Sunday 28 January 2018

Wood is Good But.....

......So is Acrylic

Dwarf Planet D
You all know how much I lurve my wooden toys (in fact just have a look at the latest post on my New additions page to see just how much I lurve wood) but sometimes a craftsman produces something (or several somethings) made from acrylic and I just cannot resist. Actually you know I struggle to resist any new puzzles no matter what they are made of.

Just before the Paris IPP we were joined by the brilliant Brian Young (MrPuzzle himself) in Birmingham for one of our MPP gatherings. Brian was showing off quite a few new and old toys (including the fantastic sequential discovery puzzle, the Louvre which kept me occupied for a VERY long time - still available here). He roamed the room chatting and solving things before finally putting us out of our misery and opening his suitcase of goodies that he had brought from Oz. We all pounced like a pack of starving hyenas and I left the MPP later that evening with quite a nice stash of toys and the knowledge that I would still have some (not enough) cash left for the IPP itself.

One of the toys I brought home was the Dwarf Planet D which is a 3 piece board burr with what looks like a captive cube inside (I had seen this before at Allard's house and decided at that time that if possible I should get one. This puzzle was designed by the incredibly talented William Hu and was the exchange puzzle given out by Jerry Slocum at the IPP in Japan in 2016 (the reason I saw it at Allard's).

Ali told me that I should have someone else dismantle it and then assemble it myself from scratch. I was rather hesitant about this because I am truly awful at assembling things even if they have very few pieces. Remember if a designer confidently presents you with an assembly puzzle constructed from just 3 or 4 pieces then there must be something really complex about it! When I got home I quickly hid all my new purchases (except the Louvre) from Mrs S to try and fool her that I had been very restrained with our money. Whack! Ouch! Sorry dear! A few days later I broached the idea that she take it apart for me so I could put it back together again - this suggestion led to me receiving a near fatal burn from the laser burning stare and I quickly dropped the idea! For some reason she really doesn't like puzzles much and will only play with something if it is truly gorgeous or contains diamonds! I was left to do it myself. The disassembly is a very nice little voyage and has some rather unexpected moves in it

There's actually 6 pieces in it!
The sandblasting of the cube pieces makes it look like a single piece
After my surprise at seeing the cube was 3 smaller pieces, I just put them all away in a cloth bag and left them for a week to give my sieve like brain a chance to forget the whole thing. It is only level 6-8-2-3-3 so I figured that it shouldn't take me too long. WRONG!!!! I think I worked on this for a week before I finally got it back together - either this is pretty tough or I am really REALLY bad at assembly puzzles. I'll let you choose which of those is correct. At various times in the evenings in late July, Mrs S actually wondered whether I was having a heart attack! There was so much muttering and groaning going on from my chair in the living room! When I finally got it back together again, I shouted aloud and further upset "she who must be plactated with shoes and handbags". I should not have been surprised at my failure - apparently there are 69 false assemblies and only one possible solution.

The Dwarf Planet D may only be Acrylic and only be 6 pieces but it is a terrific puzzle when approached as an assembly. It also is surprisingly cheap and still available to purchase from Brian and Sue's wonderful store. Go get one now and have someone else disassemble it for you first. Then be prepared for a fabulous challenge!

Pulsar Burr
Another puzzle which I bought from Brian at that MPP was the Pulsar burr by the incredible Junichi Yananose (his blog is here and puzzle store is here - run by him and his wonderful wife, Yukari). This puzzle was the exchange from Lambert Bright at the 2015 IPP in Ottawa. I was originally not going to buy it because partly it was only acrylic and also it was an assembly puzzle (sold as a pack of pieces) which I acknowledge freely that I cannot seem to cope with. Again at the suggestion of Ali (I sometimes think he doesn't like me much!) I was convinced that I should buy this one too and it was added to my pile o' puzzles. This one was then taken home and put on my shelf of stuff to be played with and then forgotten about during IPP. After that I kept picking it up in the packaging and then shying away and putting it down again - yes, I am THAT bad and frightened of them! This puzzle has a photo of the finished shape on the packaging but even with that I was too frightened of it!

Finally I saw a photo the completed puzzle amongst the collection of my good friend and fellow moderator of the Facebook Puzzle Photography group, John Haché (blog here). After mentioning that I had still not solved mine, John sort of goaded me into giving it a try.

Taking the pieces out of the package, I saw 4 acrylic boards and a wooden stick which was supposed to traverse them. Looking at the provided picture is helpful for this one. Brian wrote:
"The puzzle consists of 4 pieces of 10mm acrylic and a single wooden piece from Western Australian Jarrah. One of the acrylic pieces is quite unique to any other burr we’ve ever made. Junichi designed it with a sweeping curve cut out of the piece. 
This is a very doable puzzle from someone who’s had a little experience assembling burrs. But it is designed by Junichi so it’s not a pushover that’s for sure!"
Well, I guess I am an experienced burr solver but not assembler. There seems to be a few possible orientations of the boards but the ones pierced by the stick are pretty obvious with a little thought. After that a little experimenting is required and you quickly discover that the "sweeping curve" provides some really lovely moves. As is usual, the first few attempts trying out the more obvious assemblies just won't work. After about 30 minutes I began to take John's name in vain and put it down to stare at it and Think©. Unusually for me this actually worked! There is nothing unexpected about the solution of this puzzle, no rotations, no tricky moves, but the order and positioning to assemble this one is entirely unexpected. In the end after about 45 minutes I had it assembled and congratulated myself on taking John's advice - this is a really clever puzzle too. It is easier than the Dwarf Planet D but just as much fun. In fact, I would suggest that this is perfect for both novice and experienced puzzlers alike. Perfect despite being acrylic!

Glitter was also bought at the same time as the other ones. Again, I would not have been planning on buying it but a good friend of mine had mentioned this design to me over a year ago as being very very tough and worth purchasing. So for a very reasonable $45AUD this became mine. Designed by Osanori Yamamoto, this puzzle was also an exchange puzzle in Canada - this time by Frans de Vreugt. The description by Sue on the website is quite dramatic and made me a little worried about it:
"There are so many peculiar moves due to the rotations that it even makes it difficult to know exactly what disassembly level to classify this burr as. The printed solution has been draw with 61 steps. 
The puzzle requires rotational moves, so BurrTools can't help you much with this one!
No force at all is required to rotate the pieces;  everything just needs to be lined up just right so you’re ready to make the move. 
Sold assembled. It would be way too difficult if we sold it apart. Even though we sell this puzzle assembled we still don't think that many people will ever take it apart and reassemble it again without the aid of the solution or a computer."
I get the distinct feeling that this one is rather difficult!!! I have played with it intermittently ever since I got it and am sort of ashamed to have to admit that I have not really got very far! Initially there are not very many moves possible but as you work your way in there are more and more possibilities and most seem to end up at a dead end. Except there may be rotational moves at the dead end and I haven't noticed. I have done several rotational moves but they don't seem to help. I think I am about 20 moves in and that is it. It's back on the shelf just now and maybe I will try again soon - when I have finished with my recent new purchases. Unfortunately this one has now sold out. If enough of you pester him then maybe you can convince Brian to make some more?

Now I really must solve something or I will very soon be running out of stuff to write about. I just don't seem to get the time to solve much recently.

Sunday 21 January 2018

Puzzles to Return to

During my sick leave I had a major splurge on puzzle deliveries to give me something to do whilst forced to sit on my arse doing very little (Whack! Ouch! - sorry dear but the doctor told me to!!!) As you can tell, I had been home for so long that "she who must be feared" started to get shirty with me. She went so far as to get pretty gobby at times and on several occasions told me that I really needed to bugger off back to work! If I hadn't gone back when I did then this blog would have been no more and Mrs S might have been spending time at Her Majesty's pleasure. I do apologise for all that....I have not lost the plot - a certain Matthew Dawson challenged me to use some "special" British terms in my next blog post and ahem...there it is. One batch of puzzles that I bought came from the amazing Yavuz Demirrhan and I have to say that they are "The Dog's Bollocks"! Ok, Ok! Enough already!

One of the puzzles I had been really keen to get my hands on was the Transenna. It is a fabulous looking interlocking puzzle made from Walnut and Maple with reinforcing dowels in contrasting colours. I love this type of puzzle because it looks fantastic on display and can be a nice challenge for a rainy Sunday afternoon or a day during sick leave. This particular one was of interest because it would go on display next to another one that I had reviewed in March 2016, Volantis.

Transenna and Volantis - fabulous together
I set to with this puzzle and quite quickly disassembled it into 6 of each type of board and admired the woodwork skills that went into them.

