[Review] QUBAMI 3D Sudoku (3x3)

[Kelvin Stott]

This thread is for reviews of QUBAMI 3D Sudoku (3x3). You can vote in the poll above, but please only vote if you own this particular puzzle. When posting your review, please follow a template similar to this:

Where the puzzle was purchased:
When the puzzle was purchased:
Thoughts on the puzzle:

What are your thoughts of this puzzle? Please vote one of the options above - but please only vote if you own and have used this puzzle extensively!

 

[Kelvin Stott]

Tony Fisher's video review:

 

[Kelvin Stott]

Another video review by Twisty Puzzler:

Plus a solving video:

 

[s3rzz]

These always looked amazing. Having seen them in the past and not knowing how to get one I made my own. It took quite a while to figure out that hardest challenge solution. Just ordered one and cant wait to relive the whole process. (This time without all the sharpie on my fingers )

 

[DeeDubb]

This thing looks interesting and stylish, but there's no way I would pay nearly $60 USD for a 3x3 (and that's all this really is). I could make my own with $2 stickers, a sharpie, and some scotch tape.

 

[opi50]

This thing looks interesting and stylish, but there's no way I would pay nearly $60 USD for a 3x3 (and that's all this really is). I could make my own with $2 stickers, a sharpie, and some scotch tape.

You´re completely right. But don´t spend too much work on that. "Olivier's Stickers" is selling online two Q-Cube sticker sets V1 and V2 (picture cubes). It says in the description, that they have the authorization from the inventor for that. What type of joke is that ?!? - on one hand offering a 60+ USD 3x3x3 luxury Rubiks cube sticker mod and on the other hand authorizing a 3 USD sticker sale for the same puzzle.

That appears somehow crazy to me.

 

[Kelvin Stott]

Yes, I can confirm that Oliver has our limited permission, even though we don't make any money from his stickers. Why? Because we'd like more people to experience the Qubami challenge who might not be able to afford an original Qubami puzzle, but also we are confident enough to stand by the quality and value of our own puzzles. In fact we offer a complete refund in case you are not 100% satisfied. That's why you can read great reviews from those who have actually bought one (or in some cases several).

So if you want cheap, you can now get that. But if you want quality, and a unique personal challenge that nobody else has (because every individual Qubami puzzle is different) then you can get that, too, but it won't be cheap.

 

[Kelvin Stott]

Here's another video review from CrazyBadCuber:

And another one (in Spanish) from TheMaoiSah:

 

[opi50]

Hello Kelvin,

thanks a lot for your comment posted. I appreciate that you made the puzzle accessible at a low price level for everyone. That´s really great. We are running a small workshop for applied mathematics in Mexico and nearly none of our pupils, and also we as mini school have the budget for original QUBAMI puzzles.

In addition to that, I´d like to congratulate you for the amazing and beautiful design of the puzzle. It looks very good. The packaging also appears very nice and the idea of the QUBAMI “hall of fame” is excellent.

As you are the inventor of the puzzle I´d like to ask you something about my thoughts on the QUBAMI design. First a brief description how I tried to make two QUBAMI type puzzles:

1.- From the pieces of 2 stickerless 3x3x3 cubes I made two 3-color cubes (with adjacent faces of each color). On one of them I swapped 2 centers to get 2 different base cubes. I think, there are no more options, because a second swap will get the cubes back to the initial stage.

2.- Then I solved the 3-color SUDOKU pattern on each of both (different colors in rows and columns on each face). I think this would be the advanced QUBAMI challenges. The solve was somehow challenging and I needed to use paper and pencil to arrange the 8 corner pieces and only 6 “different” edge pieces.

3.- The last step was to change each cube solution to a 3 symbol sticker pattern and to apply them to each other one. It seems that I received 2 different QUBAMI puzzles. And both have only one unique final solve, but the “advanced” solves (only symbols or only colors) have several options, because of the 3 one-color edges and the 3x3 = 3 identical edge triples, that might be exchanged.

Solve: I also watched the “twisty puzzling” solve video and think what he was doing in the video is a method that works great. But I do not agree with “Crazybadcuber”, that you can solve the cube only by turning it. From my point of view it enough to solve the corners and change and swap after that the edges into their place. And due to the unique solution of the final challenge you don´t get into parity issues. But if you´re not a human calculator you need to fix it first on paper.

I am not sure if I understand your puzzle completely right, but I calculated 1728 different design options for my 2 puzzles.

Hoping you will post some comment on my thoughts I remain with best regards.

Good luck for selling as much QUBAMIs as possible!

 

[Kelvin Stott]

Hi opi50,

Many thanks for your kind comments and questions, much appreciated.

