Sunday 29 October 2023

Triforce From Hanayama

Hanayama Triforce
Just a very quick review today. At the last MPP, I got the opportunity to buy (thanks Steve) all three of the latest Hanayama Legend of Zelda related puzzles (Triforce, Hyrule Crest and Master Sword). They do seem to have increased in price considerably compared to the other Hanayama cast puzzles, presumably there is a premium that the Hanayama company are having to pay to Nintendo for the rights to use those names and the imagery that goes with it. Whether the extra cost is worth it to you will be something that you have to decide but, let's face it, most of us are completely addicted and cannot really resist a new one and, in the grand scheme of our puzzling habit, these are really relatively cheap. 

The Triforce has been rated with a difficulty level of 5 out of 6 by Hanayama and, by PuzzleMaster, as 9 (gruelling) on their odd scale of 5 to 10. I must say that I completely disagree with these ratings. I would place it as a 2 out of 6 or 6 out of 10 (PM).

The puzzle is quite attractive made from 2 colours of matt metal (brass and pewter colour) and looks like it has been aged. The puzzle is a diminutive 6.2 x 5.3 x 1.2cm and feels well made. The Zelda Royal Hyrule Crest insignia is on the front of the centre piece.

Obviously, the aim is to separate all four pieces and then put it back together again.

Initially, when playing there is absolutely no movement at all apart from a very slight wiggling of the pieces which might give you a hint of what is supposed to happen. At this point nothing else is possible. With a little "manipulation" there suddenly is more possible and then you seem to be almost there. Almost...but not quite. There has been a good amount of sliding as the description mentions but the pieces are still locked together. Thinking© further along the lines of what was the initial move will quickly have you separate the pieces. The picture of the pieces doesn't really spoil it but I have hidden it behind a button.

Having scrambled the pieces for a while then reassembly takes a little thought to work out what orientation and position everything should be but not a huge amount. I did find for a few days that it made a rather pleasant worry bead to fiddle with. This one will not give any seasoned puzzler much of a challenge (do please ignore the difficulty rating) but it is another one for a collection and is a nice one for newbies. The Zelda theme may attract a bunch of non-puzzlers to try it and maybe they will be hooked in our hobby too.

Sunday 22 October 2023

A Cube Without Edges

Solves With ONLY The Edge Piece Series!

The Crazy 2x2x2 trio
They all look identical but the numbers on the face describe different turning
I have had a bit of a splurge on some twisty puzzles recently and have been exploring them this last week or two with some success (to my great surprise). Here I discuss the Crazy 2x2x2 (0,0,0 version) and how it looks ferocious but solves with the simplest technique and a lot of thought.

I pretty much always have a standard 3x3 and 4x4 Rubik cube in my bag at all times. Partly because people finding out about me for the first time always ask whether I can solve a cube and then I have to show them when they don't believe it. I also have it to make sure that I don't forget my basic techniques and it does make a wonderful fidget toy.

One thing that a lot of non-puzzlers seem to think is that "there is a single magic algorithm that you can do over and over again" and the cube will miraculously get solved. I have to disabuse them of this idea but always tell them that it is possible to solve the entire thing using just one simple technique but it requires a lot of thought and planning. If I am to solve a cube quickly (ish - I have no interest in learning dozens of algorithms to discern and move quickly) then I solve layer by layer with a very basic system for the top layer which is obviously the hardest. Doing it this way, I average about a minute and I'm happy with that. Alternative techniques include the Rubik ultimate solution described by Philip Marshall and evangelised really well by Rline with his Twistypuzzling YouTube channel in which one solves all the edges first and then the corners. This technique relies on two simple algorithms - the 4 move edge piece series (EPS) and the 8 move corner piece series (CPS). It requires a bit of thought and understanding but is the simplest way to do it. I also use a block building solution, a corners first solution and for fun I do it using the EPS only.

YES! You can solve the Rubik cube with a single algorithm of just 4 moves!


I was quite surprised when I started to investigate this puzzle which, as a 2x2, has no edges and I realised that it does have edges in a way and that it absolutely requires to be solved using JUST the EPS!

The 0,0,0 designation means that 3 of the 6 faces are 0 faces i.e. turning those faces leaves the centre circles unturned (the red, green & white), whereas the other 3 have 1 faces and the circles are fixed to the outer parts. The result of this is that the blue/orange/yellow corner never separates from its' circle and you can only really scramble it or solve it by turning the 3 zero faces.