Stunning workmanship
I left the boards for a day and then worked on the reassembly. In my own personal puzzle database I have a classification for each of my puzzles and I refer to these as interlocking puzzles rather than burrs because the main challenge here is an assembly one and it doesn't really require multiple back and forth movements of the pieces. I suspect this is not a very good system but it works for me. The reassembly is a little tricky but not terribly hard with a level of (total of 33 moves). Had the puzzle been sent out in pieces then it might have been a little more challenging. I did enjoy the process and did it a few times before returning it to the shelf. I completely forgot that this one had 2 challenges to it. I was perusing through Facebook and saw Yavuz' original post about it and with a start I was reminded that I had more to do. Time to return to this puzzle and attempt the alternative assembly. This one looked easier on paper being only level (27 moves) and not requiring all the pieces. In reality, because I had not disassembled it and also did not know which of the 2 types of large boards were needed, this proved a much bigger challenge - it took me pretty much a whole evening to find the correct approach and order. Mrs S was happy that I had recently returned to work and was no longer doing Sweet Fanny Adams (aaargh! It's all Matt's fault!) and she even didn't mind me muttering to myself as I attempted the reassembly. She did flinch a little after I yelled Bob's yer Uncle as the last piece slid home. I promise....that's it, there will be no more!

Second assembly of Transenna - simpler but took me much longer.
It was definitely worth returning to this puzzle as it gave me even more of a challenge and appreciation of Yavuz design skills. It is still available on Cubozone if you want a copy for yourself.

Pinocchio - original challenge
Alternative assembly
Last week I showed off a few wire puzzles that I had failed to solve for many many months. After I returned to them and finally worked out the little trick that each of them required, Aaron posted on my Facebook page that the Pinocchio has an alternative challenge. The aim was much the same - one of the rings on one side of the string needed to be moved to join the other one on the other side. This new challenge looked really fearsome - there are a lot more interactions between the string and the main frame of the puzzle. I suspected that this one shared something in common with one or more of the puzzles discussed last week. I took it to work and had a chance to play with it whilst waiting for a critical care bed to be available for a big case I had to do. At work I could mutter to myself and jingle to my heart's content without fear of a Whack! Ouch! The current horrific state of the NHS winter bed crisis was in my favour as I ended up having about an hour to work on it.

The Pinocchio alternative shares a few moves in common with the original but after that it changes and needs some more thought - there was quite a big tangle at one point with several loops being around that central ring. After a little adjustment of the string I saw a similarity with the Balance and Wedding Vows puzzles and my Aha! moment was complete:

That was quite a challenge!
Finally I have to show off one puzzle that I have been returning to pretty much every evening since it arrived in mid December. I had showed off the recent puzzles produced by Jakub and Jaroslav's New Pelikan Workshop and over the last month I have singularly failed to solve the Lucida puzzle. Allard had told everyone who would listen that it was a fabulous puzzle and my friend Rich Gain had taken a few weeks to assemble his 3D printed copy. The premise is simple take the 2 pieces and the frame and combine them without having any sticking out bits!

Looks simple? Maybe it is but I couldn't do it!
Every single evening since mid December I have spent at least 15 minutes (if not longer) attempting this and had gotten absolutely nowhere! I definitely tested Einstein's theory of insanity (and yes I am!!) I just could not seem to work it out. During play it is quickly obvious what needs to be done but getting the pieces into a position where it is possible eluded me. Suddenly after a month a few evenings ago, I started from a new position and suddenly I saw a possibility. I have no idea why I hadn't tried or seen this sooner - my only excuse is either insanity or stupidity (I'll let Mrs choose). The first attempt with my new starting position wasn't quite right but a small adjustment and I had it! The Aha! moment was one of the best ever - this will definitely be considered for my top puzzles of 2018! I showed my success to Goetz and he mentioned that there are 2 assemblies! I felt bad that I had missed not just one but two for so long until I realised that they are mirror images of each other resulting in the grain going in different directions and the text being hidden in one:

Two solutions and I struggled to find even one!

Yet again, I prove to myself that perseverance is crucial and it's a good idea to keep returning to puzzles that haven't been solved yet or have extra challenges to them!

MiSenary box update

Last week I reviewed Michel's excellent MiSenary box and announced his auction for charity. It seems to be going well and has reached a reasonable level. To try and increase the amount earned for the very worthy cancer charity Michel has added some extra prizes which will be added if the bidding passes certain targets:

Bid above €250 : two prototypes of the CFF100 limited edition puzzle will be added.
Bid above €300 : first prototype of Larva and a second pair of sliders will be added as well.
Bid above €375 : first prototype of Ladybird will be added as well.
Bid above €450 : first prototype of 8 stars labyrinth will be added also!
This is a seriously special set of puzzles and includes prototypes which are not available any other way. Get bidding!

