Sunday 29 July 2018

Getting my Goat!

aka Kozel Zahradníkem

Kozel Zahradníkem. Part of puzzling’s deep roots in the Czech Republic.
Yet again I can say a very grateful "Thank you" to my good friend and PuzzleMad foreign correspondent, Mike Desilets, for stepping into the breach and helping me out with a truly fabulous and informative article for us. I have been really really busy recently and rather stressed as I have spent the last 3 days gathering together my appraisal information and writing it up. This has left me no time or will to write a decent blog post but luckily my hero Mike had sent me this a week or so ago. Over to you Mike...

Aloha Kākou puzzlers,

I’ve been a busy boy these past two weeks - two PuzzleMad guest submittals without a three-month gap! (Ed - yay!!!) That has to be some kind of personal record. This article was actually in the work and almost complete when it was preempted by the lovely No. 360. We return now to the vintage world but with an international flavour (Ed - aaaargh - American spelling removed!) this time. Unfortunately, there were some severe language issues researching this puzzle, so I wasn’t able to find out as much as I’d like. Be prepared for unfounded assumptions and rampant speculation (Ed - oooh my favourite!). Czech readers in particular, please feel free to correct anything and everything in this post.

Today’s feature puzzle is Kozel Zahradníkem, or in English, Goat Gardner. It’s a little-known puzzle from late 20th century, probably the 1960s or 70s, or even the early 80s perhaps. It’s hard to tell with second-wave plastic puzzles. You might deduce from the name that it is Czech, and you’d be right. Although this puzzle was clearly mass-produced, my cursory internet search indicates that it never reached a broader market outside what was then Czechoslovakia. Perhaps you can guess why, given the dates involved.

Before we get into the mechanics of Kozel Zahradníkem, let’s take a moment to acknowledge antecedents. Serious puzzlers will immediately recognize the goat theme and the overall structure of the puzzle from the early nineteenth century Get my Goat. Get my Goat is a true classic among sliders (yes, I know I say that a lot). It was patented [link PDF] in the US by John I Wiley way back on October 6, 1914. Other-themed versions were produced in accordance with the spirit of the times, such as “Katch the Kaiser” (under Wiley’s patent) and “Kapture the Kronz Prinz” (in the UK with patent applied for). Examples of these can be seen at Jim Storer’s excellent and very helpful site. The same basic puzzle was again pressed into service during World War II as “Put Hitler in the Dog House.” I’m not sure if this counts as war profiteering or patriotism. Probably a measure of both, as is often the case. Although the later versions are historically interesting, the inventor’s original concept was the charming and playful Get my Goat, so let’s stick with that.

The one that started it all.

Back-of-cover instructions, for the record. 
It is also available today in nice wooden versions:

A nice reproduction by Creative Crafthouse. Comes with handy cover.

Detail of original Get my Goat cover art. The goat has the high ground, as usual.
The object of the Get my Goat puzzle is very simple... Move the goat piece on the far right into the centre and surround it with the ‘fences.’ Once you’ve done that, you’ve gotten the goat. The element that makes the puzzle challenging is the double-width rectangular block in the upper right. All the other pieces are square. This seemingly minor feature nearly doubles the number of moves needed and it also forces you to utilize pretty much the whole board. With only square blocks, it would be more or less a 15 puzzle, strategy-wise. What makes Get my Goat a brilliant design is the single surreptitious complexifying modification, the rectangular block. (Ed - now THAT is a great sentence!)

I confess, Get my Goat gave me trouble (Ed - me too - I have the wooden version). According to Wiley’s solution, there are 31 steps. Edward Hordern was able to cut that a little to 28. I’m sure I was double that by the time I captured the goat. You know how it is with these sliders, once things start to go awry, all bets are off. You can circle around for a long time just making things worse and worse. If you are persistent enough (or for some, smart enough), you eventually begin to clean up the board and feel your way to the solution. If you do the puzzle a few more times, you might start to see patterns and visualize at least some of the solution. That’s my experience at least.

Fortunately, you don’t need to comb auction sites to find Get my Goat. Dave Janelle at Creative Crafthouse has reproduced the puzzle in a very nice hardwood edition. Those guys have really good taste in puzzles. Their craftsmanship is solid and the pricing can’t be beaten. After you have finished ingesting the weekend puzzle blogs, you should go get yourself a copy. Its required in any collection.

Kozel Zahradníkem.

An image of the outer packaging, courtesy of
My copy, unfortunately, came without it, courtesy of some dude on eBay.
Now that we have some context, let’s get back to Kozel Zahradníkem, Goat Gardner. This take on the classic does not utilize the upper left rectangular piece which is so critical to Get my Goat. Rather, it is composed of 11 equal-sized squares. The Czech puzzle is not the only variant to use this layout. Turning again to Jim’s page, we can see a number of similar puzzles such as Bullseye and ZOT!. The idea of splitting out that rectangular piece dates back at least to 1942 when it was illustrated in Anthony Filipiak’s Mathematical Puzzles and other Brain Twisters. Using this layout, the minimum solution path is 17 moves (according to Hordern’s analysis and the ZOT! packaging). I can personally attest that it’s a lot easier than Get my Goat! Hordern believes this simpler version may have originated as an erroneous attempt to copy Get my Goat. Sounds plausible. 

ZOT! from Peterson Games. Exclamation points make puzzles more fun.

ZOT! rules of play, although I’m sure the readership can figure it out.
Using all square blocks is indeed a very significant deviation from the original design. Does that mean Goat Gardner is just a watered-down Get my Goat (like ZOT!)? Absolutely not. With one relatively simple design innovation, Goat Gardner transforms the nigh trivial bullseye structure into a multi-challenge puzzle with progressively more difficult layout objectives. The key innovation is the inclusion of two dots on each of the four corner pieces. These are painted green, as you can see in the photos. Or they should be at least; the paint tends to flake off easily.

