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Squares on Cubes (Posted on 2008-04-30) Difficulty: 3 of 5
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.
But then, there is still the challenge for 6 unique faces and 8 unique vertices.

  Submitted by brianjn    
Rating: 3.0000 (1 votes)
Solution: (Hide)
At the time of posting this was my only solution. I did not have a result for the challenge.
FACES
A. 6889   B. 6561   C. 7744  D. 4489  E.  9216 F. 1296

VERTICES
a. 576   b. 484   c. 144   d. 676
e. 196   f. 289   g. 289   h. 961
Charlie took up a challenge at which I would have quaked; he wrote and modified programs to work what I would have considered a minefield.

On seeing his work it was my initial thought to do an abridgment and incorporate it here. On closer inspection that would not be sensible. Instead might I direct the reader to the following comments:

Computer solutions. This is a program listing with an example which fits my diagram1 and is different to that above.
re: Computer solutions which details 93 solutions from the previous program listing. Apparently 63 of those fit the criteria for the problem as I presented it while 30 account for 8 different vertex values.
But then,
re(2): Computer solutions addresses that list and recognises duplications.
better classification of results revisits the duplications offering 28 solutions where the 8 vertices have a distinct 3-digit-square value while,
re: better classification of results offers the program listing for that.

The power of a CPU suggests then that there are 63 configurations which match my initial citeria and 28 to meet the "challenge".

Footnote 1: "....which fits my diagram..."! The diagram on posting was incorrect; the very lowest orange cell ought to have been "Cyan".

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Image and solutionbrianjn2008-05-06 20:27:30
re: Charlie and ed bottemillerbrianjn2008-05-03 11:12:41
Charlie and ed bottemillerbrianjn2008-05-03 10:55:48
re: better classification of resultsCharlie2008-05-03 10:21:36
re: better classification of resultsCharlie2008-05-03 10:05:25
Solutionbetter classification of resultsCharlie2008-05-03 10:03:13
re(2): Computer solutionsCharlie2008-05-02 17:36:42
Solutionre: Computer solutionsCharlie2008-05-02 17:23:07
SolutionComputer solutionsCharlie2008-05-02 17:10:57
Back on Track?ed bottemiller2008-05-02 10:35:05
re: Biggest problem I see!brianjn2008-05-02 02:13:45
QuestionBiggest problem I see!Charlie2008-05-02 00:50:53
re(5): Clarifications??brianjn2008-05-01 20:42:04
re(4): Clarifications??ed bottemiller2008-05-01 12:45:22
re: Thanks! and an apologybrianjn2008-04-30 22:25:47
Thanks!ed bottemiller2008-04-30 21:52:09
Interpretations?ed bottemiller2008-04-30 21:40:34
re(3): Clarifications??brianjn2008-04-30 20:44:52
re(2): Clarifications??ed bottemiller2008-04-30 16:48:48
re: Clarifications??Charlie2008-04-30 15:37:46
Clarifications??ed bottemiller2008-04-30 11:27:19
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