Sudokube – How to Solve The Challenging Sudoku Cube
A Sudokube (or Sudoku Cube) is the combination of Sudoku and the Rubix Cube.
Just like the regular Rubix Cube, the ultimate objective of the Sudokube is to resolve each side of the cube.
But instead of having each face of the cube show the same color as with a traditional Rubix Cube, the goal with a Sudoku Cube is to have each face show the numbers 1 to 9 exactly once each.
Just like with regular Sudoku.
Unlike with Sudoku though, the numbers 1 to 9 can appear on each side of the cube in any order. You don’t have to worry about columns, rows, or how each side interacts with each other.
As long as you can get each side of the cube showing the numbers 1 through 9, you’ve successfully solved the Sudokube.
How to Solve a Sudoku Cube
Solving a Sudokube is not the same as solving a regular Rubix Cube.
This is because you’re dealing with nine different numbers instead of six colors and you’re trying to get each different number to appear only once on each side of the cube. Not group all the colors so that each side only shows one color.
Another way to think of it is to image a Rubix Cube with nine different colors and trying to rearrange it so that each color appears once on each face of the cube.
So, with that in mind, how do you go about solving a Sudoku Cube?
Step 1: Learn the fundamental Rubix Cube skills
Even though solving a Sudokube requires a different approach to solving a Rubix Cube, it’s a good idea to have an understanding of the spatial relations of the cube.
A Sudokube moves in the same manner as a regular Rubix Cube, so by understanding how the squares move when you twist and turn the cube is an important first step to solving either type of cube.
Thankfully, there are plenty of resources that teach you how to solve a Rubix Cube including this guide for beginners.
You don’t actually have to complete a Rubix Cube before you can tackle a Sudokube. Just as long as you have a good understanding of how you can manipulate the cube.
Step 2: Draw a diagram of the ‘unfolded cube’
To begin solving the Sudokube, it’s helpful to first draw a map or diagram of the unfolded cube to help visualise the spatial relations of the numbers.
All this involves is drawing six large squares arranged like in the image below to represent each side of the cube.
You don’t need to worry about drawing the internal grid lines you don’t want to.
Once you’ve drawn this on a piece of paper, it can help to cut it out and fold along the joints so that it forms a cube itself.
This will further help you visualize the spatial relations of your Sudoku Cube puzzle.
Step 3: Start with the corners
When you begin manipulating the cube, start by focusing on the corners.
Your completed Sudoku Cube should have all the numbers on each side orientated the same way.
The four faces around the middle (in other words, all the faces except the top and bottom) should also be orientated the same way.
You can use this knowledge to rearrange the cube until your corner pieces satisfy the above assumptions.
That is, when you’re looking down at the cube, the four corner numbers on the top face should be orientated the same way.
When you look at the four middle faces around the sides of the cube, all the corner numbers should also have the same orientation across all four faces.
Finally, when you flip the cube over, you four corner numbers on the bottom face should also be orientated the same way.
Achieving this setup will require a bit of trial and error.
This is also where Rubix Cube skills become useful as you’ll have a better understanding of how to move corners around so they match up.
Step 4: Write the corner numbers on your diagram
Once you’ve successfully oriented your cube, record all the corner digits down like in the example below.
Step 5: Make a list of all the edge pairs of the middle faces
An edge pair are the two digits that cover two faces between the corners.
That is, the first digit is the rightmost digit in the middle row on one face and the second digit is the leftmost digit in the middle row on the face to the right.
All these pairs are adjacent numbers that cannot be separated by manipulating the cube and share the same physical ‘block’ of the cube.
As we are only focusing on the edge pairs of the middle faces, there are four pairs that need to be written down.
With the example above, these pairs are:
- 1, 3
- 2, 7
- 7, 6
- 9, 8
These pairs will then need to be added to your diagram such that they conform to the rules of Sudoku.
In other words, add your pairs to the diagram such as below so that no face contains the same digit more than once.
Note: The 1, 3 pair will join up and read 1, 3 when the diagram is folded up to form a proper cube.
Step 6: Look for more edge pairs
Now that we know all the edge pairs for the middle faces, the next step is to lock in more values.
To do this, we’re going to look for the two edge pairs shown below.
To find these, look for two edge pairs along the same column in the example above with the question marks that match up in terms of orientation.
In this particular example, the pairs are:
- 3, 2
- 6, 5
You can then use the regular Sudoku rules to determine which one goes where. (The 6, 5 pair must go on top as there’s already a 5 in the bottom face).
Step 7: Find all the remaining edge pairs
For all the remaining edge pairs, there is only one place they can go based on their orientation.
You can resolve these without having to worry about Sudoku rules.
Following on from the example above, the remaining edge pairs for this Sudokube are:
Step 8: Check the middle numbers
By this stage your Sudokube should be fully resolved.
All that’s left to do is ensure that middle digits don’t already appear along the edges of any of the faces.
If they do, then chances are you’ve made a mistake with one of the edges.
Don’t worry if the orientation of the middle digits as there’s no way to move these squares around in relation to each.
As long your middle squares satisfy the rules of Sudoku, then you’ve successfully solved your Sudoku Cube.
Congratulations!
Assumptions about your Sudokube
The above instructions will help you solve your Sudoku Cube, if your cube satisfies the following assumptions:
- All the numbers on each side of the cube share the same orientation
- The four middle faces of the cube (in other words, all the faces except for the top and bottom) share the same orientation
- The top and bottom faces share the same orientation when the cube is unfolded
These assumptions will hold for most, if not all, good-quality Sudokubes.
If the numbers are orientated weirdly on your cube, it doesn’t mean that it’s unsolvable, just that it’ll take a fair bit more trial and error.
Play Sudokube
If you’re interested in trying to solve a Sudokube right now, you can find a free online version to play right here.
If you’d rather have a physical cube, you can purchase one from the following sellers: