Understanding Sudoku

3x3x3 Understanding the Sudoku Cube

If you cannot solve a standard Rubik's cube then you will be wasting your time on this page because this is not a solution page but a page dedicated to helping you understand the Sudoku cube so that you can solve any fair dinkum Sudoku cube.

The image to the left is a representation of one of my Sudoku Cubes.

The Cube clues are in the orientation of the numbers.

The Sudoku clues are in numbers that can or cannot appear on a face.

I have not been able to buy a smooth or speed Sudoku cube, it doesn't mean they do not exist. Most suppliers do an excellent job with the number layout, however, neglect quality when it comes to the cube. Also beware of alleged Sudoku cubes.

If this is your thing, my advice is, buy a decent cube and buy a set of Sudoku stickers from Cubesmith or Oliver's and make your own cube. If you don't know how to create a solvable number layout you can use these templates.

Too many so called solutions on personal sites and YouTube either lack in detail or are provided by those who believe that you need some foreknowledge of the solved cube before you can solve it. With a fair dinkum Sudoku cube this is a misleading and false belief.

If you do not have a genuine Sudoku cube then there is an alternate two stage method you can use to solve your cube.

The First Layer

Because all Sudoku cubes are not the same this is not a solution, it only assists you with the understanding of a solution that will help you to solve your Sudoku cube. Up and down faces here are only references to the way the side face numbers are oriented. A method for solving a cube that ensures the correct orientation of the centres, or algorithms for rotating centres, can be found on this site on the Final Layer, Edges then Corners page and the Rotating Centres page in the 3x3x3 Extras section. If you are a top down solver then Top Down Bottom Layer Picture Cube.

Let us start with the first layer. The first Sudoku solve is to establish the top and bottom face centres. We solve the first layer in the main by looking at the orientation of the numbers. The side face number on the corners and edges must be upright on the cube's side faces. At this stage we are not concerned with which centre we are building the up or down face around but we ensure as we always do, that the corners and edges are correctly oriented.

We see there is a problem the 2,5 edge (pink) and the 6,3 edge (yellow) having their numbers oriented in the same pattern, however, Sudoku rules tell us that the 2,5 edge is not permitted on the up face because a 2 appears on the up face of an obvious up face edge and the 6,3 edge is not permitted on the down face because there is a 3 on the down face of an obvious down face edge. The 8,9 (blue) edge on the top layer and the 8,2 (blue) on the bottom layer are reversible (they can be rotated in position), however, there is a another 9 on the top layer and another 2 on the bottom layer and an 8 on the bottom layer side face, determining the 8s on these edges belong on the up and down faces.

The up face solution tells us that the centre is a 1 (red) and the down face solution tells us that the centre is a 6 (red). Now we have the problem of two centres displaying the number 1 (green). Of course having solved the down face we know that the up face 1 centre is the one opposite the 6 centre. Let's look at the face with the 6 centre first then we will look at the face with the 1 centre.

The 6 centre face presents us with the problem of not knowing which way round this face should be oriented with respect the rest of the cube. There are two possible orientations, the one shown in the image on the left/bottom and a 180 degree rotation from the one in the image. Both 90 degree rotations place a 5 on the same face as the 5 centre and according to the Sudoku rules this is not allowed. For now we just have to accept the fact that there are two possible orientations.

The Equator Layer, 6 Centre Face Solved First

The equator edges on the cube are the ones with matching side by side orientated numbers on the faces. On this cube they are 1,2 3,7 5,8 and 8,6.

No matter which of the two down face orientations is correct there is still sufficient information to tell us where each of the equator edges belong. Start with the edges that appears to have more available information then check to see if they can occupy only one legal position. The 1,2 edge and the 5,8 edge, both can only occupy one position regardless of the down face orientation.

When you rotate the down face 180 degrees the 1 centre and the equator layer's, edge positions remain static and the 2's on the bottom layer simply swap places, so basically as far as the 1,2 edge is concerned both orientations are the same. The 1,2 edge cannot go between the 1 and 7 centres or between the 4 and 1 centres because of the 1 on the centre and the 2's on the opposing faces. It cannot go between the 7 and 5 centres because of those 2's on the opposing faces. This leaves only the position between the 5 and 4 centres.

When you rotate the down face 180 degrees the 5 centre remains static and the other two 5's and two 8's simply swap faces so as far as the 5,8 edge is concerned both orientations are the same. The 5,8 edge belongs between the 1 and 7 centres, because of the 5's on three of the side faces, regardless of the two possible down face orientations.

The 8,6 edge cannot go between the 5 and 4 centres or the 1 and 7 centres, they are already occupied by the 1,2 and 5,8 edges, respectively. It cannot go between 7 and 5 centres because of the 8's on the bottom layer side faces being adjacent to the 1 and 5 centres with either of the two possible down face orientation. Placing it between 7 and 5 centres would also place its 8 on the same face as the 5,8 edge's 8, so that only leaves the position between the 4 and 1 centres.

The final equator edge 3,7 therefore belongs in the only vacant position left on the equator, between the 7 and 5 centres.

We now see that the 6 centre face is correctly oriented in the image, if we rotate it 180 degrees to what was previously, the other possible orientation, we find two 3's on the 7 centre's face.

Providing we took the care to ensure that the centres were properly oriented, we are ready to solve the final layer.

The Equator Layer, 1 Centre Face Solved First

Since we have solved which 1 centre is on the up face, it is also possible to solve the cube making it the first layer to be solved. The orientation of this face in relation to the rest of the cube is as it appears in the image to the left. A 90 degree rotation in either direction places a 1 on the face containing the 1 centre and a 180 degree rotation places a 7 on the face containing the 7 centre and a 4 on the face with the 4 centre.

The equator edges have not changed, they are 1,2 3,7 5,8 and 8,6.

The 1,2 edge belongs between the 5 and 4 centres because of the 1's on three of the side faces.

The 3,7 edge belongs between the 7 and 5 centres because of the 7's on three of the side faces.

The 5,8 and 8,6 edges belong in the remaining two positions, placed so that their 8s are not on the same face, this means the 5,8 edge belongs between the 1 and 7 centres and the 8,6 edge belongs between the 4 and 1 centres.

Providing we took the care to ensure that the centres were properly oriented, we are ready to solve the final layer.

The Final Layer

Refer to the Final Layer, Edges then Corners in the 3x3x3 Extras section for the correct final layer method, for solving a Sudoku Cube. If you are a top down solver then Top Down Bottom Layer Picture Cube. This layer is solved using orientation as your guide you do not have to worry about the Sudoku rules until the final layer is solved and we need to orient it in relation to the other two layers.

To make the cross look at the side faces of the edges to see which are oriented properly then solve the cross.

Find the edge that matches the orientation of the centre on the face you are solving and position the edges.

To check the position of a corner, imagine it with the matching side by side oriented numbers on the two side faces and the other number on the face with the cross. In the imagined orientation if the corner's number on the same face as the cross is oriented the same way as the numbers on the cross, then the corner is in the correct position. Now position and then orient the corners.

All that remains is to orient the final layer with the other layers using the Sudoku rules, described in the Equator Layer outlines above.

This job is done.

Your Sudoku Cube

Although your cube may not have the same number layout the principles are still the same. Simply follow the orientation of the numbers and look to the Sudoku rules to solve the problems orientation can not.