Does this sound confusing? It is a bit of a mind-bender but is not that tough if you have mastered the EPS completely.

 So what is the EPS? It is a simple 4 moves (up, up, down, down) or the other way around. If done just once then it does what it says on the tin - it swaps three edges amongst the front edge and the UR and UL edges. It muddles up the corners but in Marshall's method we don't care about the corners yet. That does seem very simple but the fun this happens when you do it more than once. On a solved cube if you do the EPS three times (D, D, U, U) then it leaves all the edges alone and moves the corners:

Having done the EPS 3 times, the top 2 diagonally opposite corners have swapped and the two from corners have swapped up and down. 

This can be used to move corners where you want them to be using just a 4 move sequence and some setup moves - it's ingenious and devious!

This all sounds great - you can move edges around easily (and orient them) with the 4 move sequence, you can move corners around using the same sequence multiple times but what about orienting those corners? Yes, you guessed it, that same sequence can be used to rotate the corners without moving them. It is destructive when done once but if done 3 times or done in the opposite direction immediately afterwards then the destruction is undone:

EPSx2 starting L - destructive
Turn U face anticlockwise
EPSx2 starting R - undoes it
So now you can see how it can be possible to solve every part of a Rubik cube using just that 4 move algorithm. It's not easy the first time that you do it but it is fun. How can this be applied to the crazy 2x2x2?

During my initial look at the crazy 2x2 I realised that the blue orange yellow corner was the source of the craziness - it was fixed to the central circle and I effectively could not turn the blue, orange or yellow faces since doing so would move that fixed corner around and would prevent any useful moves on new faces. I needed to orient the puzzle with that corner bottom? back and then solve it moving just the 2 front and the top faces. This is an odd way to look at a cube - I had to stop thinking of it as having a front, left and right face as I normally do. 

Having scrambled the crazy 2x2 it became clear that the circle centres are effectively edges. The white and yellow opposite colours are attached to each other. If I rotate the white face then the white circle pieces don't move. If I turn the red face then it moves the white and yellow circle pieces attached to that side but moves them together, the same is true when turning the green face. Therefore the circle pieces in a pair are effectively and edge but marked by the colours of the face at either end. It takes a while to get your head around this but once you do then start solving edges first:

Pseudo-edges all solved
Opposite sides (corner block visible)
Interestingly, it is possible to get the same sort of parities with this one. The first happens to me almost 50% of the time:
2 pseudo-edges to be swapped
This is a "parity of false equivocation". Each of the faces' edges have the same two colours on them for each side (i.e. there are 4 white/yellow edges and the same for each colour pair) it is possible to place them in any of 4 positions on each face and all that is required is to take one from a top edge and place it in the other top position. It is, again, just a matter of the simple EPS.

Once the circles (edges) are solved then the aim is to solve the rest of the puzzle by turning only those front three faces. It sounds awful but it really isn't too hard. Using the EPS only in multiples of three the corners can be moved around into position until they are all in place.

Again, every other solve there seems to be a parity - I am left with 2 corners that need to be swapped. If you know the Rubik cube then you know that swapping 2 pieces is impossible - there is ALWAYS another piece or pair of pieces that need to be swapped...even if you cannot see it. In this case, the parity is caused by the edges first solution to the cube. If you try to solve edges first on a 3x3 then it frequently turns out that all the edges are in place apart from 2. The reason for this is that when solving edges first, it is possible to have the top face turned 90º without realising it and the solution is to turn it that 90º and then re-solve those edges. It is very easy and the end result is all the circles (edges) solved.
Equivalent 2 top edges swapped
All edges solved
In the crazy 2x2 it is impossible to discern this scenario until we find 2 corners alone needing to swap. Unfortunately, the solution is to go back and resolve those edges/top circles again with the top face rotated 90º in either direction. Having done that, the next time that the corner positioning is done, all the corners will be placed correctly.

Corners ready for orientation
In the beginners method we would use the down face but cannot turn that here. We need to orient those corners using just movements of those 3 faces. Easy peasy! Remember what happens when the EPS is done twice? It rotates a corner and destroys a bunch of stuff. Turn the top face until the next corner is at the front and do the EPSx2 the opposite way and it undoes that destruction (see the pictures at the top of the post).

