Sudokube: Does it Have More Than One Solution?

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Discussion Overview

The discussion centers around the existence of multiple solutions for a 4x4x4 Sudokube, a variant of the Rubik's cube where each row, column, and face must contain the numbers 1 through 16 without repetition. Participants explore the complexity of the problem and the nature of solutions for this puzzle.

Discussion Character

  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Some participants question whether a Sudokube can have more than one solution, with one participant stating that no known algorithm exists that is less than brute-force for solving it.
  • Another participant mentions that regular Rubik's cubes have a unique solution, contrasting this with the Sudokube's potential for multiple solutions.
  • A participant references a Wikipedia page suggesting that Sudokubes might have more than one solution but does not specify how many.
  • There is a distinction made between the 3x3x3 cubes discussed on the Wikipedia page and the 4x4x4 Sudokube, which has additional constraints.

Areas of Agreement / Disagreement

Participants express differing views on the nature of solutions for the Sudokube, with no consensus reached on whether multiple solutions exist or how to determine them.

Contextual Notes

Participants note the complexity of the problem and the lack of known algorithms for solving the Sudokube efficiently, indicating potential limitations in current understanding.

Dragonfall
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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?
 
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Dragonfall said:
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?
 


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...
 


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)
 


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.
 
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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.
 

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