To explain a bit about the different challenges and possible configirations / solutions for each:

Basic Challenge 1: Get the same colour on each face (two faces filled with each colour), ignoring the symbols. There are only 3 colours instead of 6, and 18 stickers for each colour instead of 9, so 2 faces can be filled with each colour instead of just 1 face with each colour. In the solved state, the 2 faces with each colour are always next to each other (although they could be opposite each other), so there are indeed 2 different solved states where the sequence of colours runs clockwise or anticlockwise around the 6 faces of the cube. Furthermore, in each case there are 3 symmetrical edges (blue-blue, red-red and yellow-yellow) which can be flipped, and 3 triplets of identical edges (red-blue, yellow-red and blue-yellow) which can be swapped with each other, so there are 2^3 * (3!)^3 = 1728 different but equivalent solved states, ignoring parity.

Basic Challenge 2: Get the same symbol on each face (two faces filled with each symbol), ignoring the colours. As with Basic Challenge 1, but with 3 different symbols instead of colours, there are 18 stickers for each symbol, so 2 faces can be filled with each symbol instead of just 1. In the solved state, the 2 faces with each symbol are always next to each other (although again they could be opposite), so there are indeed 2 different solved states where the sequence of symbols runs clockwise or anticlockwise around the 6 faces of the cube. And similarly, there are 2^3 * (3!)^3 = 1728 different but equivalent solved states, ignoring parity.

Advanced Challenge 1: Get 3 different colours on every row and column, ignoring the symbols. Here there are multiple different sudoku-like solutions, and again the edges can be flipped and/or swapped, so there are many thousands of different but equivalent solved states, ignoring parity.

Advanced Challenge 2: Get 3 different symbols on every row and column, ignoring the colours. As with Advanced Challenge 1, there are multiple different sudoku-like solutions, and again the edges can be flipped and/or swapped, so there are many thousands of different but equivalent solved states, ignoring parity.

Ultimate Challenge: Get 3 different colours AND 3 different symbols on every row and column. Here there is only 1 unique solution, which also happens to be one possible solution of Advanced Challenge 1, as well as one possible solution of Advanced Challenge 2. So in mathematical terms, the solution to the Ultimate Challenge is the intersection between the solution sets of Advanced Challenge 1 and Advanced Challenge 2, and is different for each individual cube.

Finally, each individual cube contains at least one fully symmetrical edge (with 2 copies of the same colour and symbol) that can be flipped without changing the configuration, plus at least one pair of identical edges (with the same colour-symbol combination) that can be swapped without changing the configuration. This enables all parities to be reached without having to disassemble the cube, and it also creates some interesting parity traps, for example, where just one edge piece appears to be flipped, and must be flipped back over together with the symmetrical edge piece in order to solve the cube.

I hope this makes sense, but in any case I hope you will see that a lot of thought has gone into the mathematics of the Qubami puzzle, as well as its design, so that they keep many people puzzled for many years! And I'm still hoping to see a solve video without the use of pen and paper - apparently it took Mats Valk over an hour to solve (unofficially), so at least I know it's possible!

 

[opi50]

Hello Kelvin,

thanks a lot for your answer and the detailed information you posted about your QUBAMI puzzle.

It makes me happy to read that basically my thoughts about your puzzle were ok. Thus I´d like to ask, in addition to that, if you could also comment the following observations:

Of course I did not consider any parity cases getting to the 1728 design options. The parity cases, caused by exchanged identical pieces, are establishing more solve options. Considering this, from my point of view all QUBAMI puzzles can be divided in 3 groups:
1. Full symmetric QUBAMIs: all colors and symbols are above each other in the final solve.
2. Partly symmetric QUBAMIs: only some symbols an colors have symmetric positions
3. Completely asymmetric QUBAMIs: none of the symbol and color schemes are identical
All of them with the 5 solve options. But as the owner usually does not know which type of puzzle he´s got in his hands, exactly that makes the solving a lot more exciting. Therefore, from the logical aspect the QUBAMIs of group 3 are the easiest to solve in the final stage (double SUDOKU), because they do not have parity cases.

Maybe I did not explain very well my point of view regarding the solving procedure. Of course it is “not” impossible to solve the QUBAMI without paperwork, but it will anyhow lead you to a type of trial and error procedure in the final stage of the solve.

As I know, Mats Valt is one of the best speed cubers and usually solves any 3x3x3 cube within seconds. But if it took him, as you wrote, 1 hour to solve the QUBAMI, I guess, he had also to restart several times from zero, or made a lot of swaps solving it.