If the rotated corners are on the bottom face then rotate the cube about that fixed corner until the required corners are on the top face and do it all again. This is continued until all the corners are done.

Solved it! Effectively, you have solved a 3x3 with hidden edges and used just the EPS. It is great fun and a lovely, not too tough, challenge. I urge you all to go back to your standard 3x3 and learn the EPS only solution. It is not hard and just needs some thought and planning.

Sunday 15 October 2023

Did I Pack My Dowels Properly?

Karakuri Packing by Yasuhiro Hashimoto
During my week off a couple of weeks ago, I was "forced" to construct and mount a bunch of new Billy bookcases with doors in my second puzzle room. Whilst this is a wonderful thing and I WILL be forever grateful to the present wife for allowing/forcing this on me. did mean that the week of leave was filled with DIY and chores and gardening (plus a little private practice which helps me pay for my rather expensive addiction) and I did not get to do much puzzling and did not manage to generate a nice cushion of solved toys to write about.

Watching this is like watching paint dry!
The first day back at work did give me a little time (actually quite a lot of time) to try and get something in the bag for the blog. That day was a vascular list to be done down in the bowels of the hospital (no sunlight, cold and with no prospect of a break or early release. The case was a very elderly frail lady with a rather large aortic aneurysm to be repaired endovascularly using a rather complex multi-branched fenestrated graft. Now, I know that you don't really want to know about that but it helps explain the very depths of my boredom. I am a bit of an excitement freak - I like big juicy and bloody operations that require me to concentrate and keep resuscitating as well as anaesthetising. I do a lot of large open vascular operations, big spinal operations (including scoliosis repair) and lots of revision arthroplasty which tends to prevent not only boredom but also puzzling. That fateful Monday, I discovered (again) that absolutely NOTHING interesting happens during a FEVAR! Nothing happened of any interest to me (apart from intermittent requests to stop the patient breathing for a minute at a time) for over 7½ hours. When you do your very first one it is moderately interesting but now after a decade of doing them, I have lost the ability to watch them moving a wire back and forth on an Xray screen for hours at a time. I only have a tiny mind according to "she who frightens the bejeezus out of everyone" and that tiny mind had left the building about 4 hours in. It was puzzling time!

In my bag there are always toys just in case. Sometimes it is to torture colleagues , sometimes to torture med students whilst I do a chore that can't involve them and I'm always hopeful that I might get a little time to play myself. The Karakuri packing puzzle from Yasuhiro-san had been waiting my attention for months. Allard had absolutely loved it and others I had met at the MPP had also said that it was fabulous. That Monday was my time and the pressure was on - I had to solve it before I lost my mind completely and also because the delightful Libby was watching me as I worked on it and asking rather pertinent questions. I couldn't allow myself to fail under Libby's gaze!

The Karakuri packing puzzle had won a Jury Honourable Mention award at the 2023 IPP design competition and I really had to see why. It has been created for us by Mine from some rather beautiful woods and consists of 5 oddly shaped pieces (one of which has a dowel sticking out) and two 2 voxel dowels. The box has a 3x3x3 cavity which is partially sealed by a 1 voxel lip and the pieces have 26 voxels plus the captive dowel would make 27. There are enough dowel shaped holes drilled into the pieces which would allow the 2 dowels to be included inside and also a hole for the captive one. Part of me did wonder whether the captive dowel was just supposed to protrude into the missing voxel but this would not be elegant and I very quickly abandoned that idea. Neither Mine-san nor Yasuhiro-san would make/design anything inelegant.

As I explained to Libby, the first thing to do is work out how to make the cube shape that might fit inside and then see whether the dowels would fit and finally assemble it in the box - easy peasy she said! I proceeded to make multiple attempts in front of her and she quickly realised that this was a proper challenge. I pointed out that having found a few cubic assemblies, it was possible to discount some because they required one of the pieces to be oriented in a position which was physically impossible to insert into the box. I quickly narrowed it down to a couple of possibilities and had to stop someone breathing a few times which gave me a breather to think about it (pun intended).

