Sudokube: Does it Have More Than One Solution?

[Dragonfall]

Let's say that a Sudokube is a 4x4x4 "Rubik's"-cube labelled with 1 through 16 on the little squares. A Sudokube is "solved" if on each row and column there are 1 to 16 without repetition, and on each face as well.

Does there exist a solvable Sudokube with more than 1 solution?

 

[DaveC426913]

Let's say that a Sudokube is a 4x4x4 "Rubik's"-cube labelled with 1 through 16 on the little squares. A Sudokube is "solved" if on each row and column there are 1 to 16 without repetition, and on each face as well.

Does there exist a solvable Sudokube with more than 1 solution?

If this is a teaser, shouldn't it be in the teaser forum?

 

[hover]

I hate sudokubes. They can such a pain to figure out. Regular Rubik's cubes are so much easier. I don't really know how many solved solutions there would on a sudokube. For any regular Rubik's cube though they only have one solution. Well there's my 2 cents...

 

[Dragonfall]

No it's not a teaser, it's a hard problem. I don't have the answer. I don't think anyone does. (No algorithm which is less than brute-force is known)

 

[hover]

Look at the Wikipedia page for http://en.wikipedia.org/wiki/Sudokube" . It says that these type of cubes might have more than one solution. How many though, it doesn't say.

 

[Dragonfall]

The wiki page describes 3x3x3 cubes. The 4x4x4 cubes with the additional constraint that all rows and columns contain the first 16 numbers is different.