Twisting My Corners to Madness

4x4 Curvy Dino Cube

Elite Skewb

Yes, I know that most of you puzzlers that read my blog don't really like twisties but you should give them a try - they are worth it and not that tough!

Phew! Thank goodness this week has ended! I/we have had a horrendous week - it started with my 9-hour marathon rota writing marathon last Saturday leaving me thoroughly knackered and then after my restful Sunday of gym and blog we had a very unforeseen (and VERY expensive) visit to the emergency vet with a very poorly distressed cat! My pharmacology knowledge was tested over the subsequent few days after further vet visits and finding ways to dose our poor boy with all sorts of drugs to help him feel better. It settled then flared up and required rather large doses before finally settling again. Needless to say, sleep has been minimal, stress has been high, arguments have begun and gone secondary to it all and I am feeling quite frazzled. Puzzling was not high on my agenda but, like when I first began this odyssey all those years ago after a stressful event, playing with a toy certainly helped me focus my attention on something less horrible and get some stress relief.

Looking at the photos above I know that you are thinking how can one of those awful twisty puzzles possibly provide stress relief? Surprisingly, these particular designs are remarkably soothing and one definitely needs to concentrate on them which forces most other thoughts out of my head - "She who must be listened to" would say that there is absolutely nothing in my head at the best of times and she might not be wrong!

Twisty puzzles really do not need to be a source of anxiety and despair - I agree that the initial part of the learning curve is a little steep but once some basic ideas have been acquired and understood then solving a lot of puzzles is just a matter of understanding and a little time for experimentation. You should have noticed that both of these puzzles share a common feature - the cuts are oblique across the faces - they are corner turning puzzles. Straight away that should give you hope that the solve process will not be too difficult.

I started with the 4x4 Curvy Dino Cube which is a combination of a slightly deep and a shallow cut puzzle. Here is what a few simple turns look like:

Just a few turns

Dino Cube

The Dino cube is a very simple corner turning puzzle where the corners are the full length of an edge but not beyond the centre of a face. It consists entirely of edge pieces and is solved using a very simple up, up, down, down algorithm which effectively cycles 3 pieces into each other's positions. In the 4x4 version, the cuts have been retracted slightly and curved. They still do not cross the centre of a face and the end result is to create corner pieces and deeper corner pieces as well as more edges. However, the resulting puzzle can still be solved using the basic up, up, down, down mechanism. The difference is that one has extra pieces that need to be solved separately (the corners). The worry that using the up, up, down, down algorithm might ruin things positioned elsewhere can be ignored as the even number of moves of each adjacent corner means that the corner pieces do not get rescrambled. I attempted this puzzle first and scrambled it without even bothering to search for algorithms - I was that confident! Foolish? Yes! Always and proud of it!

Horrific? Nope! It's easy!

Looking at the picture above, it quickly can be seen that the top face should be pink and the right face should be blue - if you are not sure look at the top front corner and the pieces further in, then look at the far right corner and pieces further in. It should quickly dawn on you that these corners and deeper pieces (even 2 layers in) do not get scrambled out of their orbits - they are just rotated around. Therefore the first step is just to rotate all the corners in each layer into the appropriate face. It only takes a few minutes and then a good bit of the cube is solved. After that, the other pieces need to be moved around and into place. If one carries out an up, up, down, down on a double layer then you can see that the result is this:

A three cycle involving shallow edges and the deep edges

This simple algorithm has moved 3 blocks of pieces in one go. Now, something that moves lots of different pieces is seldom useful but here we can focus on just the inner edges. On that top left edge, the diamond-shaped blue and white pieces are actually one piece - it's a single edge as they cannot be separated from each other (think about it and the geometry). So if we just ignore the outer edge pieces we can use the basic algorithm to position ALL of the inner edge pieces alongside their corners first. It takes a while but, as long as one is systematic about it, and tries to end with edges on a single face as the last trio, then this is a fun thing to do.

Next, we only have the outer edges to return to position. It might occur to you to ask: "what if we do the up, up, down, down but mix the shallow cut turns and the deep ones?" Good question! It does something beautiful:

A remarkable 3 cycle

Suddenly we can see that we have isolated the outer edges and not moved anything else! At this point, it is useful to understand the concept of a "setup move". If the 3 pieces to be cycled are not in exactly the right places to be cycled easily then all that need be done is to perform a setup move to temporarily move a piece to the correct position, perform our wondrous 4 move algorithm and then undo that setup move. These setup moves can be simple or complex - as long as one remembers to undo them after the algorithm then the solution to this cube is trivial!

Yep! This twisty can be very soothing to the troubled mind!