When I got back to the puzzle and the patient could breathe again, I made a rather special discovery...there was always one particular piece that would not fit in the box. Or, if I did fit it in early then it blocked the rest. Time to think©. I knew there was a rather special Aha! moment to this puzzle that separated it from the standard packing puzzle. I always seemed to get stuck on one particular piece which made me wonder about special techniques and, in front of Libby, I got struck by the Aha! moment and did something. The pieces all slid into place and both me and Libby had our wonderful jaw-dropping moment. Of course, she managed to look attractive doing it whilst I just sat there looking stupid with a big grin on my face. This is very very clever. I think it took me about 30 minutes including several breath-holding phases which is just about right. I think it is probably not very suitable for a newbie or non-puzzler but is an essential purchase for everyone else. The assembled puzzle is behind a spoiler button even though there is almost nothing really there to provide any info. Don't look if you are worried.

If you get a chance to play then go for it.

In the meantime, I was forced to start clearing my desk which I had not seen in months

This was from months ago and it had gotten worse
Finally after multiple moves up and down stairs, I could see where the desk had once been:

Hooray! Nearly there - soon my ears will stop bleeding.
I did find a puzzle stand without a puzzle:

I had no idea what this belonged to
The helpful guys on FB chipped in to tell me that it was from Juno's SDCB but Shane, being even more helpful said that it was to display a VERY special "Rubic cube" - please note that was his spelling and, if you know Shane, then that's pretty good for him! So I found a bunch of VERY special Rubic cubes to show the stand off properly:

The one in the stand is one of just 3 Hexaminx crystals ever produced, to the left is a Master Rex cube and the right is a Master curvy copter (both very rare and special). Behind it is Kevin’s burr designed and made for me by Jose Diaz (later produced in greater numbers by the late Eric Fuller).

My new cabinets now have a few lovely cubes inside:

Sunday 8 October 2023

It Would Be Nice To Have Enough Hands For This Burr

Handy Burr by Jerry McFarland
Jerry McFarland has an attention span problem! He makes fantastic puzzles which are always immediately recognisable - I am sure that all serious puzzlers could look at the photo above and know the creator without reading the caption. He gets inundated with requests to make his toys by the puzzling community and happily starts manufacturing puzzles and earning some money and then he quickly gets bored and distracted. Before he knows it, he's thinking about something new and abandons his order book to play with his beautiful wood and, if you've been following his creations from the last few years, his very strong magnets. 

He contacted me a few weeks ago to ask whether I would be interested in looking at his latest creation - the Handy Burr and I practically bit his keyboard off and sent him a bunch of PayPal. The puzzle winged its way across the Atlantic faster than I've ever seen and I got my grubby hands (due to DIY) on it in just 4 days! I did not get much chance to do more than fiddle and admire for the first few days because of said DIY but I could tell straight away that the magnetism was strong in this one.

It is a beautiful cuboid containing 23 pieces of wood and an unbelievable 32 magnets (16 of which are in the key piece - Jerry says this must be a record). There are 2 obvious pins in the puzzle too with some obvious tracks for the pins visible in the key piece. The wood choices are stunning - Mahogany, Bubinga, Walnut, Cherry, Maple and Bloodwood.

Jerry had been initially working on a 3D coordinate motion puzzle but this did not work out so he moved on to a springy puzzle with magnets and this is definitely that.

I started work after I had finally finished constructing my cabinets (still empty) and found that there are 6 pieces that can be pushed in varying directions and need quite a bit of pressure to push them - those magnets are STRONG! If you loosen your grip even momentarily then it all springs straight back into the original shape. Having played with quite a few of Jerry's creations over the years, I sort of had an inkling what to do and managed with 6 fingers plus holding on to various other bits of the puzzle for stability and suddenly the key piece sprung upwards. Progress!

It only sprung up one voxel and the magnetic pieces stabilised. I was then able to work on manipulating the pieces and getting the key piece extended further and further until it stopped dead. Time to explore and find the release mechanism. Here I got stuck for a while and in the end I reset the puzzle by pushing it all back to the bottom and manipulating the magnetic sticks as I went. The final push of the key piece flush with the top releases the magnetic pieces all together and there is a truly wonderful CLACK! as it all reset.

I got stuck here for rather a long time - back and forth to the almost released position and stopped dead in my tracks each time. I couldn't seem to find the correct path - Jerry had hidden it all just out of sight inside. Despite doing this dozens of times, I never tired of the wonderful noise of the reset (this is a feature of a few of his magnetic puzzles).

