CSP Queens - Analysis Of The N-Queens Puzzle

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

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, achieved 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!

I've written here about some of the programmer's catalytic conversations that Martin and I shared on this project, and on some of our developmental roller-coaster rides as we nudged our algorithm into its current state.

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've had two integer sequences accepted into
The On-Line Encyclopedia of Integer Sequences ...

Our count of Tentative Queen Placements (See A140450)

Our list of First Possible Solutions (See A141843)

I heartily recommend a visit to Walter Kosters' N-Queens bibliography.
It shows the huge variety of contexts from which this N-Queens puzzle has been studied,
from as long ago as the mid-19th Century!

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.

Credits And Acknowledgements

The web-integration and display of our 3D N-Queens solutions is possible
thanks to the JavaView Lite 3D geometry viewer by Konrad Polthier

Thanks for these free .GIF images goes to -
UVic Humanities Computing and Media Centre
and their associates at Half-Baked Software

Other chess-board and cube images on this CSP Queens site
are copyright © Colin S Pearson and
copyright © Martin S Pearson

Contact:

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

Page updated: 21st August 2010

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've had two integer sequences accepted into The On-Line Encyclopedia of Integer Sequences ... Our count of Tentative Queen Placements (See A140450) Our list of First Possible Solutions (See A141843)
	I heartily recommend a visit to Walter Kosters' N-Queens bibliography. It shows the huge variety of contexts from which this N-Queens puzzle has been studied, from as long ago as the mid-19th Century!
	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.

Credits And Acknowledgements
	The web-integration and display of our 3D N-Queens solutions is possible thanks to the JavaView Lite 3D geometry viewer by Konrad Polthier
	Thanks for these free .GIF images goes to - UVic Humanities Computing and Media Centre and their associates at Half-Baked Software
	Other chess-board and cube images on this CSP Queens site are copyright © Colin S Pearson and copyright © Martin S Pearson

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, achieved 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!
I've written here about some of the programmer's catalytic conversations that Martin and I shared on this project, and on some of our developmental roller-coaster rides as we nudged our algorithm into its current state.

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

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