Sunday 14 January 2018

A Chance For You to Win and Perseverance Pays Off...

MiSenary Box from Michel van Ipenburg and Robrecht Louage
It's being auctioned for charity on Puzzle Paradise
OK! Normal service resumed! My first week back at work was fairly horrific! I had got quite used to getting up at 8am instead of just before 6 and definitely got used to having a very leisurely start to the day! After 7 weeks off for recuperation (including a week of annual leave) I got thrown in at the deep end and had to sink or swim with 3 of VERY big complex cases! Luckily, after 25 years as an anaesthetist I had not forgotten everything and the patient survival rate was 100%!! I, on the other hand, was absolutely shattered! I was so tired and haven't been able to solve anything all week! Thank goodness I have a few things saved up to write about.

I'm going to start off with a lovely little puzzle which I bought from my friend Michel van Ipenburg and which you now have the chance to win in a charity auction. I have communicated with him for several years now and know he is one of the foremost puzzlers in Europe with tremendous skills at both solving as well as design. I got to meet him for the first time in person at the IPP in Paris last year and enjoyed playing with his latest design in the design competition. The MiSenary box has a strange name which I did not fully understand at the time (partly because I did not realise it was Michel's entry). It is a box....yes I know! I don't collect boxes, but I DO collect N-ary puzzles and this is a Box AND N-ary. In fact, being 7-ary and made by Mi-chel, it is actually MiSenary. Get it? Yeah! It took me a while.

I first picked this up at one of the design competition tables and had absolutely no idea what was going on inside (the description did not hint at being N-ary). There are things sliding around inside as you rock it back and forth and sometimes it opens a bit and other times closes a bit. Occasionally it seems to close all the way and others it won't. I was totally confused and expressed this to Goetz, who was sitting next to me playing with something else. It was he who finally told me that it was N-ary and he finally had pity on me and said that someone had left it at a midway point of the solution. He gently took it from me and using what seemed to me to be a fantastically complex sequence of moves with multiple turns and twists, he reset it to the beginning and handed it back saying it was ready for me to solve. I am sure I must have looked rather foolish looking at him with my mouth agape but he was polite enough to not mention it. I played again for another 10 minutes or so before it was time for another event and needless to say, being not terribly bright, I got absolutely nowhere with it. I just had no inkling of what was happening inside.

Over the 3 days of the IPP I kept going back to it (it was usually partly solved when I picked it up) and at no point did I manage to understand it. Mental note to one of these after IPP if Michel makes them available.

At the beginning of November Michel let me know that he had made a second batch of the box and offered me a chance to purchase one. Needless to say I practically bit his emailed hand off! The whole world knows that I am a sucker for N-ary puzzles and having struggled so much during IPP I could not possibly resist (Mrs S says I seem unable to resist any puzzles and she has a point!) Just before Xmas a nicely packaged copy arrived - mine is no 1 out of 10 from batch 2. It would appear that Ali had also got one and promptly opened his so I set straight to it. This time I spent time looking through the slot at the front at the grid and tried to imagine what it was. I slowly experimented and got things moving. An small inkling began and I made about 10 moves before having a minor panic attack and back-tracking and failing to manage it! Aaaargh! I was stuck part way into it. Yet again I had moved without really visualising what I was doing. Mrs S told me in no uncertain terms that I had to put it down because it was Xmas eve and I had to cook - it was cheese fondue (yummy!).

After dinner and having eaten more cheese in one sitting than I should have eaten in 2 or 3 months, I settled down with Mrs S in front of the TV and made more attempts at the MiSenary box. In my cheese induced hallucinating state, I suddenly had a vision of what might be inside the box and what was happening as I made various moves. With lots of annoying muttering and counting to upset Mrs S I finally managed to open it. Very clever idea and beautifully made.

Solved! Michel and Robrecht say "Well done!"
This puzzle is a delight and you now have a chance to get hold of a copy for your own collection. The very last one in batch 2 and the last one that will ever be made has been put up for auction on Puzzle Paradise. It is 125x50x60mm in size made from Tropical hardwood, Trespa and Steel - Michel says that the copy for auction is the best looking of them all. If the price goes particularly high then Michel has said that he may add a bonus prize for the winner. The important thing is that the auction is for charity - the beneficiary will be The Antoni van Leeuwenhoek foundation / Netherlands Cancer Institute. This is a very worthy charity so please bid high and often.