After a whole day of trying the same thing multiple times, it was time to think© which did hurt quite a bit. I know that Jerry is quite sneaky and I got wondering in the evening whilst watching TV. What if I??

I tried my new idea and found that I needed more than 2 hands - Jerry had sent me a couple of little envelopes with clues in it and afterward I had finally saved it, I opened the envelopes and had a proper laugh out loud moment. I had looked at she who must be feared during the evening whilst wishing I had more hands/fingers/useful body parts. Each time I thought of asking her, I decided that was probably not a good idea. 


Eventually after I dislocated a digit moving it into an appropriate place, I suddenly had the key piece free and I could see how well disguised the path had been.

Key piece removed (JM mark revealed with serial number on other side
The cat was not impressed with me dropping more wood on his head but he puts up with it. I put it back together immediately and then found that I could not repeat the process - that will teach me to watch TV at the same time as playing with something complex.

The following day, I managed to work it out again and was delighted with how it resisted solution but when you do the right thing it shoots out. I couldn't resist a full disassembly:

Awesome puzzle!
After taking the above picture I did scramble all the pieces and then attempted the reassembly - Jerry very helpfully writes the frame piece portions on them to ensure that the fit is good when reassembled and then I got a bit stuck on the assembly of the mechanism and had to create it outside the frame before attempting the final assembly - picture of mechanism is hidden behind a spoiler button:

This is a very satisfying solve and after reading the supplied solution sheet, I realised that there is another aspect to it that I had not seen. I tried the suggested approach by Jerry and this was even better and adds more understanding to the name. Jerry will be making a few more of these in the future and it will be worth while contacting him to ask to reserve one.

Sunday 1 October 2023

An Edgy Puzzle - But Still Intuitive

Son-Mum 4x4 cube (v1)
The Son-mum 3x3 cube was released back in 2018 and I loved it for the challenging thought processes it required and the nice parity that I had to think through. It was even mentioned in my puzzles of the year as one of the best challenges.  Then a few years later, those evil twisted men and women at MF8 decided to create a new "harder bigger" version and the 4x4 version was released. I bought it at the end of 2021 and had a little fiddle and shied away from it as impossibly difficult and likely to end in tears for me and laughter for Mrs S. I kept looking at it lying on my desk where it taunted me for nearly 2 years and upset Mrs S because she couldn't stand the mess that my desk was in but I could not bring myself to pick it up. I spent a bit of time on holiday in Scotland 2 weeks ago and having limited space to pack puzzles for the journey, I brought a couple of twisties with me as likely to keep me busy for a while. When I finally got around to pick them up, I actually realised that I had not solved any twisties at all for a very long time and was a bit rusty. I needed to play with this as a 3x3 and a 4x4 a few times to remind myself of the very basic techniques (you really should all try to learn how to think about the basics - it really is NOT difficult to solve basic cubes once you have an understanding about the simple edge piece series and corner piece series and how they can be used - I have discussed them previously with multiple other puzzles and Rline has a wonderful set of video tutorials here.

So what is special about this puzzle? First off, you can quickly see that the centres are formed from 16 pieces instead of the usual 4 and it looks impossible to separate many of them. Here is where the fun starts - of course you can do a standard 4x4 scramble but then it is possible to do a 45º turn of the middle layers and then continue to turn the faces - this not only splits up the centre pieces but it also allows the edges to be swapped with centres and the outer edges to be tilted. Here is the puzzle after just 3 turns with a 45º turn done:

This is why I kept picking it up and putting it down
Interestingly, there appear to have been no English language solution videos posted on YouTube which may have given an indication of the extreme difficulty of the puzzle - at least that was my thought process. 

As usual with any new twisty puzzle, I experiment with the edge piece series and the corner piece series to see what they will do when you add in the fancy moves that each new puzzle allows. Interestingly, the corner piece series was absolutely no use to me whatsoever! It either did nothing and the puzzle just remained solved at the end of the simple sequence or there was no real pattern to what it did (in fact one attempt was blocked by the bandaging caused by the 45º turn). Then, as usual, sob, I lost track of what I had been doing and ended up with a partially scrambled puzzle that I could not back out of. Damn! Oh well, I had better get on with it...

