Search results
Results from the WOW.Com Content Network
Nauck also extended the puzzle to the n queens problem, with n queens on a chessboard of n×n squares. Since then, many mathematicians, including Carl Friedrich Gauss, have worked on both the eight queens puzzle and its generalized n-queens version. In 1874, S. Günther proposed a method using determinants to find solutions. [1]
Min-Conflicts solves the N-Queens Problem by selecting a column from the chess board for queen reassignment. The algorithm searches each potential move for the number of conflicts (number of attacking queens), shown in each square. The algorithm moves the queen to the square with the minimum number of conflicts, breaking ties randomly.
A mathematical chess problem is a mathematical problem which is formulated using a chessboard and chess pieces. These problems belong to recreational mathematics.The most well-known problems of this kind are the eight queens puzzle and the knight's tour problem, which have connection to graph theory and combinatorics.
Some of the better-known exact cover problems include tiling, the n queens problem, and Sudoku. The name dancing links , which was suggested by Donald Knuth , stems from the way the algorithm works, as iterations of the algorithm cause the links to "dance" with partner links so as to resemble an "exquisitely choreographed dance."
The N queens problem is the problem of placing n chess queens on an n×n chessboard so that no two queens threaten each other. A solution requires that no two queens share the same row, column, or diagonal. It is an example of a generalized exact cover problem. [5]
A dominating set of the queen's graph corresponds to a placement of queens such that every square on the chessboard is either attacked or occupied by a queen. On an 8 × 8 {\displaystyle 8\times 8} chessboard, five queens can dominate, and this is the minimum number possible [ 4 ] : 113–114 (four queens leave at least two squares unattacked).
There is no polynomial f(n) that gives the number of solutions of the n-Queens Problem. Zaslav 04:39, 12 March 2014 (UTC) I believe that paper provides an algorithm to find a solution to an N-queens problem for large N, not to calculate the number of solutions. Jibal 10:17, 7 June 2022 (UTC)
This page was last edited on 10 December 2005, at 09:48 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may apply.