These curious little dots are meant to represent cabbages. As I gather from google translate, the running story and theme of the puzzle involves a struggle between farmer and goat to protect and eat the cabbages respectively. It’s a very clever twist on the original Get my Goat concept, pressing into service a classic Czech cultural reference. Kozel Zahradníkem, Goat Gardner, is a play on the proverbial Czech expression "udílat kozla zahradníkem", to make the goat the Gardner. This isn’t generally recommended! Goats garden according to their nature and are steadfastly focused on one aspect, the harvest. The expression can be used in many everyday situations, especially with respect to short-sighted management. Pavla Horakova provides a much better explanation, including a bunch of other great Czech goat proverbs. If you are still hungry for goat, I also suggest checking out the 176 goat proverbs from around the world at It’s interesting and also pretty hilarious, especially if you’ve ever known a goat personally. (Ed - I think you need to get out more, Mike!)

Back to the puzzle. Thanks to the addition of the cabbages, Goat Gardner presents the puzzler with four distinct challenges, each performed sequentially. The starting position for the next challenge is the ending layout of the previous challenge. As you surely know, I really enjoy the sequential approach to multi-challenge puzzles. It’s more elegant and far less bothersome. (Ed - I like the idea of these but I am sooo awful at them that I tend to shy away!)

The first challenge is basically the bullseye-ZOT! challenge: get the goat into the centre and replace all fences. The literature gives a 24-move solution, but we now know that it can be done in 17. When solved, you will quickly see that this is not an ideal place for a goat (unless you are the goat). So the next challenge is to remedy the situation by moving the cabbages outside the fence. This means moving the upper right fence to the lower left and the upper left to the lower right (and vice-versa), then returning the goat to the centre. The literature gives a 40-move solution for this. I’ll take their word for it. 

Starting position.

Challenge 1: same as ZOT!

Challenge 2: cabbages safely outside.
The goat, now feeling utterly cheated, becomes angry and charges the fence. The fence starts to give, so the farmer decides to fence the goat more closely so that he cannot run. For the third challenge, then, you must reverse the upper-lower and left-right fences to make a small box around the goat. This should take you at least 33 moves.

Challenge 3: fenced in tightly.
The farmer eventually takes pity on the goat and puts him outside the fence, with free access to half the cabbages (the ones on the right of course). The fourth challenge thus requires one to put the flat (non-cabbage) fence segments back to their original positions, and place the goat back outside the fence. If the literature is correct, this will take at least 74 moves. Remember that these solution paths were generated by hand back in the 1970s, possibly earlier. With computer assistance, one could most likely find shorter solutions. Perhaps some enterprising PuzzleMad regular can attack this issue? (Ed - if anyone does then please comment below or use my Contact page)
Finally, if you are up for it, you can return the puzzle from the end of challenge 4 back to its original starting position. The literature presents this as kind of an informal challenge, without a solution. 

Challenge 4: cabbages for dinner.
I enjoyed the whole process and found Goat Gardner delightful to play. It was reasonably challenging, but not overly so. In fact, I didn’t notice a massive difference in the solving difficulty between challenges. This is probably because I took much more time than was necessary on the easy problems and then managed to be reasonably efficient on the hard ones. It all seemed to average out. Because of the bullseye “all-square” design, there were no major time-consuming hang-ups. You just need to keep your objective in mind and, to a certain extent at least, have a rough plan of action before you start moving things around.

Overall, I would say it is a very enjoyable, low-stress puzzle, suitable for all ages and skill levels. (Ed - MUCH too difficult for me!) Veteran solvers will doubtless make short work of it. Slider specialists might find it too easy. But if you are a sliding block fanatic like my good friend Amanda, you need to find a copy. Considering they are not terribly old and are cheaply constructed, prices should be reasonable. You’ll have more luck searching European sources. I don’t know how many ever left the Czech Republic, but it can’t have been that many. Happy hunting!

Solution pathways provided with Kozel Zahradníkem. Possibly not the shortest, but fully functional.
Before we wrap up, I want to point out one final interesting aspect of this puzzle, and why my copy is dear to me. I didn’t realize until after I purchased and played with it, but my copy’s literature bears an important stamp on the first page.  It is the name and address of the great Czech puzzle designer and collector Stanislav Tvrdik. Veteran puzzlers will recall his best-known design, the Ježival style hedgehog-in-a-cage, dating to 1966. It was the biggest advance on the classic hedgehog since its introduction around 1886. Although I spend an inordinate amount of time on this hobby, I remain woefully deficient in many international aspects. Luckily I recalled Mr Tvrdik from Radek Micopulos’ description of his excellent 2015 Ježival reproduction which, as fate would have it, I had recently purchased.

How cool is this?
Ježival, produced by Radek Micopulos. Get one!
PuzzleMad Tip: Don’t even consider buying the old Bits and Pieces/Eureka version, which was produced (and patented) without the designer’s permission. Buy a quality-made puzzle with the designer’s blessing instead. Get Radek’s version (Ed - I reviewed new special versions here). You’ll have a nicer puzzle and you’ll sleep better. (Ed - oooh sleep would be nice! I am such an insomniac!)
Radek gives a great history of the hedgehog puzzle on his website; it's required reading (Ed - use Google Chrome and it will offer to translate it into English - Fab!). If you wander around the site enough, you will eventually encounter a sobering and crushing update from Radek. Stanislav Tvrdik passed away in late February of this year (Ed - yes I heard about this on FB when it happened - very very sad). Yet another great puzzle personage gone. 

