TomZ Constrained Cube 90

As the name suggests, each face is constrained to turn by a quarter turn. Constrained Cubes Ultimate and 180 had enough freedom of movement to allow the use of normal algorithms, albeit adapted to contend with the puzzles' turning limitations. This is no longer the case with Constrained Cube 90. Losing the option to execute a Sune algorithm removes many solving options from rotating corners to permuting edges.

 

Solution

Step 1: Solve the White Edges

Intuitive

I have not figured out if this is the optimum way of solving the puzzle but I solve the white cross in such a way that one edge can be turned in the opposite direction from the other three. For example, one turns clockwise, the others anti-clockwise. This gives me one corner where I can execute a sledgehammer algorithm.

White becomes the bottom face.

Step 2: Solve the E-Layer Edges

Intuitive.

This is extremely fiddly. Moving edges around the puzzle is not easy with turning options so constrained.

Step 3: Orientate the Yellow Edges

I try to do this at the same time as step 2 but it does not always work out.

Step 3: Permute the Yellow Edges

This is a challenging step that requires some thought.

Step 4: Permute the Corners

This is fiddly but not as difficult as as it looks.

Step 5: Orientate the Corners

This step is not that difficult, especially compared with the steps.

This is a very challenging puzzle and, hence, all the more satisfying to solve. It is least an order of magnitude more difficult to solve than its brothers, Constrained Cubes Ultimate and 180. I would advise becoming familiar with at least one of those before tackling this puzzle.

TomZ Constrained Cube 180

As the name suggests, all of the sides on this puzzle are constrained to a half turn. It is slightly more difficult than the Constrained Cube Ultimate.

 

Solution

I did not find it necessary to do anything outlandish to solve the puzzle, following steps that would be familiar to veteran twisty puzzle-solvers.

 

Step 1: Solve the White Edges

Intuitive. The easiest way is to get the edges into position and then double turn the requisite face to put the edge into position.

 

I prefer to have the green, orange, blue and red centres fully turned in one direction or the other. The centres can be flipped later on to allow flexibility in turning. I don't worry about the white centre but it will affect the yellow centre later on. If white is fully turned, then the yellow centre will be in the middle of its turning arc when solved and vice versa.

 

Step 2: First Two Layers

Normal block building or F2L techniques work here but with the need to work around the constrained faces. It is fiddly but I did not find it too difficult.

Step 3: Orientate Yellow Edges

I try to do this at the same time as step 2 but it does not always work out.

 

Step 4: Solve the Yellow Corners

Normal algorithms can be used here but attention must be paid to how faces turn. Some flipping of centres may be necessary.

 

Step 5: Permute the Yellow Edges

The final step is a little fiddly but not too difficult.

This is a satisfying puzzle to solve. Compared with the Constrained Cube Ultimate, the loss of freedom on the yellow face has a greater impact than gaining the ability to turn the white face. This makes the puzzle slightly more difficult to solve.

TomZ Constrained Cube Ultimate

A Constrained Cube is a puzzle where the freedom to rotate the faces is restricted.This cube has five constrained faces. The white face cannot be turned at all, the red and orange faces can be turned by a quarter turn, the blue and green faces by a half a turn and the yellow face is unrestricted.

Turning was is a little stiff on my cube, especially the yellow face. Corner cutting is poor but it is not a puzzle for speed solving so I don't see this as a problem.

Solution

This puzzle is obviously more difficult to solve than a regular one but it is not as difficult as one might imagine. Complete freedom to turn the yellow face is a major boon, while the inability to turn the white face is little or no handicap after the white edges are solved. It is not a problem to flip the orientations of the green and blue centres allowing some flexibility.

Step 1: Solve the White Edges

Intuitive. 

Solve in such a way that it is possible to execute an M-move on the white/green/yellow/blue layer. This makes it easy to flip the green and blue centres later on. Also, solve the green and blue centres such that they can perform a full half turn.

The white face becomes the D-layer.

Step 2: First Two Layers

Block building or F2L techniques work here, but I had to work around the limitations of the constrained faces.

 

Step 3: Orientate the Yellow Edges

I try to do this at the same time as step 2 but it does not always work out that way.

Step 4: Solve the Yellow Corners

Regular algorithms work here but some inventiveness is necessary to work around the constraints. Obviously, the bottom layer cannot be used to rotate the corners.

Step 5: Permute the Yellow Edges

All that remains is the relatively simple task of putting the yellow edges into their solved positions.

It is a very satisfying puzzle to solve, not as difficult as it looks.

Katsuhiko Okamoto's Void Cube

Void Cube

When I saw this cube, I just had to have one. It is a very clever piece of design and engineering. It still works like a regular cube but the centre pieces are missing with a void that runs right through the puzzle. It is one Katsuhiko Okamoto's inventions.

Turning is not as smooth as a regular cube and corner cutting is out of the question, due to the way it is constructed.

The puzzle is slightly more difficult than a regular cube due to the lack of a centre piece to act as a reference but this is not much of a hurdle. The more interesting obstacle that this cube introduces is the possibility of a parity issue. If, after solving the top layer, the middle layer is solved next with the bottom layer done last, there is a 50% chance that the middle layer is rotated by 90°. This will prevent the final layer from being solvable.

Parity

To show more clearly the parity issue on the void cube, and the concept in general, please see the picture of the regular cube below. The centres on the middle layer are deliberately mis-solved by 90°, i.e. a qurter turn, out of alignment...

If we then try to solve the yellow face, we discover that it is impossible. To solve this layer, we need to swap two edge pieces...

Regardless of what algorithms are used to move the edges around, at least two will always be in the wrong place. Hence, we have an odd parity case. We can infer from this, that performing a quarter turn on the E-layer is an odd number of edge swaps. Counting them confirms this.

It is obvious on a regular cube but the lack of centres on a void cube makes this potential displacement of the centres invisible.

Solution

To avoid the possibility of an odd parity case rearing its ugly head, I solve this puzzle following the steps below. Obviously, the algorithms that work with a normal cube are applicable here, too.

Step 1 - Solve the White Face

This is an intuitive step.

 

Step 2 - Solve the Yellow Corners

This can be solved with one only algorithm or at the most two.

Step  3 - Solve the Yellow Edges

Again, nothing special about doing this.

You could solve three edges and then use the fourth one to rotate the middle layer's edges but you will need to ensure that you are rotating them to the correct orientation.

Step 4 - Solve the Middle Layer

Use the gap in the yellow layer to facilitate the process, permuting the middle pieces at the same time if possible.

This is a fun puzzle. It is possible solve using any method used for a standard cube but using an extra algorithm to solve an odd-case parity if it arises. I prefer to solve in such a way to avoid the parity issue.