Keep on trying.....

Back in March last year I showed off a nice big batch of puzzles designed and made by my friend Aaron Wang. I managed to solve a few over the subsequent weeks and one of those (Santa's socks) even became one of my top puzzles of 2017. The Clover was Aaron's entry into the design competition and was one of the most complex puzzles to solve from that batch but still possible for me within a reasonable amount of time. There were, however, 3 puzzles in the group that I struggled with....for months and months and months! I really don't know why they took me so long but I just could not seem to get my head round them at all.

Between Christmas and New Year's eve I got the 3 remaining puzzles out again - Mrs S was feeling mellow after Xmas and I decided to risk jingling a bit in the hope that firstly I might have a moment of genius (or more likely, luck) and secondly that I might get away without a Whack! Ouch! I was lucky on both counts. The aim of the Balance (and the theme of this bunch) is that the balls must end up grouped together on one side of the puzzle. The idea should have been very similar to the Wedding Vows puzzle from PuzzleMaster that I reviewed way back in May 2015. The Wedding vows looks impossible but with a bit of fiddling with the loop in the middle it quickly becomes clear what to do. I was certain that the Balance was a variant of this but for some reason I just could not see the trick to it. I went back to it on and off for 9 months without finding that breakthrough Aha! moment. I spent a whole evening fiddling with this and developing a knot in the centre of the puzzle around that pesky ring. After a couple of hours of back and forth I noticed something familiar. I must have been at exactly that position many many times over the 9 months and just not recognised what was going on. Having noticed that familiarity I knew what to do and a few minutes later I had this:

OMG! It took 9 months!
Balance IS very similar to the Wedding Vows puzzle but has just enough difference to it that it confused me a lot and took me such a long time. I am sure that most of you would be able to solve it within an hour but I, being not terribly bright, took a while! This one is not currently for sale as yet but a decent collection of Aaron's puzzles (he is also known as Wang Yulong) are available from the Felix puzzle company.

The Elephant was immediately attempted after my success with Balance and again it kicked my butt! Just like Balance and Wedding Vows, the aim is to arrange the rings next to each other on one side of the puzzle. I thought that the same things I had done with balance would help me with Elephant and I set to. Oh boy! I was seriously wrong! I'm sure that you geniuses out there can see straight away that this one does not share much in common with Balance. The central loop is trapped but doesn't form the same string configuration as the previous 2 and again I got stuck! There was a fair bit of effing and blinding before Mrs S gave me "the look" and I put it down again.

Over the next few days I tried again and again to understand this damned puzzle. In the end I gave up on my thinking that it shared anything in common with the Balance and had a good look at it. Unfortunately looking doesn't help! It took me several hours before my Aha! moment occurred and it was fantastic!

At last!
It has a totally different solution path to Balance and is really clever! Unfortunately I am not really clever.... I couldn't reset the puzzle to the beginning. Luckily Aaron has started using these nice little catches on his puzzles to allow quick reset (especially if you have a big knot). I cheated with the catch and started took me another 24 hours and I finally properly understood the puzzle. This puzzle forced me to think© and it hurt! Absolutely brilliant and finally time to crack the last remaining puzzle, Pinocchio.

This puzzle again is similar in basic shape and premise to the antecedent but, with the extra ring and the loop in a different place, it was a significantly tougher challenge. Just like before I was filled with hope at my success at the Elephant and I immediately tried the same type of moves...I got a knot! Quite a big knot! Thank heavens for the catch again. Clearly this puzzle is totally different and I should have realised that Aaron would not release 2 puzzles with identical solutions at the same time!

I played with this one for a couple of weeks again and failed repeatedly. One morning in despair, I actually emailed Aaron to ask for just a small clue. Yes it was that bad! That very evening I had not had a reply and I sat down again with the puzzle and had a proper think. Something began to filter into my dense skull and I had an idea, tried it and failed but noticed something else. I tried something counterintuitive and AHA!!!!

My goodness! That was difficult!
The general technique is similar to the Elephant puzzle but the new morphology changes the exact sequence of moves. Half of it is quite simple and then it requires some fairly complex reorganisation of the string before the next critical move is possible! I was able to email Aaron back and tell him that no help was needed even before he had responded - Phew! That is one VERY clever puzzle.

All of these share a basic idea but have radically different solutions - they all need one to Think© which is something I am not good at.

Thank you Aaron, I cannot wait for some new ones from you!