Stanislov Tvrdik, a man I would have liked to meet. (photo from
If you are looking for information on Mr Tvrdik, you won’t find very much, in English at least. Perhaps the best you can do is watch this Youtube video. Most of us won’t know what he is saying, but it is interesting nevertheless, and one is rewarded with a small glimpse of his collection.

Naturally, I am now extremely curious to know if Goat Gardner is a Tvrdik design. I searched and searched but could not find an answer to this. I asked Radek about it, being the only Czech I know, and he was not familiar with the puzzle nor who had invented it. I certainly would like to think it was Mr Tvrdik’s. We do know that he took the classic hedgehog, a very old puzzle, and updated it with a clever new design. Goat Gardner, very similarly, is an ingenious new take on a classic sliding puzzle. They both likely date to the late mid-century period, a period during which Mr Tvrdik was known to be quite productive. I think the circumstantial evidence leans to the positive, but I’ll leave it to our friends in the Eastern European community to resolve. Either way, it is a great puzzle to have and I treasure it as much as my artisanal puzzles, perhaps more.

This has turned out to be quite an odyssey. Thanks for sticking around until the bitter end. If you have any information, thoughts, or remembrances to share, please don’t hesitate to comment below. And don’t worry if this post is three years old by the time you read it. Blogs are like little wormholes through time, so just go for it. Back over to you Kevin...

Wow! Wow! Wow! What a fantastic article you have written there for us! Tremendous work and research has gone into it, I am almost ashamed of my own posts now and am wondering whether I should just hand the site over to you permanently? I'll need to buck up my ideas and produce better quality articles in the future! Thank you so much for helping me out again...I really appreciate it!

If anyone else would like to have an article published then please use my Contact page to get hold of me and we can discuss it. I have been contacted by a few professional web writers over the last few months and would like to discourage them - I really want well-informed articles and opinions from genuine puzzlers and not something generic.

Enjoy the rest of your weekend guys - see you again in a week.

Sunday 22 July 2018

This Unicorn is Real and I'm Not Crazy!

The Crazy Unicorn Cube
After just one corner turn followed by a top face turn!
The lurgy has continued in both me and Mrs S (who is making some rather interesting gurgling/coughing noises) and has not helped my puzzle solving abilities much and has not helped her mood at all. She was seriously unimpressed at the abrupt expansion of my collection recently. Luckily she is too incapacitated to commit violence upon my person! Hopefully, our health will improve soon or I will be murdered in my bed and I hope that I will actually be in a position to solve something before I run out of puzzles to write about!

I have previously discussed the Unicorn cube - a fabulous cube that I initially found rather tough until I found my Aha! moment and understood that it could be solved by simple reduction techniques. It consists of a simple 3x3 Rubik cube with 4 deeply cut corners that can be twisted too which splits the edges in two and also cuts pieces off the centres. In the end, I found that it needed little more than intuition and simple 3x3 methods making it a rather wonderful puzzle for anyone who wants a challenge just one step up (OK maybe a BIG step) from a simple 3x3. At the same time, MF8 released a crazy version of the Unicorn puzzle which of course, I had to purchase (my arm was twisted) but I never expected to be able to solve it. In fact, when I took the top 2 photos, it scared me enough that I didn't pick the puzzle up for another 2 months after that! Eventually, an FB friend showed off his ability to solve the puzzle and encouraged me to give it a try. he said that I would be pleasantly surprised by it. GULP!

Luckily it is quite lovely scrambled - there is a high chance it would remain this way!
I threw caution to the wind and scrambled it using a similar process to the ordinary Unicorn cube. It ended up looking fairly horrific and I was fairly certain that it would stay that way forever. The first thing I realised was that this puzzle was going to have to be solved differently to the plain Unicorn cube. There would be similarities but much of it would be different. The circles are fixed and do not turn with the outer parts hence making this a full "circle cube" and not really one of the Crazy planet cubes that I extolled the virtues of many years ago. The Crazy planet cubes have various combinations where the centres do or don't turn with the outer parts making for a very challenging series (which I really should go back to). I am told that a circle cube, where all the centres are fixed, is actually a simple puzzle in its solution process. I was delighted to see that these were not going to be a crazy series although it would appear that there is a simple piece inside that can be flipped over to change the way each face functions and I guess that it will not be long before the twisty crackpots begin to turn this into a planet series too.

Generally, before I scramble a new twisty, I spend a while exploring to see how the pieces interact with each other and maybe if possible, to see whether I can work out any simple algorithms. I usually end up scrambling the damn thing before I manage to work very much out. This time, however, I did realise that some of the circle pieces are much more limited in their movements than I initially expected. Some were trapped in 1 of 3 positions and others followed a particular orbit. This would greatly simplify the process. If you have not yet solved this puzzle and do not want any help then do not read any further as I plane to describe my process...

My first step was very similar to the plain Unicorn cube. I needed to realign the faces to allow the corners to turn again. As you can see above, the use of 90º turns at the end of the scramble causes the corners to be blocked from further rotation. Unblocking the corners is mostly just intuition and judicial use of the 4 move edge piece series to ensure the edges are positioned and oriented correctly.

All the corners are now free to turn
Do you notice anything in the picture above? Look at the small triangles inside the circles - they are trapped in 1 of 3 positions. It is a trivial thing now to place them and produce a completed square in the centre:

Centre squares completed
After that, it may be that something else is obvious? I suspect that it's hard to say that from the photo but when playing with the cube it is fairly obvious that the circle edges that are not part of the turnable corner can only be on that face. There is actually no physical way to move them anywhere off the face and it is then fairly trivial to move them.

