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The N + k Queens Problem -- Home PageResources related to the problem of placing k pawns and N + k mutually non-attacking queens on the squares of an N-by-N chessboard.
http://www.npluskqueens.info/
Resources related to the problem of placing k pawns and N + k mutually non-attacking queens on the squares of an N-by-N chessboard.
http://www.npluskqueens.info/
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The N + k Queens Problem -- Home Page | npluskqueens.info Reviews
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Resources related to the problem of placing k pawns and N + k mutually non-attacking queens on the squares of an N-by-N chessboard.
npluskqueens.info
Papers - The N + k Queens Problem Pages
http://www.npluskqueens.info/papers.html
The N k Queens Problem Pages. Here are preprints of papers we've written:. The Queens Separation Problem" published in Volume 69 of Utilitas Mathematica in March 2006. Note: Table 2 in this paper is faulty. Go here. Independence and Domination Separation on Chessboard Graphs", published in Volume 68 (2009) of the Journal of Combinatorial Mathematics and Combinatorial Computing. Note: Table 1 in this paper is faulty. Go here.
Background - The N + k Queens Problem Pages
http://www.npluskqueens.info/background.html
The N k Queens Problem Pages. In 1848, Max Bezzel first posed the Eight Queens Problem: Place eight queens. On a chessboard so that no two queens attack each other. This problem was generalized in 1869 to the N-Queens problem. N mutually non-attacking queens on an N-by-N chessboard). In 1995, Michael Anshel of the City University of New York. In 2004, the Chess Variant Pages. The contest participants soon asked about generalizations, such as "How many pawns would it take on a larger board? It turns out t...
Solution Counts - The N + k Queens Problem Pages
http://www.npluskqueens.info/solution-counts.html
The N k Queens Problem Pages. 2,316,725,816. 3,595,861,446. 1,474,699,536. Table 1. Number of N k Queens Problem solutions. Ie, number of ways to place N k Queens and k Pawns. On an N x N board so that no Queens attack each other. Table 2. Number of fundamental solutions to the N k Queens Problem.
Talks - The N + k Queens Problem Pages
http://www.npluskqueens.info/talks.html
The N k Queens Problem Pages. Here are slides from some of our talks related to this subject. I gave a colloquium talk to the Department of Mathematics and Statistics at Eastern Kentucky University on September 29, 2006. [Note: In this talk I stated that in 1910 Ahrens gave the first proof of the existence of n-queens solutions for all n 3. Actually, as stated in the survey by Bell and Stevens, E. Pauls published the first proof in 1874.]. On October 13, 2007 (apparently a busy day for us), John Miller g...
Programs - The N + k Queens Problem Pages
http://www.npluskqueens.info/programs.html
The N k Queens Problem Pages. Here is a recreational applet where you choose a small N ( 16) and k and then attempt to solve the N k Queens Problem: Applet (Javascript). Here is a Python 3 program to find all . Solutions to the N k Queens Problem for small N and k: . If you have the Zillions of Games program, here is a file you can use to play with various N k Queens problems. http:/ www.chessvariants.org/index/msdisplay.php?
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The N + k Queens Problem -- Home Page
The N k Queens Problem Pages. This site is a collection of materials related to the N k Queens Problem:. Given a positive integer N and a nonnegative integer k, can we place k pawns and N k queens on an chessboard with N rows and N columns so that every pair of queens on the same row, column, or diagonal have at least one pawn between them? A solution to the 8 3 Queens Problem. For more information on the origins of this problem, see the Background. Page and the Talks. Gerd Fricke, Walter Kosters. Thanks...
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