Don't forget the auction on Puzzle Paradise everyone - bid high and often for charity!

Sunday 7 January 2018

The Diamond 13 Puzzle

L.E. Ott’s Diamond 13 - Upending the classic magic square.
Well time for the first blog post of the year and I am extremely grateful to Mike Desilets, the PuzzleMad foreign correspondent for jumping to my rescue. I have been trying to solve a few new and old toys but this week have barely managed anything. On top of that I have just begun to go back to the gym after 8 weeks off for my surgery and am absolutely shattered! I suspect that 45 minutes of cardio for my first time was not a good idea but then you know that I am not terribly bright. It is really useful every now and then to have Mike (or anyone else who wishes to write something interesting) take the pressure off. Over to you Mike.....

Aloha kākou puzzlers,

As you may have noticed, it’s been quite some time since I’ve filed a report with Puzzlemad. Work has gotten the best of me lately and I just haven’t been able to muster the energy to sit down and write anything (Kevin makes it look very easy (Ed - if only that were true!)). It got so bad that my dear editor even sent me a note asking if all was ok (Ed - I just like to keep in touch with my friends). That was really nice, and just the kind of thing you can expect from a puzzle friend. Things are indeed ok, and with the holidays upon us, I now even have time to catch up on my backlog. Although I haven’t made time to write, there are several interesting puzzles that I’ve been itching to talk about.

You’ll recall many many months ago we dove (Ed - as an American, I will let you away with that but all of us Brits are cringing and shouting the word "dived" at you now) into a small but happy corner of the vintage puzzle world. Thanks to my friend and puzzle compatriot Amanda, we were able to explore some very cool old sliders. Around that same time I managed to pick up a great puzzle from the redoubtable (and long defunct) Embossing Company, makers of the Time Puzzle and Line up the Quinties. I don’t think I went into any detail about the company at that time, not wanting to stray too far afield. However, the history of puzzle companies is a sideline interest of mine, so please indulge me for a bit. This is all stuff you can google for yourself, but I’ll save you the trouble. (Thanks!)

The Embossing Company was not a proper puzzle company, in truth, but rather more of a toy company that carried a wide range of wooden toys, games, and “novelties.” Their early puzzles were of the simple edge matching, construction, or pattern making type, all made using their trademark embossed blocks. “Toys that Teach” was their motto. The company was founded in 1870 in Albany, New York and stayed in business for 85 years, finally selling out to Chicago wooden (and plastic) toy giant Halsam Products Company in 1955. Halsam was a relative newcomer, having entered the business in 1917. The owners, however, invested heavily in automation and quickly dominated the market. After the acquisition, they continued to manufacture the Embossing Company’s successful and well-regarded ABC blocks, dominoes, and checkers at their Chicago factory. I find no indication that they continued to produce Embossing Company puzzles, however.

Very fine detail achieved by the Embossing Company.
Embossing Company products, including their puzzles, were made using an embossing process (did you see that one coming?). Embossing of wood involves the application of heat and pressure to imprint a pattern or design. You’d have to ask a woodworker to be sure, but it seems to me that the compression makes these wood game and puzzle pieces significantly more dense, and thus harder, as well. The examples I have are very robust and likely capable of withstanding much abuse, which I imagine the children’s toy block line received. The embossing process also supported very fine design detail. Upon close inspection you will find very small and highly detailed patterns pressed into the wood.  If you are in the market for a very nice set of dominoes or checkers, think about hunting down an old Embossing Company set. They are as good as the day they were made and are prized by top checkers players particularly.

Nice durable pieces, courtesy of the Embossing Company, but be careful with the cardboard!
Ok, enough context. Let’s get to the actual puzzle. Today we have The Diamond 13 Puzzle, listed as No. 911 in the Embossing Company line. The Diamond 13 was invented by a certain L.E. Ott, probably in the 1940s or 1950s. A quick patent search pulled up nothing, so we can’t be exactly sure. This puzzle falls into the “Pattern” class, but somewhat uncomfortably in my opinion. You’ll understand better as you read on. (Ed - it looks like being in the Pat-Numb category of the Dalgety-Hordern classification)

The Diamond 13 is a descendant of the Magic Square family, including as it does the vast menagerie of ‘magic’ shapes that have been explored more recently. These puzzles are a mainstay of the recreational math community and have a very long history. Because the literature is so vast and most of the readership are likely familiar with them, I won’t go on and on. Also, recreational math is far from my strong suite. If I attempt to hold forth, I will eventually put my foot in it, betray my ignorance, and bring shame on Puzzlemad (Ed - NEVER!!). That said, you can’t appreciate the Diamond 13 without knowing the basics. So for new initiates, here is a very quick overview:

Magic squares present the puzzler with a square matrix of a certain size, the object of which is to fill the cells with numbers (the numbers representing the number of cells, specifically) that all sum to the same total—horizontal, vertical, and diagonal. The order 3 (3x3) magic square is the all-time classic, having only one Real (ℝ) solution (i.e. discounting rotation/reflection). Each magic square that is solvable has only one Magic Constant, being the number that must be totaled. Order 3 is 15, order 4 is 34, order 5 is 65, and so on. The number of Real (ℝ) solutions for magic squares increases extremely quickly (order 3=1, order 4=880, order 5=275,305,224 and order 6 is a staggering 1.8 × 1019, or thereabouts. No one knows the exact amount because no method has been discovered for its calculation). 

2 7 6 15

9 5 1 15

4 3 8 15

15 15 15 15
Order 3 Magic Square. Known and pondered since 650 BC.

(Ed - My goodness I've had to do some html editing here - getting the Real number sign and superscripts and that table with arrows in it was a bit of a challenge)

Magic squares are the original ‘magic’ shape, but you can apply the concept to just about any shape you like, and people have done so over the years. Probably the second most well-known magic shape is the magic hexagon, discovered by William Radcliffe in 1895. There is only one solvable magic hexagon: order 3 with a magic constant of 38. It’s an interesting shape because the totaled rows are of variable length, ranging from 3 to 5 cells. This structure hints at how to speed up your solution search.  The magic hexagon is one of the very few magic shapes to have transitioned from the mathematician’s page to an actual physical puzzle. Professor Puzzle produces a serviceable version in their Great Minds line. They are very widely available and cheap. I picked up my copy at Barnes and Noble.

Order 3 magic hexagon from Professor Puzzle.
Pieces are a loose fit, but they need to be in order to manipulate and work the puzzle.
There are all kinds of other possible magic shapes including stars, triangles, cubes, circles, pan-diagonal tori, and the mind-bending magic tesseracts (4 dimensional hypercubes). To learn about any and all of these objects, I highly recommend you go to Harvey Heinz’s website. You can spend hours there (Ed - I have!). I’ve only scratched the surface of what he offers. Harvey also has a page that will be of interest to mechanical puzzlers, in which he presents a number of magic mechanical puzzles supplied to him by Jerry Slocum.

Mr. Ott lays down the rules.
Totaling structure for the Diamond 13.
Now that we are all up to speed, lets return to the Diamond 13. Mr. Ott employs a magic diamond as his base shape. This is one of the least explored magic shapes. In fact, I can find almost nothing about them, even on Harvey’s site. No matter though, because the Diamond 13 is not intended to be a magic shape in the traditional sense. Rather, this puzzle requires one to create separate diagonal and horizontal/vertical totals, which are two different numbers. In the third challenge, for example, the four diagonals need to total 7 while the vertical and horizontal must total 21. Click the Show/Hide button to see what D-7 HV-21 this looks like solved.

The puzzle also diverges in its piece values. The diamond has 13 pieces ranging in value from 1 to 7. There are two 1s, three 2s, two 3s, two 4s, one 5, two 6s, and one 7. This is quite a mixture and certainly a departure from the sequential approach used for traditional magic shapes. Likely the major developmental work for the puzzle was in finding a mix of values that would generate the most ‘magic number’ problems. The image below shows 26 sample problems provided with the puzzle, and there are clearly more to be discovered. We take multi-challenge puzzles as a matter of course today, but they were not nearly as common in previous eras.

Sample problems for the Diamond 13 Puzzle.
D=diagonal, HV=horizontal/vertical.
With those radical departures from traditional ‘magic shape’ construction, one might reasonably ask if this is really even a ‘magic’ puzzle at all. The magic is usually to be found in the symmetry and deep patterning inherent in shaped arrangements of sequential number sets. And the magic constant of course underpins the whole edifice. The Diamond 13 takes great liberty with these rules, tossing most of them out the window. However, it still successfully exploits our primal fascination with the intersection of geometry and arithmetic, the quality responsible for the experiential “magic” felt when pondering magic squares or hexagons. From a historical perspective, at least, the relationship is crystal clear. The Diamond 13 was born conceptually from the magic square. 