A few 180º rotations od the faces left me filled with confidence! So far the puzzle was being solved mostly by intuition and a bit of trial and error. I am not sure why I chose this order to approach the puzzle but it just seemed the right thing to do at the time. At this point, I had the squares complete and the circle edges on the non-turning corners in place with minimal effort. Now it was going to get a bit tougher!

So far, not too hard!
My next aim was for to try and complete the circles. This looks fairly impossible but I quickly noticed that there was a peculiarity of the remaining circle pieces...they are actually bound in pairs like a single edge piece. For example, in the picture above the small green circle piece below the MF8 logo is actually bound to the small white circle piece on the red face. They CANNOT be separated. This means that the G/W circle piece needs to be taken away from its current place and put back in that face but to the right where there is currently an O/Y circle piece (to the right of the MF8 logo). At least initially, it is a trivial thing to move these paired circle pieces into an unsolved position and then put them back into the correct place. Again, like the rest of the puzzle, it is mostly intuition and using a simple 4 move algorithm. As more and more of the pieces are placed there is much less room for play and the substitutions get tougher but during the movement, it quickly becomes apparent that each time you position one of these pieces, you are just carrying out a 3 cycle. Once this next Aha! moment has been passed it becomes a simple thing to arrange it such that the final 3 pieces to be placed can be done in a single 3 cycle. Once you have done the positioning sequence 4 or 5 times it becomes second nature. The process does not upset the pieces that have been solved already. One ends up with a circle cube with split edges:

All the circles are complete and now just the split edges to reduce
This is now looking rather like the plain Unicorn cube. Time now to reduce the outer edge pieces. Here it is just a simple matter of using the 4 move edge piece series to cycle the edges where you need them without upsetting the circles. Once a small edge segment is placed in an adjacent position to the corresponding large edge section, a simple turn of the corner pairs them up. Of course, that corner turn ruins the circles and hence care is required to use that same edge piece series to move the completed edge into a storage position and then turn the corner back again to re-complete the circle. Just as before (and in the plain Unicorn) it gets harder and harder to do this as there is less and less space to work in. In the end, they need to be positioned in such a way that the last 3 edges are solved simultaneously. It takes a bit of playing around to achieve this but really does not require anything fancier than an edge piece series and some planning. At this point I had a simple circle cube:

All circles are whole and the edge pieces are paired together
It still looks fairly fearsome to someone not familiar with Rubik type puzzles but this simply solves like a standard Rubik cube as long as you stick to algorithms that use paired movements. Taking advantage of Marshall's "Ultimate solution" which uses nothing more than the now infamous edge piece series and the corner piece series, it is a simple thing to solve this puzzle without ruining the centres. In fact, this puzzle is almost easier than the plain Unicorn cube! The pathway to completing the circles ensures that none of the parities that I saw in the plain version appear in the crazy version. I would again say that if you can solve a 3x3 and want a little extra challenge then the Unicorn cubes (both of them) are a really good path to take. They look great, they frighten your friends and family and solve with only a little extra from what you can do already.

Go buy them at HKNowstore or at PuzzleMaster whilst they are still in stock. You won't regret it!

Sunday 15 July 2018

Possibly the Most Beautiful Puzzle in the World?

And of course, it's Mathematical Too!

Simply stunning! The Pi box by Jesse Born
I am forcing myself out of my deathbed to bring you a quick blog post today - this summer cold is proving really bad and even after being forced to take a couple of days off work I am still not much better. In true male fashion, I am not complaining much and just being very brave and soldiering on. Unfortunately, I have infected the current wife with what I thought had originated with her in Scotland. But, judging from the effect it has had the last few days, must have been picked up here and seems to have mutated into "She-bola". Now I am sure you will be shocked to hear that she has been muttering vile things about what she plans on inflicting upon my person should she survive. I suspect that a Whack! Ouch! will be very mild compared to what she has in mind! Gulp!

As you ALL know, I am not generally a puzzle box collector (despite what Allard's latest post says about me). Some of my puzzles do have cavities in them but to me, that is an incidental feature! I love good puzzles and if they are beautiful then that adds to the attraction for me. I have been watching Jesse Born on Facebook for a while and was very excited when he showed off something new (I had enjoyed his entry into the IPP design competition last year but had been unable to solve it). It looked to me to be a fairly classical box and hence was not something I was particularly going to buy. This one, however, whilst being a box, was simply gorgeous and I therefore had to make an enquiry about purchasing it. Jesse is great to communicate with and a month or so after my enquiry a rather large cardboard box flew across the Atlantic to Sheffield. After the usual tussle with Her Majesty's revenue and customs department and a moderate bribe was paid, it landed here.

Even the base is beautiful
A nice certificate too
Every detail about this puzzle is stunning - the choice of woods, the detailing on the slipfeathers, the unusual nonagonal shape, the design of the hinge (at least I assumed that it was a hinge at that stage) and of course, the Yosegi design on the lid. Even Mrs S admired the beauty of it before commenting on the rather large dimensions! Luckily I was able to reassure her that it was destined to go on display in the second puzzle cave upstairs.

The slices of the pie appear to slide towards the centre (at first quite a lot of them could slide) and at that point, that seemed to be the only thing that was possible. It was time to be systematic and see whether certain slices would allow other things to happen. I was not disappointed!

I continued fiddling and realised quite quickly that if I got the right moves then progression was easy to achieve. About 3 weeks into my intermittent playing I realised that there was a definite mathematical pattern to the puzzle which I was able to confirm by racing through almost all the moves towards the end. I could not believe how Jesse had managed such an amazing sequence of moves. Then....I hit a brick wall. What I thought was the final move would not seem to happen. Was I completely wrong? Had I incorrectly gone down all these moves to be stumped so close to the end? I assumed that I was wrong and started again but the clue in the name of the box kept haunting me...I could not be wrong!

