<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In this paper a new method for solving the problem of placing <italic>n</italic> queens on a <italic>n×n</italic> chessboard such that no two queens directly threaten one another and considering that several immovable queens are already occupying established positions on the board is presented. At first, it is applied to the 8–Queens puzzle on a classical chessboard and finally to the <italic>n</italic> Queens completion puzzle. Furthermore, this method allows finding repetitive patterns of solutions for any <italic>n</italic>.</p>
</abstract>

In this paper a new method for solving the problem of placing n queens on a n×n chessboard such that no two queens directly threaten one another and considering that several immovable queens are already occupying established positions on the board is presented. At first, it is applied to the 8–Queens puzzle on a classical chessboard and finally to the n Queens completion puzzle. Furthermore, this method allows finding repetitive patterns of solutions for any n.

An alternative algorithm for the <italic>n</italic>–Queens puzzle

Recreational Mathematics Magazine

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

An alternative algorithm for the –Queens puzzle

In this paper a new method for solving the problem of placing n queens on a n×n chessboard such that no two queens directly threaten one another and...

An alternative algorithm for the n–Queens puzzle

Published Online: Oct 22, 2021

Page range: 39 - 73

DOI: https://doi.org/10.2478/rmm-2021-0003

Keywords
Chessboard, –Queens puzzle, NP-completeness, Patterns

© 2021 David Luque Sacaluga, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

An alternative algorithm for the n–Queens puzzle

Published Online: Oct 22, 2021

Page range: 39 - 73

DOI: https://doi.org/10.2478/rmm-2021-0003

KeywordsChessboard, –Queens puzzle, NP-completeness, Patterns

© 2021 David Luque Sacaluga, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Chessboard, –Queens puzzle, NP-completeness, Patterns