But there is really only one question that matters. Does it work as a puzzle? In my opinion, yes, it works very well. I had tremendous fun working out the various number sets. The sample problems are challenging but quite manageable. The Diamond 13 hits the sweet spot for my taste. I enjoy tough puzzles too, but for pure enjoyment, a puzzle like this can’t be beat. Part of the enjoyment is due to the fact that this isn’t just a hunt and peck puzzle, where you are simply exhausting possibilities. The structure of the puzzle can be used to your advantage, but the way it does so evolves with the changing target values of the magic numbers. Note that the diagonals are only three units long, with only one value not shared with another diagonal. The horizontal/verticals are five units long, sharing only one common piece. As you play through the first few challenges, the dynamics of the structure become apparent. Another pleasant surprise was the approach (not given in the instructions, I did it out of laziness) of transitioning from one solved state directly to the next solved state. Doing the challenges progressively, in other words, without scrambling the pieces between challenges. I recommend this style of play. Some of the transitions can be done in very few moves, if you can see them. Exploiting the structural limitations really pays off here. This form of progressive play is reminiscent of the Time puzzle.

The Diamond 13 Puzzle is yet another great, underappreciated example of mid-century puzzle design. Although it may seem a bit contrived compared to the mathematical elegance of a pure magic shape puzzle, I can assure you that the design functions as intended. It provide a series of moderate-level challenges that force you to exercise both trial-and-error and strategic thinking. The designer began with a magic square-like concept, then rewrote the rule book. This might easily have proved disastrous and it’s a tribute to the designer that the puzzle works so well. 

Well as it works, we certainly don’t see the Diamond 13 in stores today. I’m not always sure why certain puzzles catch on and others don’t. In this case, the Diamond 13’s fate was probably linked closely with that of the Embossing Company itself. Like most game and puzzle companies, the Embossing Company relied mainly on a line of anchor products — tried and true classics — for the bulk of their sales. But they also tried to liven things up occasionally with new innovative products. The Diamond 13, the Time Puzzle, and Quinties were beneficiaries of the Embossing Company’s drive to distinguish itself from all the other companies making similar products (toy blocks, checkers, and dominoes principally). When the Halsam Products Company took over in 1955 however, only the best selling products, those with over a half century of name recognition, were retained. The more innovative puzzles, probably never great sellers in their own right (and often included only within larger sets) were not retained. I’m reasonably sure Halsam’s acquisition was more about buying market share than buying a product line anyway. Halsam would go on to be purchased by Playskool in 1962, which would ultimately be bought by Milton Bradley, which itself would even more ultimately be bought by Hasbro. 

The Diamond 13 Puzzle. Unlikely to be reissued by Hasbro.
Although there are a diminishing number of Diamond 13 puzzles out there for puzzlers and collectors, they are not especially uncommon. Both Amanda and I have copies, which should tell you something right away. But you don’t need to buy the actual Embossing Company puzzle, great as it is. All you need is paper and pencil. This hold for all the magic shapes, bar the terrifying magic tesseract. If you close your eyes and concentrate, you might even be able to do the order 3 magic square in your head. Try it. 

One final thing. The question of whether L.E. Ott’s diamond shape has a magic constant in the traditional sense may have crossed your mind. Looking at the layout, and thinking about the numbers involved (1–13), I would have to say I think not. But don’t take my word for it. I really don’t know and, embarrassingly, haven’t lifted a finger to try (Ed - shocking!!). But I will give it a go and report back in the next guest post. If anyone out there in the Puzzlemad Army wants to take up the challenge, please do. Even better, can you prove mathematically what the constant must be, or alternatively why there cannot be one? It’s an interesting problem which I am entirely unequipped to solve. Some enterprising rec math enthusiast should have a go at it. I’m sure you could get a paper out of it. Minimally, my editor will splash it all over Puzzlemad. (Ed - I definitely would even if I couldn't understand it)

That’s about enough for this post. Usually I try to squeeze in a few different puzzles for variety, but this seems like enough for one Sunday. Thanks for tuning in. Back to you Kevin . . . 

Thank you so much for that Mike.....really GREAT article! I certainly do need to try and find some of these vintage puzzles for my own collection. 

Tomorrow is my first day back at work and I am seriously not looking forward to it but I daren't be at home much longer or there will be a murder! "She" has already told me that I am NEVER allowed to have another operation that needs time off and I am never going to be allowed to retire! It would appear that I really got in the way AND pissed her off! Whack! Ouch! Ooops! Caught!