All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Numbers
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.

See The Solution Submitted by brianjn    
Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(4): Clarifications?? | Comment 8 of 21 |
(In reply to re(3): Clarifications?? by brianjn)

Please, some more clarifications.  You cite three 3-digit squares which contain the same three digits as a different 3-digit square, but I am not sure how your criterion of "unique" is applied in these cases.  In two of the cases (144,441 and 169,961) one could look at each as a single case, just reading clockwise or counterclockwise -- where the third (256,625) has the same digits but not as a reversal.  Do the specs mean that we could not use both 144 and 441 (or 169 and 961) at different vertices? And is there any reason not to use 169 and 961 on separate vertices?  I note that three of the 3-digit squares (121, 484, 676) are palindromic: since you hinted that "direction" might be a factor in uniqueness, could the same square be used twice, just be adding an assertion regarding direction of rotation?  I am also assuming that by uniqueness you are not requiring that the same digit not occur more than once in any square (e.g. that 225 could be used).  All of these questions could lead to different interpretations of the problem set.


  Posted by ed bottemiller on 2008-05-01 12:45:22
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (8)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2024 by Animus Pactum Consulting. All rights reserved. Privacy Information