Sudokube: Does it Have More Than One Solution?

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A Sudokube is a 4x4x4 cube that requires each row, column, and face to contain the numbers 1 through 16 without repetition to be considered solved. The discussion centers on whether a Sudokube can have more than one solution, with participants noting the complexity of the problem. While regular Rubik's cubes have a single solution, the Sudokube's unique constraints may allow for multiple solutions, though no efficient algorithm is known to determine this. References to Wikipedia suggest that while 3x3x3 cubes may have multiple solutions, the specifics for 4x4x4 Sudokubes remain unclear. The consensus is that the problem is challenging and lacks definitive answers at this time.
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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.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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