One last slice of pie and it won't move!
After some help the pie was complete
In the end, I had to contact Jesse. He always responds very quickly and initially started with encouragement on the path I had taken and then when it was just not working, he gave me an instruction on using an external tool to make the final move. I did what he said with some trepidation and had my Pi box open - it is just as beautiful on the inside:

At last! Even the interior is gorgeous!
What was the problem? Nothing really that was down to Jesse's workmanship. The weather here has been VERY hot and pretty humid for the last 4-6 weeks and the simple sliding bolt latch that the final pie piece pushed was very very tight. Having used my external tool to open it I was able to gently move it back and forth a few dozen times and now it works very smoothly.  I have opened and closed the box a number of times since and it works perfectly now. I am sure that in the winter it will be very smooth.

Amazingly Jesse has made it possible to see the mechanism of the box. A pin can be pulled and the lid can be taken apart. The physical representation of a mathematical idea looks very abstract when separated into pieces but after a fair bit of play and some doodles, I was able to visualise how it works. This new puzzle designer is a genius. I know that Allard enjoyed his work as did the perpetually puzzled and inebriated surgeon, Steve.

Jesse has another design in the making just now and I cannot wait to see it. If you are interested then express your interest on his signup page here.

Sunday 8 July 2018

Pyrigan's Model Number 360

Pyrigan’s Model No. 360
Hi guys, today I am so so grateful to have yet another interesting post from the Puzzlemad foreign correspondent on a puzzle I have only recently heard about. For some reason, despite being the sucker that writes the on-call rotas for my department, I have found myself having to work 2 weekends in a row. The good weather in the UK has brought out all the usual crackpot behaviour, including climbing things, falling off things, driving too fast and losing control. The emergency department in my hospital is also a regional major trauma centre and thus it seems to become mayhem...especially whilst I am on call! On top of that taking up my time and my sleep, Mrs S has just returned home from visiting the outlaws in Scotland and brought one of those vicious England-hating colds with her which immediately pounced on me. Not only am I on call all hours but I feel like hell at the same time...sigh! Thank heavens for Mike Desilets stepping in to take the pressure off me. Thank heavens also that he has put in a LOT of work to get a fabulous article for you:

Aloha Kākou puzzlers,

I’ve been lying low on the puzzle scene for a little while, but our friend John Partridge has given me cause to whip up this fresh Puzzlemad submission. You remember John, founder and lead designer at Pyrigan & Company? Of course, you do. You may even own No. 808 (Ed - I missed out!), his first major release about a year ago. If you do, then you probably also know by now that he has just released a follow-up puzzle named No. 360. If not, this will be your wake-up call.

No. 360 was released on June 9 and the limited edition of 100 has been selling quite fast. Batches went to the usual retailers in Canada and Europe. The first batch on Pyrigan’s Etsy site sold out by June 20. Puzzlemaster is sold out. At this rate, I’m not sure if it will be available by the time you read this.

As you can see from the pictures, No. 360 is a very attractive metal puzzle machined from T6061 aluminium. It measures 107 x 34 x 34 cm and weighs in at 325 grams. Not insubstantial by any means. It has good heft and feels very solid in the hand. The body of the puzzle is aluminium, but Pyrigan has wisely chosen to plate it with nickel to give it a more lustrous and durable finish. Even though it is strikingly beautiful out of the box, know that as you play it will definitely tarnish in short order. It's not a fault with the puzzle, per se, just an unavoidable result of the oils in one’s skin. I was sensitive to this, but even washing my hands before handling it was not enough. After 30 minutes of play, the finish smudged up nicely. That’s just the nature of it I suppose. It is reversible, however. You can get the original finish back with a little Brasso (just a very light buffing, don’t overdo it!).

Trapped prize
Perhaps the most striking and unique feature of No. 360 are the four circular cut-outs and the turquoise marble trapped in the centre. Although not necessarily associated with the solution (as far as you know) it’s a very attractive design element. Without this feature, it would just be a metal box. But with it, you have an object of beauty apart from the puzzle aspect. It practically begs to be picked up and examined.

A mysterious rune from the ancient world. Or perhaps just the sound of P.
As always, the Pyrigan symbol is etched into the puzzle, this time on one of the ends. John hand-paints the Pyrigan logo on every copy. My last article on Pyrigan had enough going on that I didn’t research or think to ask John about the logo. I did some homework this time though. The Pyrigan symbol is actually the fourteenth letter in the Elder Futhark runic alphabet. It is the sound of the letter p and it also means ‘game,’ from what I can gather. Something about a pear tree too. I can’t figure out exactly what’s going on, but maybe John can fill us in.

The other end.
The puzzle is constructed in two symmetrical parts, the separation of which releases the marble and solves the puzzle.  Like No. 808, this puzzle is of the hidden mechanism take apart type. Based on John’s comments, as well as my own experience, this one is much tougher than the 808. Tolerances are very fine and the mechanism is more complex. Puzzlemaster rate No. 360 a 9 on their peculiar 5-10 scale. I think they have it about right. It might even warrant a 10. On this point, I have to admit that I have yet to solve No. 360. Here at Puzzlemad we almost always solve puzzles before writing about them, for obvious reasons (Ed - blush...not always!). However, exceptions are sometimes made. After many, many hours of toil with No. 360, I believe it is going onto my “long-term effort” shelf, to be taken out periodically and worked on. If I waited to solve it before writing, it could be a very long time indeed. I have stuff that has been in ‘long-term’ for years (Ed - me too), so I thought it best to just get some info out there for the readership before we all turn grey (more grey that is).  