Next on to the Elite Skewb (can be bought from PuzzleMaster if you live in North America). This is based on the Skewb and the Master Skewb which I discussed back in 2013. The Skewb is a very deep cut corner turner (think of it as like a corner turning 2x2 Rubik cube) and the Master version has shallower cuts too (this should be thought of as a 3x3 version).

Skewb - a 2x2 corner turner

Master Skewb - a 3x3 corner turner

I consider the Master Skewb as one of the best twisty puzzles out there and not too hard for anyone who wants to go just a bit beyond the basics - I really should one day revamp my Twisty puzzle advice for beginners post to include it. The Elite Skewb is really the next level up - it is not a 4x4 puzzle but a 5x5 (I suspect that the "elite" name has been used incorrectly and maybe it should be a Professor skewb? The difference with these from the Dino cubes is that all the cuts are beyond the centre point of the square faces:

Just 3 turns

I usually spend a little time with more complex puzzles trying to find algorithms by carrying out simple ideas like the up, up, down, down or others to see what effect they have and then undoing them before trying something else. Once I have a few ideas then I scramble it deliberately. Unfortunately, this time I had a catastrophe - I got distracted and lost count of turns - I quickly had a mess:

Ooops! Now I'm in trouble!

With many of the higher order puzzles, the aim is to reduce the puzzle to a smaller one. Hence a 4x4 or 5x5 Rubic cube is reduced to a 3x3 by combining pieces into giant edges and centres. It seemed like a good idea to try and reduce this to a Master Skewb. I would need to find a way to move all the tiny edges into pairs (there's one pair already made at the top front right edge above), then try to fill in the small squares between them to make nice big edges. After that, if I could pair up all the rectangular pieces then I would effectively have a simpler puzzle to solve. Easier said than done!

My accidental scramble of this happened at the end of last year and I had only managed to work out a little bit of it. Pairing up the tiny edges proved pretty simple - the first 4 are trivial, just move the pieces into position next to each other. Then the rest are done by moving a piece into place, swapping a double-edge out with an unpaired one and undoing the slice turn to ensure the earlier solved pieces were put back into place. It takes just a minute or so to do them all....trivial!

I quickly found a way to pair up all the large rectangles - Again a slice move can pair them up and then another up, up, down, down sequence will move the newly paired up pieces out of play and then that slice move is undone. This ensures that the tiny edges and other already done rectangles are not dismantled. The aforementioned up, up, down, down when performed on diagonally opposite corners swaps out centre rows in a 3 cycle like this:

4 moves and the whole centre sets are exchanged

So, I had a way to move the small edges, the inner rectangles but I needed a way to move those blasted inner squares about. I was stuck! I have been trying to find a way for a good month or so now and not managed it. I sometimes go back to a modelling software called Gelatinbrain to help me play with different moves on my computer but it has not run on my Mac for over a year now. A week or so ago, during a frustrating and unsuccessful attempt I had a bit of an explosion - the whole thing destroyed itself and I was forced to reassemble it back to scratch and start again. This time, how about using that up, up, down, down but on just the inner slices?

My usual 4-move cycle has ONLY moved squares

Looking at this, it would appear that 5 of the squares have been swapped around (this cannot be right if you know the "law of the cube". If one does it again then it is clear that 6 pieces actually swap - there are 2 groups of 3 which separately perform a 3 cycle. If the blue face is pointing towards you, then the top front red square swaps to the bottom right square which moves across to the bottom left. Now, this 3 cycle would be very useful if I did not get all the others moving at the same time. Time to Think© - it is trivially easy to swap out those combination edges (including the squares) around as one needs, using the usual algorithm. What would happen if I moved the top front combined edge to the side (blue-white position above) and in the process moved the bottom front edge up to that place? I could then undo the very first 4 move cycle that I did (i.e. up, up, down, down in the other direction).

AHA!

It required three 4 move cycles, with the last being the reverse of the first, and I had found a "simple" way to 3-cycle the square pieces. I was on the way. I managed to find that move on Sunday evening whilst trying to calm my nerves after my cat problem and I was on my way. After discovering this method, it would be easy to reduce the Elite skewb to a scrambled Master skewb. The following day at work, whilst the radiologists were doing something under local anaesthetic and not requiring anything from me, I had a nice half hour to play. Reduce to Master Skewb? Check! Solve Master Skewb? Easy! Check! You should have seen the look on the nursing staff and other consultants' faces when I suddenly arose with a completed Elite skewb. The feeling of victory was wonderful! Yes, they all think I am crackers but I don't care!

I have scrambled and redone this puzzle multiple times since then and have not found any unusual parities - it is a truly wonderful puzzle - an essential purchase for a twisty puzzler and really not too tough once one understands the 3 cycles required. There are NO complex algorithms to learn, it JUST requires the up, up, down, down method in multiple different places. Go buy one - you will not be disappointed.

Next up I have some new toys from Stephan Baumegger.