I applied one of the digits 1 through 9 to each cell of the provided net of a cube.
My object was to create a unique 4 digit square number on each face. At the same time I required each vertex to be a 3 digit square. I failed in that objective!
I have 6 unique 4 digit squares but I have duplicated just one of my vertices.

To emulate my "feat":
- a [Magenta] Magenta cell is both the first digit of a 3 and 4 digit square
- an [Orange] Orange cell signifies the first digit of only a 4 digit square, while
- a [Cyan] Cyan cell signifies the first cell only of a 3 digit square.

The digits must be applied to each face by rotation, the direction is defined by need. "A" through "F" represent the 6 faces of the cube while "a" through "h" represent the vertices of the cube when fully assembled. Note: Within the range allowed several squares utilise the same digits, and this is allowed by virtue of the commencement cell.

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But then, there is still the challenge for 6 unique faces and 8 unique vertices.

I was beginning to draft an interim response to you both but Charlie has come back with more for me to think.

Firstly Charlie, I admire your diligence, no dedication is a better term, in programming this, not once but in revisions!  Let me take stock, but I think I will need assistance prior to a release of the "official" solution.

Secondly ed bottemiller, yes we had some "crossed" comments which improperly allowed me to assume that all was well (I did read the comment #5, albeit in that context).  I do appreciate your critique. 

At the time of this post, my monitor, as will be yours, is displaying an erred graphic; the lowest square with an "h" designation, and coloured orange.   "Solid" jpg/gif images have a formal site procedure before they can be posted.  The image on screen is NOT at this date either of those.  It is a quite complex XHTML format which our director  levik would throw his arms up if I asked him to edit.  Even so,  levik has commitments which do not bring him immediately here. 

By yours and Charlie's notes I trust that levik will have made an appropriate image switch within a few days.

Edited on May 3, 2008, 10:58 am

Posted by brianjn on 2008-05-03 10:55:48