Note the seams.
No. 360 is indeed a very tough nut to crack. The tolerance’s being what they are, there is virtually no movement between the two halves. The marble can be rolled around and you will find a little surprise on it. However, you will likely scuff up the turquoise if you fiddle with it too much. It’s in there tight against the metal. A very minor concern,  but for those wanting to keep their puzzle pristine, worth mentioning. The puzzle provides some feedback. To my ear, there are at least two distinct noises. Something is sliding or rolling (or both) at either end. Although the noise could be a decoy, I highly doubt it in this case. The noise is enough to give you some rudimentary ideas. Naturally, you will try all the standard movements, as I did (Ed - did you submerge it in gin? That often works!). But the mechanism is clearly too complex for this, and more original as well, I can only assume. After I had completely run out of ideas, I turned to the brute force approach. Not literally brute force, but statistical brute force (i.e. if you try enough random movement for long enough, eventually something will happen). Not the most elegant approach I admit! But despite John’s effort to make No. 360 a ‘fair’ puzzle (see his write up here), the clue potential from the feedback was lost on me. With the very tight tolerances, the unsystematic approach may not bear fruit for quite some time. This is too bad because I am insanely curious to see what’s inside. 

To make up for the breach in the Puzzlemad review protocol, I offer the readership another interview with the designer, John Partridge. John is a swell guy and a pleasure to interview. This will hopefully give you more insight into the man, the method, and the inscrutable No. 360. 

Mike: Before we get to Model No. 360, can you fill us in on your personal puzzling over the past few months. Any good discoveries (new or classic), solving triumphs, new interests? In other words, what have you been up to when not working on 360? 
John: Well, in terms of puzzling related stuff, most of what I’ve been up to is on my blog. As you probably noticed, I reproduced some other people’s designs (e.g., Stewart Coffin, Dic Sonneveld), and that’s always a fun way to get the creative juices flowing. These days I am also working on a new puzzle design (it doesn’t have a number yet); frankly, I’m not sure it will even work! I’ve been 3D printing prototypes and it remains very fiddlesome.  I did have a solving triumph a week or so ago - I was able to solve Roger’s R2D2 puzzle. I love his puzzles and solving them always feels great. I also play around with home science kinds of projects. For example, I made a reproduction of the old Atomix toy and I tried my hand at making a Kalliroscope but it needs some refinements. 
Mike: Picking up from where we left off last time, what exactly is the source of your puzzle numbers? First an 808, and now a 360. Are they connected to the mechanism? Can they be taken as clues in some way? 
John: The numbers are totally random, I’m afraid. I heard through a friend that someone claims to have deduced that the number 808 is a clue to solving Model #808. I would love to hear how because it would be very cool if it turns out my subconscious is actually leaking clues! 
Here’s an alternative answer: The numbers are carefully contrived clues of the most devious kind. For example, “808” is displayed prominently on the Joker card found in the popular Bicycle brand playing cards. If you read the history of why it’s there, you will be able to solve my Model #808 with your eyes closed. And “360”, as I’m sure your readers know, is the sum of Euler's totient function φ(x) over the first thirty-four integers. I should think the solution is now obvious. 
Mike: Judging from the relatively short gap between release of the 808 and 360, you must have been able to take advantage of lessons learned from the last effort. That said, the 360 was in some sense under development concurrently with 808, so it probably has a longer timeline than one would suppose. So when did the concept for 360 first come to you, and is the final puzzle the same as your original vision? 
John: You’re right, the #360 design is much older than the #808 design – I think I came up with the #808 in 2014 and the #360 dates back to 1996 or so. Yes, I applied a lot of what I learned from the #808, mainly things about mechanical engineering, how machinists think, and how I as a designer had to be thinking about manufacturing considerations, not just functional requirements. That’s one of the reasons the final version differs as much as it does from the original vision. That’s not a very specific answer, I’m afraid, because I don’t want to give something away! 
Mike: Back in November 2015 you mentioned that you thought the 360 might be your first puzzle to go into production. This obviously didn’t come to pass. What made you shelve the 360 in favor of the 808? 
John: Basically, I was trying to follow the “crawl, walk, run” approach to trying anything completely new. The #808 was my first attempt at “crawling” and is a much simpler mechanism compared to the #360. I hoped that because it was simpler it would be easier to have made, and less expensive too. That last part is important because you never know if a puzzle is going to flop or not and if it was going to be a flop, I didn’t want to have lost a lot of money. 
Shiny and irresistible.
Mike: Can you give us any info on puzzles that inspired the 360, without undue spoilers. If not, we complete understand! 
John: Hmmm. That’s hard to answer without giving too much away. I would say that the whole category of metal puzzles – Wil Strijbos’, Marcel Gillen’s, Rainer Popp’s, Gary Foshee’s, Roger D’s, and there are many others – I just love playing with those puzzles. So my brain kind of marinates in a broth of brilliant puzzle ideas all mixed together until, who knows how, a new idea bubbles up to the top and behold! Inspiration.  
Mike: It was great to get insight on your approach to puzzles and your general aesthetic sense from the recent 360 blog announcement. We all have our sensibilities, and although most everyone in the community strives (rightly) to be exceedingly diplomatic, tolerant, and good-humored, I think there is also value in laying one’s cards on the table. Especially for designers. Anything you care to expand upon, for the historical record? Has your puzzle ethic evolved over the years, and if so how? Have your early puzzle views softened, hardened, or just gone in other directions?  
John: Are you calling me diplomatic?!? Them’s fightin’ words! (Ed - hahaha!) Look, I’m in no position to criticize designers who have dozens if not hundreds of great puzzles to their name when I have come up with, wait for it …, two. We all have personal preferences in music, movies, books, and not surprisingly, puzzles. At the moment I personally don’t care for magnet based mechanisms but I could see how that might change. I ran into a puzzler who keeps a magnetic field viewer handy whenever he goes to puzzle parties so he can quickly figure out what he’s up against. That seems to me to address my concern that magnets make puzzles “unfair” when you don’t know a magnet is inside. Is it worse than holding a puzzle up to the light to see what can be seen through the gaps? Is it worse than X-raying the puzzle to see what’s inside? All I can say is that I don’t like puzzles I have to bang on and I do like puzzles that rattle and give up their secrets incrementally, but that’s just me.  
Mike: Back to the puzzle itself. The inclusion of the ‘marble’ and the four circular cut-outs is a pretty radical (and beautiful) modification from the 3D printed prototype you produced back in 2015. How did this come about? 
John: Thanks! Well, there was always going to be a token of some kind inside the #360 – my intention is to have all my puzzles contain one – so the design modification was simply to make it visible while the puzzle was still unsolved. For some reason I think it makes the puzzle look more intriguing because you can see what the goal is. Anyhow, once I decided it should be visible, I had to decide what material to use and for a while it was going to be a glass marble. As I was poking around eBay looking for glass marbles, I came across ones made from garnet and turquoise and malachite and all kinds of minerals. Eventually I picked turquoise because I thought it would look good with the nickel finish. 
Mike: The 360 was so attractively proportioned, I just had to check on the ratio of the short sections to the long sections along the long axis when closed. As expected, it’s very close to the Golden Ratio. Intentional or intuitional? 
John: I really really wish I could say “intentional”! From experimenting with different proportions I decided I really liked how the puzzle looked when the width was one third of the length. I guess that’s kind of “intuitional” in that it kind of intuitively looked good…? 
Mike: Do you use any formal or informal testing program for the puzzle, getting peer feedback on prototypes or that kind of thing? 
John: Oh yes, I have a very formal testing program with a staff of four. Well, maybe “staff” isn’t the right word. One of the great things about having kids is that until they reach a certain age, they’re basically hostages. “Staff” sounds so officious; let’s go with “hostages”. 
Mike: I spent a good deal of time on No. 360 and could unfortunately make no sense of the sounds and movements which I could clearly hear inside. It seems substantially tougher than the 808. Is there any hint you can give to the frustrated puzzler?
Hint #1: It’s harder than the #808.
Hint #2: The tolerances are tighter on #360 than on the #808. (Actually, that’s not really a hint, is it.)

