24

After searching around, going through Hungarian Rings, I finally stumbled on Radosza's Rings, which seem to be educational toys. Link


14

I'm afraid this is not possible to solve using normal moves. Two things could have happened: 1. The cube was taken apart or some pieces popped out, and then it was reassembled incorrectly. 2. The cube is loose enough that during scrambling or solving a corner got caught on another piece and twisted in the middle of a move. In the latter case you can ...


11

First, what do we know about this puzzle? There are 5*7*8*11 = 3080 possible positions. Moves do not affect each other, so if you have a good set of moves, you can do them in any order. There must be at least one move of the 8 ring, but not necessarily any of the others. Given this, it is a relatively simple algorithm to find the shortest sequence of moves....


10

That specific one looks like a Varikon tower to me. See http://www.cs.brandeis.edu/~storer/JimPuzzles/MANIP/VarikonTowers/VarikonTowers.pdf http://www.jaapsch.net/puzzles/tower.htm


9

If you reach the last step after all parities are solved, and your middle layer is flipped, you can flip it with / (6, 0) / (6, 0) / (6, 0). If you're not sure what this looks like, or want a video, see this one. Other than that, though, you've got the right algorithm. You can do the parity algorithm you know. Perform your parity algorithm to swap those two ...


9

Brute force shows that for the example there are: $8$ solutions if rings are not considered* $0$ solutions if rings are considered* Call the left of the three faces at the top of your net $L$, the middle one $F$, the right one $R$, and the one underneath $D$. In the current configuration there are: four tips $(tip_0, tip_1, tip_2, tip_3)$ which have ...


7

Here's how I solve it: Solve the middle layer Solve the corners 2.1 Resolve middle layer parity and centers (if there is a problem) Move the edges to the correct layers Move the edges into the correct positions Rotate the edges into the correct orientations 0. Notation I'm using R, L, B, F to indicate a 180-degree turn of each side. This is because, as ...


6

It seems to be called "Tower of Babel" or "Babylon Tower". Some sites refer to it as a "Hungarian Tower of Babel", others as "Ivory Tower". http://www.passionforpuzzles.com/2012/09/hungarian-tower-of-babel-puzzle.php http://www.jaapsch.net/puzzles/ivory.htm The puzzle was designed by Endre Pap and patented on 2 December 1982.


6

Here are some examples of nice patterns in the other orbits. Twist orbit: Flip+Swap orbit: Flip orbit: Swap orbit: It is very hard to combine a Twist with a Swap and/or Flip to produce something nice. This is because the former is associated with a 120 degree rotation around a corner, leading to only 3-cycles and even permutations of both the pieces and ...


6

Yes. This is a 3-cycle of the corners, and all three of those corners also need a twist in the same direction. Both of these things can be done individually. I put that position into Cube Explorer, and it gave the move sequence R' F U2 F' R F R' U2 R F'.


5

As you say, you are implementing a type of Douglas Engel's puzzle, an "Enigma". Given the colour set and the fact that you are ignoring the orientation of the triangular wedges ("corners" in twisty puzzle lingo) in your implementation makes it a either a "Turnstile" or "Avenger" (I believe one with orientations is called a "Puzzler"). Since, in your ...


5

Solving this puzzle is actually rather easy once you know how, but first, we need to establish a couple things: Puzzle turning notation I'm going to use the standard L/R, U/D, F/B notation for twisting the puzzle; however, you'll note that the puzzle pulls apart along the three axes. In order to execute an L move, for instance, you will need to pull the ...


5

The 3x3 and 4x4 are very different. If you had fun in trying to solve the 3x3 by yourself for years and don't want to enter speed contest then you can probably enjoy the same feeling on the 4x4 (or on the 5x5 which might be closer to the 3x3). You can try to solve other formats by yourself, it will take time so you can keep practicing on the 3x3 to improve ...


4

In my opinion you should look up the Fridrich method for the 3x3x3. At least the first 2 layers (F2L) methodology is really nice in this method. You will see that it is very natural feeling, no algorithms are needed for this. The top layer you can solve with the beginner method then. After a short while you will be able to solve the cube in under a minute. ...


4

That's funny, I just finished finding my own set of algorithms. My base algorithm is effective in select situations. I found a 2-2 swap from [A]=RU'RURURU'R'U'R2' swapping right-up edge and back center in additon to the left center and left-front edge. The key comes in the setup move [B]=R2F2x. (reminder: x is rotating the entire cube as if you were doing ...


