Sunday 25 July 2021

The Good, The Bad and the Very Beautiful

Obscure burr
I am very grateful that Jerry McFarland keeps in touch with me! He is a truly lovely man and always pleased to have feedback on his new creations. Pictured above we have a lovely cuboidal puzzle that is immediately obvious as Jerry's work. He has called it the obscure burr. I was allowed to buy a copy at a very reduced price as it is just a prototype - even his prototypes are beautiful.

I am the third person to receive a copy and I hope that I am the one that Jerry is pleased with the outcome. The whole point of this is that the solution is based on an obscure mathematical idea - at least that was the description given by Jerry's brother after he described it to him.

Jerry had sent this to both Brent (of FiveSinatras fame) and also Bill Cutler (who is a proper mathematician having been a maths professor) and both had solved it but...

they cheated!!!!! 😜

The aim, as usual is to dismantle the interlocking cube (obviously by removing the central key piece which, here, stands out as a vibrant Padauk). Yes I can hear your gasp of horror! They cheated? Well, sort of. Some of you may recall some of Jerry's much earlier puzzles - the Quadlocks were stunning works of art that had multiple moving pieces in several dimensions that literally had to be solved like picking a lock. It has been quite some time since I played with them but they were quite a challenge for me.

Quadlock 1 (way back in 2011)
Quadlock 4 (from 2012)
So, the main aim of the Obscure burr from Jerry's point of view is to solve it using the mathematical technique that he wants you to find. This should be a "good" puzzle but I am really "bad" at solving mathematical puzzles (although I am pretty good at Sudoku, Kakuro etc). I could see that Jerry was really quite disappointed that both Bill and Brent had succumbed to the urge to get the solution quickly and they lock-picked it open. Despite that, I do think they both enjoyed the puzzle even if it wasn't terribly hard to do.

I promised Jerry that I would not give up so easily (he said that as soon as I pick it up then I will see the strange feature and use that to help me. After my initial photos, I could see that there were a whole lot of magnets in there - the light brown burr sticks can move freely in each direction and snap into place at each position thanks to these rather powerful magnets. The white burr sticks were fixed and would not move. Lord! The temptation was there to put pressure on the central key piece and move the sticks around to feel what was happening in side...but nope! I was going to be a "good" boy! 

The strange feature that Jerry had promised was a 3 digit number stamped into the end surface - in my case it was the number 177. What on earth did that mean? I had no idea. There are 5 sticks that can move but only 3 positions for each one - each of those sticks is also stamped on one end with a number (1 to 5 from the bottom) - did this matter? I tried to make 177 up using various combinations of the 1-5 and 3 positions. Nothing really worked. 

Off to Google to find any interesting theorems or combinatorics that involved the number 177.  Well there were some really interesting features to that number but none of them helped. Jerry insisted that it was very solvable but that he was working on having a clue built into the puzzle but covered by a magnetic plate. After 2 weeks, I had to ask for the clue and Jerry replied with just a single English word and a number:
With that clue, I had some definite ideas and within a couple of minutes I had the key piece removed I have put the next picture behind a button because there potentially might be a spoiler there and I don't want anyone to work out how it was supposed to be solved from my picture:

It was a "good" feeling to finally understand the obscure mathematics behind it and I felt "bad" for not having worked it out. But...I actually don't think that it would ever have been possible for me to work it out myself. I don't think there is enough on the puzzle for the maths to be visible.

The next step is to take it apart and that also was not trivial. It doesn't just dismantle after removing the key piece. There is a particular trick that Jerry has used before and it took me a little while to spot the trick and remember what he had done before - I soon had a nicely arranged set of pieces and some seriously strong magnets which keep clamping them together when you let go.

So we have "the good" aka me
"the bad" aka Brent and Bill (plus a rather obscure puzzle idea)
AND the beautiful - nothing Jerry has ever done is ugly
Having solved it the "good" way, I decided to assemble it again and see what it was like to solve the "bad" way and lock-pick it. Placing pressure on the key piece and moving pieces around in various orders left me with a solved puzzle in just a matter of minutes - it is pretty easy to cheat with this puzzle - almost trivial for anyone with any experience. Jerry had already thought about it and designed a mitigating mechanism which he thought might require too many hands to solve by cheating but in my opinion that will not work.

Jerry has had quite a lot of requests to purchase copies of this puzzle and he really wanted my opinion about the viability of this as a puzzle - what should I say? I obviously don't want to upset a very good friend but also feel that you all as potential purchasers need honest feedback and Jerry should know whether it is actually a "good" puzzle. Here is part of what I wrote to him:
"Your clue was just what I needed. It took a bit of experimenting to work out but I worked that out and managed to take the key piece out and dismantle the puzzle. Very nicely made and nice idea. Having taken the key out, I did like your signature well hidden next step. It took me another 15 minutes to find that move.

I then went back and lock picked it instead and that is almost trivial to do. I definitely don’t think your suggested locking mechanism will prevent lock picking. The only way to prevent that is to deliberately create several "false set" positions. That will throw off all but the best lock pickers and will mean it has to be solved mathematically or by huge amounts of trial and error which would not be fun.

Do I think it is a great puzzle? That is difficult to say. It is a fabulous idea but I think only a tiny minority of  puzzlers are mathematicians and almost none of us would get it without a clue. Why would we choose this mechanism? Without the clue, I would never have known to try what I did. As you have seen with Bill and Brent, most puzzlers will not try and figure out a mathematical puzzle. They will just lock pick it and maybe be a bit dissatisfied because doing that is pretty easy. On the other hand, your puzzles are extremely collectable and many people would buy it just so that they could have another of your puzzles in their collection. 

Whilst this would earn you some money, I don’t think that you would be happy knowing that you had a puzzle that people wanted to buy purely for who made it rather than for the solution process. I myself am delighted to have another of your puzzles and it took a supreme amount of self control to stop myself lock picking it from the beginning.

I really hope this helps you decide what to do."

In the end Jerry has decided that the idea and the tactile feel of the puzzle is too good to leave on a shelf and will make a bunch for interested puzzlers. I have to agree with him - it is a really lovely thing and a clever idea. If you lock pick it then it will literally only take you a few minutes and then you will just have the more minor challenge of dismantling and reassembly. If you try to use the methematical solution then maybe you will work it out - I am sure that you all are a lot brighter than me but Jerry will put a clue in the puzzle to help you. 

Of course, I am only too delighted to have another of his puzzles in my collection and I am positive that you will be too (the Burrlephant remains in pride of place on my mantlepiece).

Elephants to remind me of my mother (she grew up in Kenya)

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