CSP Queens - Analysis Of The N-Queens Puzzle

On My Adventures In 2 and 3 Dimensions
With The N-Queens On An N x N (x N) Chessboard Puzzle

I've added a new section on a 3-dimensional version of this puzzle
so please choose your area of interest from my links below. Thanks.

Click the chessboard on the right for my original notes on this 2-dimensional puzzle.

Here I stake my claim to being the first person to find specifically the guaranteed first possible solutions (not the only solutions) for most of the 'huge' boards up to 49 x 49 squares, and I explain the basis of my claim in detail.

I show the exact queen arrangements for each of these first possible solutions, and I invite you to muse with me on their fascinating lack of predictability.

Click on the cube for my most recent work on this puzzle - in 3 dimensions - and in collaboration with my son and his younger and sharper intellect!

I use the free and versatile JavaView Lite utility to show user-interactive, 3-dimensional (3D) solutions to the 11x11x11 ( or 11³ ) and 13³ cubes.

A key feature of these 3D solutions is that they are maximally populated. Under the rules of this puzzle, no more queens can be placed into the cubes!

My son Martin has his own, rather more attractively presented series of websites
including two sections on this N-Queens puzzle.

Click the board on the right to visit Martin's 2D related Queens On A Chessboard web site, where he describes his own work on this puzzle and his own insights into its solutions. His explanations are crystal clear and beautifully illustrated, using 100% hand-crafted PHP and html!

He also includes a full board diagram for every one of the 2D First Possible Solutions we have solved, and most of which he has verified using his own program written in Turbo Pascal.

One of Martin's PCs is currently working on finding the solution to our 46 x 46 board.

Martin's more recent work takes us up "Beyond The 2nd Dimension", and he describes how we found our solutions to the 11x11x11 ( or 11³ ) and 13³ 'cubes'.

He explains why some cubes will never yield any fully populated solutions, and then he invites us to consider possible solutions for 4 dimensional or even higher-dimensional 'boards'!

Links to other related sites

OEIS From our calculations while solving the 2D puzzle, we have two integer sequences in
The On-Line Encyclopedia of Integer Sequences ...

Our count of Tentative Queen Placements (See A140450)

Our list of First Possible Solutions (See A141843)

The NQueens@Home project uses 'BOINC' technology on hundreds of internet-connected PCs to seek
the total number of solutions for each board size
(unlike my project here which seeks only the FIRST solution for each board size).
The NQueens@Home contributers are currently (as at March 2009) counting the solutions on a 26 x 26 board.

I hope you've enjoyed reading about our work on the N-Queens puzzle.
To find a wealth of further information about this puzzle, especially in its original form as
The 8 Queens Puzzle, I strongly recommend its dedicated page
on Wikipedia, The Free Encyclopedia.

Contact:

You may contact me via this feedback page, although I can't promise to respond to every message or question.

Page updated: 1st May 2009

Content on this CSP Queens site by Colin S Pearson and Martin S Pearson is licensed under a
Creative Commons Attribution-Non-Commercial-Share Alike 2.0 UK: England & Wales License.
Permissions beyond the scope of this license may be available via the feedback page.

Links to other related sites
OEIS	From our calculations while solving the 2D puzzle, we have two integer sequences in The On-Line Encyclopedia of Integer Sequences ... Our count of Tentative Queen Placements (See A140450) Our list of First Possible Solutions (See A141843)
	The NQueens@Home project uses 'BOINC' technology on hundreds of internet-connected PCs to seek the total number of solutions for each board size (unlike my project here which seeks only the FIRST solution for each board size). The NQueens@Home contributers are currently (as at March 2009) counting the solutions on a 26 x 26 board.
	I hope you've enjoyed reading about our work on the N-Queens puzzle. To find a wealth of further information about this puzzle, especially in its original form as The 8 Queens Puzzle, I strongly recommend its dedicated page on Wikipedia, The Free Encyclopedia.

I've added a new section on a 3-dimensional version of this puzzle so please choose your area of interest from my links below. Thanks.
Click the chessboard on the right for my original notes on this 2-dimensional puzzle. Here I stake my claim to being the first person to find specifically the guaranteed first possible solutions (not the only solutions) for most of the 'huge' boards up to 49 x 49 squares, and I explain the basis of my claim in detail. I show the exact queen arrangements for each of these first possible solutions, and I invite you to muse with me on their fascinating lack of predictability.
Click on the cube for my most recent work on this puzzle - in 3 dimensions - and in collaboration with my son and his younger and sharper intellect! I use the free and versatile JavaView Lite utility to show user-interactive, 3-dimensional (3D) solutions to the 11x11x11 ( or 11³ ) and 13³ cubes. A key feature of these 3D solutions is that they are maximally populated. Under the rules of this puzzle, no more queens can be placed into the cubes!

My son Martin has his own, rather more attractively presented series of websites including two sections on this N-Queens puzzle.
Click the board on the right to visit Martin's 2D related Queens On A Chessboard web site, where he describes his own work on this puzzle and his own insights into its solutions. His explanations are crystal clear and beautifully illustrated, using 100% hand-crafted PHP and html! He also includes a full board diagram for every one of the 2D First Possible Solutions we have solved, and most of which he has verified using his own program written in Turbo Pascal. One of Martin's PCs is currently working on finding the solution to our 46 x 46 board.
Martin's more recent work takes us up "Beyond The 2nd Dimension", and he describes how we found our solutions to the 11x11x11 ( or 11³ ) and 13³ 'cubes'. He explains why some cubes will never yield any fully populated solutions, and then he invites us to consider possible solutions for 4 dimensional or even higher-dimensional 'boards'!

On My Adventures In 2 and 3 Dimensions With The N-Queens On An N x N (x N) Chessboard Puzzle

On My Adventures In 2 and 3 Dimensions
With The N-Queens On An N x N (x N) Chessboard Puzzle