One Of Many Solutions
To The 3-Dimensional N-Queens Puzzle
Rendered In Interactive 3D With JavaView Lite

In this interactive 3D model of a virtual cube, each 'queen' is represented by a yellow dot.  The model shows one arrangement of queens occupying 121 of the 1,331 'squares' in the 11 x 11 x 11 'board'.  As 121 is the maximum number of non-competing queens that can occupy this cube in the terms of the N-Queens puzzle, I refer to this as a 'maximally populated' cube.

If a 3-dimensional cube does not appear below here, then please check the System Requirements for JavaView Lite.

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Naturally, as you rotate the cube, the queens will appear to form other lines or rows of various lengths. However, in accordance with the rules of this puzzle, each of these 121 queens sits unchallenged - In her own rank (in the x-plane) In her own file (in the y-plane) In her own column (in the z-plane) Along each of her 10 diagonals - on this virtual 'board'.

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To Interact With The Cube
You can rotate the cube by clicking and dragging it with your mouse.

Other display options are available by right-clicking in the JavaView panel, or the same options can be obtained by pressing and holding the keyboard keys below while simultaneously dragging with your mouse. (The 'r' (reset) key works immediately and doesn't need the mouse.)
Note that options chosen with the right-click menu stay in effect until you press the 'r'eset key, whereas the effects of a keyboard+mouse-drag are temporary.

o	Orbit mode. Rotate the cube by dragging with the mouse (this is the default mode)
s	Scale mode. Move the cube closer (by dragging upwards) or further away (by dragging downwards)
t	Translate mode. Slide the cube around without rotation.
r	Reset the 'camera' viewpoint and the cube's orientation to their default positions.

Note also that unlike the full JavaView which can be installed on your PC like other development tools, JavaView Lite does not have a control panel or any other dialog. Its functionality is restricted in order to have the fastest download and startup times.

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About The 3D N-Queens Solution Displayed Above:
This 3-dimensional N-Queens solution was searched for and discovered in a joint project between myself and my son Martin.

• Martin describes his work on our joint project on his own website Queens On A Chessboard.
• In his Beyond The 2nd Dimension page he also discusses the prospect
  of taking his work further into 4 dimensions and higher! 
• My own notes on this 3D extension to my 2-dimensional project are here.
  

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• Click    to return to my 3D overview page.
  
  
• Click    to return to this site's Home page.

Page updated:  21st April 2009

With the exception of any downloaded JavaView Lite components, 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.