My statement about the need of doing some brain work with pencil and paper (not being a human calculator) just referred to the logical aspect of the QUBAMI solve. And this, for sure, is not to solve a 3x3x3 Rubik´s cube using any type of algorithms. My objective was to point out, that you can solve the QUBAMI more straight and “logically” doing some brain work before starting to solve it physically. Some of these logical conclusions for example are:
1. you may never have two diagonals of the same color or symbol ending/starting in the same corner.
2. you may never have two corners with the same double color or symbols on one same cube edge.
3. The two 3-color or 3-symbol corner pieces have to be in one layer/edge (not in opposite corners)
... and so on.
And these conclusions will help you to solve a second, third or more QUBAMIs, like SUDOKUs. Right?

Well, there are a lot of twisty puzzles around, being solved just by applying certain algorithms. And that´s for me, simply spoken, not a big deal. But what I like very much while solving the QUBAMI is the logical aspect of the puzzle. For me, knowing how to solve the 3x3x3 Rubik´s cube, is just a tool, needed to get the QUBAMI physically done, or let´s say, to transfer the logic solve of the solved pattern to the puzzle.

The logical solve of each QUBAMI scheme is a great and new challenge. And that, thanks a lot for that, does not need algorithms – that´s really great.

Oh, sorry! Forgot to mention that my name is Olaf.

Hoping to be able to read some more news from you about my comments I remain with best regards.

 

[Kelvin Stott]

Hi Olaf,

You are correct that different colours and symbols may coincide on only some faces, or even no faces, but they can't coincide on all 6 faces otherwise the Ultimate Challenge would be identical to Advanced Challenges 1 and 2, with many solutions. So there must be a disconnect between the colours and symbols on at least one face to ensure that the Ultimate Challenge has only one unique solution...

I wasn't there when Mats solved the Qubami (I was only told about it via a comment on YouTube), but others have reported a lot of trial and error, trying different permutations after running into dead ends. Some even got well into the last layer before they realized they couldn't complete it, and had to start from scratch!

Regarding your "logical conclusions" (numbered), I don't think you can make any of those assumptions. Or at least I don't see why they must be true, but I may be wrong...

Finally, *all* Qubami puzzles (and individual challenges) have potential parity issues, because they all contain at least one symmetric edge, and one pair of identical edges. So getting one of these in the wrong position and/or orientation will create parity traps. But that just adds to the fun/frustration!

Thanks again,
Kelvin

 

[opi50]

Hello Kelvin,

thanks a lot for your fast answer and of course it shall be correct what you wrote about the parity. I was thinking that it might be possible to design a perfect asymmetric QUBAMI. But for sure I did not try all 1728 options. ;-)

Back to my conclusions for the solve. As I wrote in the first post, my starting point was to make the two possible, different 3D SUDOKU cubes out of 2 stickerless 3x3x3 cubes. After trying to solve the first, I noticed that there seem to be a lot of curiosities or parity issues. Then I thought it might be better to solve the 3D SUDOKU first on paper and apply it pater to the cube.

So I made six 3x3 squares with numbers from 1 to 3 for each side. 3 x 2 identical for each center and arranged them on the table like a typical 6 sided cube sticker pattern (lying cross). I chose numbers, because the orientation of each number would indicate what turning angles already have been applied. (0° - number top up, 90° - numbers top left, 180° numbers top down, 270° - numbers top right). Please see attached picture.
Now, sure that this will bring me to the solution I thought about all the possible 90° turns and concluded by myself, that just turning for ?? times 6 squared papers won´t be very smart. Thus, to reduce the amount of possible positions for these squares, I started thinking about this 3D SUDOKU and made some assumptions (I will refer to the same numbers posted before).

1. No same color diagonals ending in the same corner:
All characteristics of the QUBAMI corner pieces are even,
- eight (8) corner pieces
- two (2) 3-color corners
- six (6) double color corners (a pair (2) for each color)
Based on that I assumed, that the solved 3D SUDOKU need to have somehow equivalent properties, but if you connect same color diagonals with double color corner pieces that would mean, that 3 out of 8 corner pieces connect all 6 diagonals of the cube.
That did not make sense to me. So I decided to focus on parallel diagonals of the same color.

