After my previous post about the Sudokube, I decided to build one as my father's birthday present. A quick recap, a Sudokube is like a normal 3x3 Sudoku, except the numbers wrap around the edges of a 4x4x4 cube. Clear?
The Finished Result
The cube took a few hours to build, hence my slightly frazzled state in this video.
I'd scoured the web for ages until I found a suitable puzzle. There's a surprising lack of them out there.
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.
- It would be possible to work out which face a number should be on by seeing which way up the number is.
- 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.
The above image shows the stickers, solution, the code and the start of the construction.
Keeping the faces of the physical Sudokube and the paper puzzle was a little tricky.
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....
So, there you have it. A three dimensional Sudoku puzzle where every face, row and column has 16 unique symbols.
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!