4

I used to have this puzzle, but now I don't. I apologize if these instructions have a few holes in them - they should be complete, though, as I tested them on a 3x3. The general method for solving this puzzle is: Solve the middle layer pieces (as you've done) Rotate the top corners and edges so that the slices are turnable (as you've also done) Solve the ...


3

In your standard layer by layer method, you presumably start with a cross, i.e. the four edge pieces in one face. It is fairly easy to make sure that whenever you solve one of those four edges, the two adjacent edges are correctly oriented. In this way you will have 5 of the 6 centres correct. When solving the rest of the first two layers, those centres will ...


3

You probably don't need to disassemble it, after all, the child who messed it up didn't. Twist the shifted layer about a quarter turn. This puts it at about 45 degrees compared to the adjacent middle layer. There should now be enough room for you to shift the gear of one of the edges of the middle layer by one tooth relative to the twisted layer. This will ...


3

Like Jonathan Allan, I wrote a program to search for solved states. I'll present it in Mathematica/Wolfram Language, but I'll also provide a Python script that works the same way. Encoding Here is the pyramidix pyramatrix pyramadix triangular Rubik's cube I started with: The corners are labeled A-D and the faces are labeled 1-4. The tip pieces (cyan) ...


3

Here are a couple interesting Youtube videos on solving the larger cubes layer by layer. 13x13x13 Solve Part 1: Layers 1 through 3 - by SuperAntoniovivaldi Tutorial #5: How to Solve a 5x5x5 Layer by Layer (Part 1) - by europeancubers However, no matter which way you try to solve the 4x4, you will run into parities of some form. For the classical single ...


3

To get the balls to the ball layer so they can be dropped to the outer pockets, you need to flip the inner ball so the counterweight is pointing up after which it catches and will only rotate one way. This can be done by quickly rotating the entire ball around. I do this by quickly rotating the ball from where the black is horizontal to where the are ...


3

I'm not sure of the math involved in actually proving this (even by brute force), so I made a program that will just keep randomly scrambling the Pyraminx and checking if its state is a valid solution. So far it has made 87.5 billion random moves, and hasn't located a solution other than the one given above. It's possible that it hasn't visited every state,...


2

My answer is completely subjective, but personally, I find that puzzle-solving can be summarized as "having fun while finding new solutions to problems" (i.e. solutions you don't know). If you think that you can "find" a new, more elegant, or faster solution on your own - then keep playing with the 3x3x3. If you feel you are going nowhere with the 3x3x3 or ...


2

I'm going to quickly preface my answer stating that I'm not going to use any computer aid, but merely what can be done intuitively. I am also going to accomplish what you want by permuting some of the U face edges. I will preserve the orientation of all the pieces though. Can a corner swap be performed using commutators and conjugates only Yes. You ...


2

No, it cannot be done with purely commutators. Commutators are of the form $ABA^{-1}B^{-1}$, so consists of an even number of moves. The permutation it does of the corners is therefore also even. A single swap of corners is an odd permutation on the set of corners. It is therefore impossible to achieve with only commutators. You can get on odd corner ...


2

Done! @Dr Xorile's idea leads to success. Once each top edge is 90 degrees from where it needs to be: FB' UD' f U'D F'B solves. The middle "f" rotates the four corner pieces without moving anything else. To recreate the position in the question from a solved cube: FB' UD' f U'D F'B FB' UD' B' U'D L2 F'B U FB' L2 UD' B U'D F'B U2 The "f" moves rotates the ...


2

It can be solved. This seems to be the antisune case which can be solved with the algorithm:


1

Use a method of your choice for solving it as though it is a standard 3x3. Once it's only the centres that are messed up, just continue to repeat a single algorithm that only rotates adjacent centres. The following algorithm rotates the centres of the U (top) and L (left) faces. $V'H'VUV'HVU'$ The same site also lists a way to rotate a single centre ...


1

As someone who can solve a 3x3x3 but only after learning an iterative technique I would say that it is a worthwhile skill. I find it can be fun to impress people when I find one lying around their house. I thought about learning a 4x4x4 but for me I just think it is going a bit far to "mildly surprise" people. I get enjoyment from figuring out a puzzle and ...


1

I've been able to solve the 3x3x3 cube for probably 15 years, always using the same basic algorithm. I rarely pick it up anymore. Perhaps 3-4 years ago (maybe longer, can't remember) I decided to go for the 4x4x4. I had some trouble applying my standard technique to the new cube, so I went back and looked up speed cubing techniques for the 3x3x3. Got ...


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