2. No same color pair corners in one edge:
OK, if same color diagonals are not connected, some different color diagonals need to be connected. And that brought me to the assumption that there must be 2 chains of all 3 colors could be connected. And that would be symmetric (joined together like the two parts of a tennis ball).
But coming from point 1 there are always 2 parallel diagonals of the same color and two corner pieces with the same paired color appeared somehow difficult for my chains. There is only one mirrored position how to allocate these pairs in one edge. That appeared very restrictive to me. So I decided to try to avoid this. OK. Finally it was no 100% possible and I left with 2 of these pairs on each cube. One of them on starting/ending points of the chains. ***

3. 3-color corner pieces in the same edge:
If you join the two 3-diagonal chains together (tennis ball) you have always a starting and ending point of each one of these chains in an opposite cube corner. That means that always 2 starting or ending point of these chains are in one common edge.
Based on this I assumed, because I only had 2 chains, that one starting or ending point of each 3-color chain might be one of the two 3-color pieces.
And this leads to the conclusion, that these 2 pieces cannot be in opposite corners of one layer, only in the same edge or in opposite corners of the cube.
But If you have the 3-color pieces in opposite cube corners that would be the same like in the original solved 3 color scheme. That did not make sense to me.

Conclusion:
I don´t know. Maybe it was just good luck, making these assumptions and/or conclusions, but I solved both 3D SUDOKUs based on that. And both cubes show exactly the described characteristics.
I also made some assumptions about the position of the same color edges, but the only one that has been confirmed was, that all 3 of them definitely cannot be in one same layer.

Anyhow. It was a big fun to play with my “self-made” 3D SUDOKUs and QUBAMI. I will ask a friend to take some pictures of my 3 puzzles to publish them in this thread. Hope that helps.

Best regards.

*** Modified after checking the cubes again - due to my error with the parity cases in the last post.

PD: for better understanding of the 3D SUDOKU solve procedure with numbers this picture might give a better explanation:

 

[opi50]

Hello Kelvin,

Sorry, but I can´t get your puzzle out of my head until it is solved (for me).

In addition to the previous posts I´d like to ask you in this one something about the final solve of a QUBAMI puzzle.

Am I right, assuming that the two 3D SUDOKU solutions are the key to be able to solve any existing QUBAMI puzzle?

The procedure to solve the QUBAMI would be as follows:

1) All you need from any QUBAMI puzzle is only the center scheme (colors and symbols). The centers are fixed and never may change. Symbol and color scheme of the centers, each of them represent exactly one 3D SUDOKU, different ones or the same, doesn't matter.

2) The second step is to solve each of the two 3D SUDOKUs independently. Well, they are already solved, but have to be aligned exactly to both QUBAMI center schemes (colors and symbols).

3) In the last step you'll only have to put both 3D SUDOKU solves together. Or let´s say to put the symbol solution above the color solution. Well, and finally to transfer the solution to the puzzle, like on a maze or picture cube.

TEST SOLVE:
In the starting section of this thread and also on the Oliver´s Sticker website are links to a “Youtube” video, made by “Tony Fisher”. So I took from that video the center information and made a virtual solve of a QUBAMI puzzle that I do not own – really funny. My final result and the process how I tried to solve the “Tony Fisher video” QUBAMI are shown in the attached picture. Hope that the solve loop is easy to understand.

Looking forward receiving any comment from your side I remain with

best regards.


*** Picture attachment should be removed, because it is incorrect.***

 

[Kelvin Stott]

Hi Olaf,

I'm not sure I follow your long posts, but I think I understand your overall approach to superimpose colour and symbol solutions onto each other with different orientations. This sounds plausible in theory, but wouldn't that give only 24 possible solutions (4*6 = 24 orientations of one solution superimposed on the other)? In reality, there are thousands of different Qubami puzzles, each with its own unique solution, so I think you are missing something...

And actually I just checked the solution of this particular puzzle (357HEA0OAR3LOV0L0OB2) in our database, but it does not match with the solution in your image, so clearly the colours and symbols on the edge and corner pieces (which you ignored) are critical. You have assumed that the colours and symbols are all fully ordered at the same time, but that's actually not the case (the solutions to Basic Challenge 1 and 2 are always different configurations).

But in any case, it's probably easier (and more fun) trying to solve each puzzle individually and progressively by deductive reasoning (i.e., like a true sudoku puzzle), rather than trying to remember and superimpose different orientations of different solutions in your head. Of course, you could use a computer, but that would kind of spoil the fun and defeat the whole point of having a puzzle. So on that basis I can't really help you any further (I've said too much already LOL), but I do appreciate your interest.

K.

 

[opi50]

Hello Kelvin,

thanks a lot for your prompt answer.

Regarding the turns of already solved 2D 3x3x3 SUDOKUs I calculated 4^5=1024 possible turns, because you can take one face as fixed reference and the other 5 may have 4 different 90° turn positions each. That was the reason why I was starting to think a little about a probable, more logic approach for the solve (please see attached picture ”.,,solve_by_faceturning.png”).

