | 724 |
| 11 | 341 | 2,680 |
| 12 | 1,787 | 14,200 |
| 13 | 9,233 | 73,712 |
| 14 | 45,752 | 365,596 |
| 15 | 285,053 | 2,279,184 |
| 16 | 1,846,955 | 14,772,512 |
| 17 | 11,977,939 | 95,815,104 |
| 18 | 83,263,591 | 666,090,624 |
| 19 | 621,012,754 | 4,968,057,848 |
| 20 | 4,878,666,808 | 39,029,188,884 |
| 21 | 39,333,324,973 | 314,666,222,712 |
| 22 | 336,376,244,042 | 2,691,008,701,644 |
| 23 | 3,029,242,658,210 | 24,233,937,684,440 |
| 24 | 28,439,272,956,934 | 227,514,171,973,736 |
| 25 | 275,986,683,743,434 | 2,207,893,435,808,352 |
| 26 | 2,789,712,466,510,289 | 22,317,699,616,364,044 |
| 27 | 29,363,495,934,315,694 | 234,907,967,154,122,528 |
The six queens puzzle has fewer solutions than the five queens puzzle. There is no known formula for the exact number of solutions, or even for its asymptotic behaviour. The 27×27 board is the highest-order board that has been completely enumerated.
-
Clone 'n-queens' from git:
git clone https://github.com/black-fractal/n-queens.git -
Change the directory:
cd n-queens-main -
Install the requirements:
pip3 install -r requirements.txt -
Enjoy the program:+1:
Use following command to update to latest version:
git pull
- To run with the ASCII visualizer:
cd src
python3 n-queens.py
Sample output
This tools is licensed under the GPL-3.0 License. take a look at the LICENSE for information about it.
