The Finished Result

The cube took a few hours to build, hence my slightly frazzled state in this video.

The Puzzle

I'd scoured the web for ages until I found a suitable puzzle. There's a surprising lack of them out there.

Sudokube (C) Uwe Wiedemann

Uwe Wiedemann has a great selection of Sudoku variants.

Solving the Puzzle

Conceptually, it's no different to a normal Sudoku, you just have to adjust how you move along lines. Liz and I managed to solve it in about an hour.

Constructing the Sudokube

My first challenge was this: What numbering system to use? As any fule no, the numbers on a sudoku don't make a difference, they can be any symbols as long as they are unique. So, I could use 1 - 16, 0 - F, or Greek Letters should I so wish. There is a problem using numbers, though. They have no rotational symmetry. This poses two problems for the Sudokube.

1. It would be possible to work out which face a number should be on by seeing which way up the number is.
2. The corner pieces will provide clues as to which way up the numbers will be.

I initially tried to find 16 different symbols each of which had an order of rotational symmetry of four. So squares, diamonds, crosses, squares within diamonds, crosses within squares etc.  It quickly became apparent that it was confusing to look at and fairly ambiguous.

So, I settled on 4 shapes and four colours.  White, Red, Green, Yellow.  A dot, a square, a circle and a blank.  In retrospect, the circle and square can look quite similar; I should have used a circle and a cross.

Starting The Build (click for bigger)

The above image shows the stickers, solution, the code and the start of the construction.

Two Faces (click for bigger)

Keeping the faces of the physical Sudokube and the paper puzzle was a little tricky.

Completed Sudokube (click for bigger)

Eventually, the cube was finished.  I think it is a thing of beauty.  But rather than just being an objet d'art, it's a puzzle for my dad's birthday.  So, there's only one thing left to do....

Mixing it up (click for bigger)

So, there you have it. A three dimensional Sudoku puzzle where every face, row and column has 16 unique symbols.

Notes

I bought the blank cube from eBay - it was only ~US$10 and came with all the stickers I needed.

Building the cube took a few hours - mostly spent solving the puzzle.

I had to use a Sharpie to draw on the stickers.  The ink from regular pens just wasn't clear enough.

Have a helper! I really couldn't have done this without my wife, Liz.  She was instrumental in solving the Sudoku and stopped me from making stupid mistakes as a placed the stickers.

It's a huge amount of fun to build and - I hope - as much fun to solve.  Good luck, Dad!

Puzzle Cube

While this would be a diverting little puzzle, it isn't properly a Sudoku. Getting each face to have 1-9 may be more challenging than a traditional Rubik's Cube, it doesn't have that beautiful arrangement that Sudoku has. Indeed, it's rather ugly as each row is 12 squares whereas there are only 9 digits to play with.

To that end, I wondered if it would be possible to create a 4*4 faced puzzle cube. Such a cube could have the digits 1 - 16 on each face, row and column. What larks! I first thought about this two years ago, but never got very far with it.

If you can't visualise it in 3D space, here is how it would look flattened out. Lines have been added to show where the continuation points.

The Sudokube

So, this looks fairly do-able, right? Wrong! While it's easy to start, it rapidly becomes more and more difficult to generate a solution to this cube. This is, if you will, a multidimensional Sudoku puzzle. But without the starting numbers.

I've had a look through various maths, puzzle and sudoku forums and I've yet to find any attempts at this - let alone a solution.

So is it possible and - if it is - will it be next year's big puzzle sensation?

Any help gratefully appreciated.

Update

Turns out there's a whole bunch of deep mathematics required to create such a puzzle. And, like everything on the Internet, one of the solutions has already been found.