OMG! That was probably not a good idea!
This thing would now barely move - so many of the turns were now blocked by either a twisted edge piece lying across a face (see the red/blue edge above) or by a pair of tilted centre pieces lying across a face (see the green centre piece at the top right). What the hell do I do now? There were no instructions anywhere so I guessed that I had better figure it out. First step, get it back to cube shape - so blocked up that no algorithms are possible so just use intuition. To my huge surprise, it was just intuition to achieve this up to a certain point. Once a few pieces had been aligned either properly in a centre or on an edge then more faces would turn and it was time to try and put the edges where they should be. Here we just have to use the edge piece series aka "up-up-down-down". Yes, it's just a 4 move sequence - it cycles 3 edges around. I realised that if you can do a 45º turn to put an errant edge pair back and then cycle a centre pair out then gaps start to be filled:

Errant edge pair in a centre
Edge pair turned 45º onto an edge
Edge pair now front left & centres in place
If the centre stripe is turned back that 45º then then one edge part and centre set are in place. This will need to be done repeatedly and where there are single edge pieces out of place they will need to be turned and moved until they can be lined up in a pair and then rotated into an edge using the edge piece series. It is surprisingly fun and apart from the frustration of the bandaging forcing a bunch of preparatory moves to clear the way, it doesn't take long to get a near cube:

Sort of cube shaped
Here is where I have really struggled. I have edges and centres where they are supposed to be but a bunch of the centres are tilted. I have not managed to find an algorithm to easily flatten them and had to make something up. If there are 8 or 16 of them tilted then that makes either 4 whole faces or 4 half faces on a layer out of kilter and all that is needed would be to turn the slice 45º, use the edge piece series to place an edge in it and then turn another 45º to place the centre that came out into the next position along. If you do this 8 times then you have broken and recreated every edge and centre in a slice. Sounds awful but is, again, entirely intuitive. What I have not worked out how to do with ease is what to do when there is not a multiple of 8 tilted edges. I can fiddle with my 45º turns and break up the flattened centres and with some thought I can make it so that a multiple of 8 are left tilted (I either add some or fix some). It works but I don't really know a definite sequence. Either way, it is, yet again, mostly done by intuition. Once the centres are flattened it looks less horrific:

Nice and flat
Now it's time to recreate the 2x2 centre pieces
To most puzzlers who don't do twisties, it still looks awful but from now on, it is actually really simple and fun. All that is needed is to pair up the single cubies. In the picture above, there is an orange pair top right of the centres and another pair bottom left but inset a little. Another 45º turn and a face turn will allow them to be linked together:

45º slice turn
After turning the front face and replacing the slice
Once each centre 2x2 is formed then it is moved out of harms way and another one worked on until they are almost all done. There is plenty of leeway here as there are only ever four centres that are affected by that simple sequence and when you are down to just a few then placing two identical colours in opposite faces is trivial and means that 2 centres can be worked on in isolation.

After just have a 4x4 cube to solve which, if you are working on one of these, shouldn't be any difficulty. I had been expecting some sort of parity like I saw with the 3x3 version but this does not seen to occur with this puzzle. The 4x4 parities are still a possibility but nothing new.

All in all, I was rather surprised at my ability to solve this monster. I had been frightened of it for nearly 2 years and the lack of anyone on YouTube showing it off made me think it was impossibly tough. However, it is surprisingly a lovely process and requires nothing more than intuition and the Edge piece series. Thank heavens to Rline for showing that sequence to me all those years ago and making me truly understand the power of those 4 little moves! If you can solve a 4x4, then you should buy this puzzle.

After this one, of course I couldn't rest and I went to work on another monster! the Master Mixup type 1:

30º mixup turns will lead to a monstrous challenge!

I have been a very lucky boy - Mrs S got very angry with me! Yes, that is lucky. She got so fed up with the state of my desk that she "forced me" to go online to Ikea and buy some more bookcases. Whilst on annual leave I have been arduously constructing and mounting them and am just about ready to start clearing my desk into them.

Puzzle room number 2 is ready
All nice and level no thanks to Barratt homes!
In the process, I discovered that my house was built by 14 year old apprentices with no skills! The floor is horrendously off level! It has taken a lot of effort to get these cabinets level. Lucky me has 3 double Billies on the opposite wall and now 2½ on this wall plus a closed one for less beautiful toys.

Thank you to Mrs S! 😇😇😇