No. 360 standing tall. Bit of a perspective issue here. The hole is actually dead centre.
Mike: The No. 808 can truly be considered a smash success, selling out in very short order. I don’t know the current status of No. 360, but I would expect a similar result. This must be very gratifying given the great deal of effort you put in. I know you have your family’s support for your puzzle work, but still, this must be some form of vindication. Minimally, there should be absolutely no eye-rolling in the Partridge house when dad gets into mad scientist mode and retires to the laboratory. True or false? 
John: I’m very lucky that way. The family thinks it’s great that once or twice a year the playroom gets overrun with boxes, metal parts, paint, paint remover, and loud noises. If I were into model ship building I think they would be equally supportive; it just so happens that puzzles are my thing. It’s true, we were all very surprised by how popular the #808 turned out to be. We’re hoping people enjoy the #360 just as much. 
Mike: Now for the inevitable look-ahead. No. 360 is barely out of the gates, so I apologize for asking so soon, but what’s in the works? No. 518, No. 921, or something unheard-of? Or are you going to taking a well-earned breather perhaps? 
John: Right now I’m really unsure on the design of my next puzzle. I’ve sold a little under half of my #360 stock so that will keep me busy for a bit. When I get some inspiration I’d really like to try my hand at a sequential discovery puzzle (“I’m trying to think but nothing’s happening!” – Curly). Model #921 is really tempting but I think it’s going to be hard to get it to work reliably. Model #518 is an even older design than the #360 but I worry it will be super expensive to fabricate. Plus there are two more designs that don’t have numbers yet so I guess the short answer is, “I have no idea!”. 
Mike: Finally, thank you, from the puzzle community for the tedious hand-painting of the Pyrigan logo. You’ve mentioned it more than once on the blog, so I know it’s no trivial matter. It truly does add that final bit of polish to an otherwise beautiful creation. Anyway, it does not go unnoticed, I assure you. 
John: You’re very kind! I whine too much about it but here’s what’s going on. The #808’s are bead blasted before they’re anodized. That bead blasting gives them a beautiful matte finish but unfortunately the red Testor’s enamel I use will simply not let go of it. It drove me nuts as you have read. Well, 106 of the #808’s later, lesson learned, right? I figured that nickel-plated aluminum will provide a really smooth surface that nothing would stick to. Boy was I wrong. There are microscopic little grooves left behind from the hand-buffing the machine shop provides and even after nickel-plating, it turns out those grooves really like paint. Aargh! Maybe I’ll make my next puzzle out of glass.
Thanks so much for that interview John, we all really appreciate your candour and good humour (Ed - correct spelling added!). Good luck with current and future endeavours (Ed - sigh and again!). If and when No. xxx is released, I will surely hound you for another interview to keep this thing going. 

That’s it for this issue folks. But before we go, I want to reiterate something John mentioned above. Namely, that Pyrigan occasionally makes and sells reproductions of certain selected classic puzzles. The most recent was Stewart Coffin’s #167 “Cruiser” packing puzzle, produced with Mr Coffin’s permission of course. I have a copy and it’s a fantastic little puzzle, especially for the price.  John’s version is in laser-cut acrylic with nice vibrant colours. I still love my faded, crumbly vintage plastic puzzles, but these modern acrylics are really slick.  And there can never be enough copies of Coffin classics. Back to you Kevin...