Yes, of course the solution I sent could not mach. SORRY!!! I made a mistake. If the centers are correct the attached image should be better. Well, assuming that I have read the centers correctly from the video. At least this picture shows a solved QUBAMI pattern. (please see attached picture “...solve.png”)

Of course you are absolutely right, saying that solving a QUBAMI individually may be much more funny and exciting. And I really do not recommend to anyone spending such amount of time, like I did, in better understanding of the QUBAMI puzzle concept. For me it was a pleasure to dig for a while a little deeper into the logic and theory of the puzzle. It´s really a great 3x3x3 twisty puzzle.

But there´s a point in your last post I cannot agree on. My solve approach does not ignore the corners. The corners are unique and in any symbol or color solve (3x2 faces of identical symbols or colors) they have a 100% defined position. Taking this as a base for the 3D SUDOKU solves, both should be correct. And any QUBAMI is a puzzle of two overlapping 3D SUDUKUs defined by the position of their centers. Assuming that all QUBAMIs have only one unique complete solve, this final QUBAMI solve has to be a combination of the two overlapping advanced solves. The only reason why each advanced solve by itself seems to be different are the equivalent edge pieces that may be swapped (the parity cases). Only the 3x3 identical edge pieces in both 3D SUDOKUs are creating parities, not the corner pieces.
And because these pieces usually look different, because of the symbols or colors from the other 3D SUDOKU scheme, the other 3D SUDOKU pattern appears scrambled. But in reality it is always the same 3D SUDOKU solution for each color or symbol pattern.

Resuming this, there also should be an opportunity to solve the whole QUBAMI just making one of the advanced solves. But that may require hundreds of advanced solves to get to the right one.

Finally I´d like to thank you again for the time and patience you took for reading and answering my posts. Also from your comments I learned a lot.

Best regards.

 

[Kelvin Stott]

Thanks Olaf,

I would just like to clarify your last point before I end here:

"But in reality it is always the same 3D SUDOKU solution for each color or symbol pattern".

Actually that's not true; there are multiple *different* sudoku solutions (which are not equivalent by flipping/swapping edges, etc.) even if you consider only the colours and ignore the symbols, or vice versa. In fact that's why I had to combine colours and symbols in the first place: to ensure only one unique solution in each case. It certainly wasn't superficial, just to make them look different - otherwise it would have been a lot easier (and cheaper!) to make them all the same with colours only (no symbols).

Trust me, I have explored and developed these possibilities over many years. ;-)

K.

 

[opi50]

Hello Kelvin,

Ups, looks that I forgot something. Regarding your question about only 24 solutions, I need to explain something. Hope you are not angry or somehow worried.

I think, that, if the two applied 3D SUDOKUs are identified by the color or symbol scheme there are 6x6x4 = 144 possibilities left to solve the QUBAMI. Each face of one 3D SUDOKU can be placed on each face of the other one, and of course turned around (0°, 90°, 180°, or 270°).

But please let me get back to the thousands of different QUBAMIs you mentioned.

Of course that´s correct, but only from the design aspect. Coming from the 144 possibilities to combine two known 3D SUDOKUs on one 3x3x3 cube, for sure there are 3 more possibilities to combine unknown 3D SUDOKUs. #1 with #1, #1 with #2 or #2 with #2. The forth option, #2 with #1 exists only in theory (absolute probabilities), because visually it will be the same.
So we get with 3x144 = 432 different QUBAMIs.

If we now consider additionally the possible exchange of symbols and colors that gives you another factor 3 for each of them. And than you will get a minimum of 9x432 = 3888 different QUBAMIs. (might be also 6 for each scheme, 36x432 = 15552). And if you think about additional colors (I saw in one video a QUBAMI with green stickers, very nice) there will be a lot more QUBAMIs. And each of them is an individual puzzle.

But in a real puzzle, that you hold in your hands the situation seems to be somehow different. All possible combinations of colors and symbols are taken off, because they are defined. The 6 centers indicate exactly which 3D SUDOKU schemes has been used (for the colors, and also for the symbols), please see attached picture. And in that stage you are only left with 144 possibilities to combine the two 3D SUDOKUs solves correctly.

For the last step you have to connect the two 3D SUDOKU schemes in one “unique” center. That takes off the positioning issue (144/36 = 4), and turn it around until it matches with the others (4/4 = 1). And that should be the final QUBAMI solution.

Best regards.

 

[opi50]

Hello Kelvin,

thanks for your last post. Sorry, but I saw it after sending mine. It is no problem for me. We can close here.

Take care and best regards.

 

[Kelvin Stott]