Thank you so much, my friend! I am looking forward to future articles from you - they always add something new for me as well as my regular readers. This has been edited and is all set to go live whilst I am working. Please if anyone has any comments for Mike then feel free to leave a comment below or contact me using my contact page. Any other authors are welcome to make guest posts if you have anything interesting to tell the puzzlers of the world.

Hopefully I will get more sleep than I did last Friday!!!!

Sunday 1 July 2018

Continuing the JCC "Entanglement" Puzzles

Double twist-U - How it was sent out
A better presentation?
Looks trivial? Hell no!
Here I continue my odyssey into the latest batch of puzzles from the incredible Jean Claude Constantin (probably to be exclusively available from Wil Strijbos). The batch of 10 has proved to be a huge challenge! The Spiral-U-U which I struggled to disassemble last time remains in pieces on my puzzle chair and despite 3 weeks of annoying "she who must be kept more than an arm's length away", I just cannot seem to put it back together! Every construction I make just falls trivially apart, no matter how much complexity I put into the assembly process. I know better than to ask Wil for help - remember rule number one of fight club...erm puzzle club?
One of the next puzzles I attempted looked a lot easier. I have named it anatomically the Double twist-U puzzle because of the 2 twisted pieces which look like an elongated standard nail puzzle with a U added to it. The left picture is how it arrived but I was quickly able to move it into a much more attractive conformation which I think is nicer. This puzzle looks MUCH easier than some of the others but is probably about the same difficulty level. The twisted nails are surprisingly interlocked at first and the U really gets in the way. I am always very careful to try and keep in memory the movements I make but, as can be seen from my struggles to reassemble some of them, this often fails. I find that the more complex the shapes are the easier it is to keep orientation memorised but with this, I found it quite difficult. There are a number of initial moves possible but none seem to get me anywhere. The solution was made even trickier by the puzzle consisting of 2 identical pieces so closely aligned. After an evening of play, I had my first Aha! moment:

To be honest, that was not what I expected to happen!
Having achieved this partial solution I backtracked to the beginning again and realised that this was not an easy feat! I did manage it eventually but found that the positioning requires very accurate placement and again, I struggled to remember the exact set of moves. Having got it back I tried to undo it again and even struggled with that! Either I am not very bright or this is a pretty challenging puzzle - I will let you decide which it is...comments below, please. Finally, on my second evening of play, I was able to repeat the process and decided to do the step. This is pretty much what you would expect from an intertwined nail type puzzle except there is an extra twist to it. After 2 days, I had my pieces for photography!

Phew! Unexpectedly hard!
OK! Time to put it back! I had mastered the final assembly stage so expected it to be fairly simple...except it's not! As is common with the better nail puzzles, you are lulled into a false sense of ease with it and don't truly pay attention to the conformation during final extraction (of course everyone thinks that these are trivial). Suddenly I realised that putting the two 'nails' back together wasn't happening. Again we have an "Entanglement puzzle". Eventually, I got it and was able to marvel at the beautiful movement required...that curve at the end of the nail really adds an extra challenge. Having struggled for a while it again took me 20 minutes or so to reattach the U piece. This is a lovely puzzle and really quite challenging - probably a little too tough for a beginner but a nice medium challenge for an experienced puzzler. Be careful, though, it jingles!!! Whack! Ouch!

Balls on rod-U
This is one of my favourite of the bunch. Again we have the experimentation with the U which adds an interesting solution. The addition of a loop of string makes for a more complex puzzle which is rather hard to keep track of movements. It is possible to pull the rod through the larger ball dragging the string loop through it which really makes for some complex conformations. Most of the tangling that troubles a string puzzle is easy to back out of because the loop is short and cannot go very far. Random idle play let me suddenly take it apart within only an hour but with no idea how I had done it:

Easy peasy! Gulp!
It had not taken me very long so in a fit of self-confidence I put the pieces away for an hour which I discovered was a very silly thing to do! Having taken it apart with very little idea of the exact moves I had made, I found myself in the enviable position of being completely incapable of remembering anything about my disassembly. I could barely remember my own name or that of the strange woman glaring at me across the room! Whack! Ouch! To my horror and the strange woman's amusement, I took 3 days to find the assembly. That string is really clever and I am not! I love this one - it is actually not that tough once you know it but finding the Aha! moment took me longer than expected.

The Spira-U-Heart puzzle is particularly delicious for the clever movement that is required for the disassembly. There are 2 features of the puzzle that deliberately lead you astray...these features appear in other types of disentanglement puzzles and are key to the solution but in this one, they do not play a part. This could leave you attempting impossible moves and getting fixated on the wrong feature. Luckily for me, I was not fooled by these shapes and rapidly saw that a different approach was required. I had it apart in about 20 minutes and sat back to admire the rather interesting sequence.

Such complex pieces would be expected to be difficult to dismantle but it's not that bad.
Again, I left the pieces for a while and went back to it after a ½ hour or so. I was certain that I knew the exact sequence but could not get it done straight away. The crucial thing which I had forgotten was that the start position for reassembly is critical and if you cannot quite remember it then it won't work. To my horror, it took me another ½ hour to find the start position and reassemble it. This puzzle is probably one of the best for beginners and experts is not easy but can be worked out with some investigation. It makes a great, if rather large, worry bead!

I have only solved one of the 3 remaining puzzles - that one is rather fun and repeatable too (a future review will show it). This leaves 2 of them sitting on my puzzling chair - I have been working on them for a good few weeks now and, apart from realising that trying the same move over and over again doesn't work, I have been unable to find any way to advance. I'll keep at them until they are might take me months! Many of Aaron Wang's puzzles have been beating me for over a year!