Sunday 16 June 2019

Packing with Purpose

Box Rebellion
This post follows a little discussion I had with my friend Dave Holt (of the Metagrobologist) who has an absolute fixation on packing puzzles...the more complex the better! He had shown off a picture of one of his recent acquisitions from Tom Lensch, the CRUMB/Melting Block puzzle designed by Bill Cutler and John Rausch.

Dave's CRUMB puzzle
The CRUMB consists of a full set of 28 lettered pieces shown above in their larger storage box with one non-lettered piece as a small spacer to fill the box. There is also a standard box to work on all of the many puzzle challenges and a 3 sided 'corner' box with dimensions of the bottom, sides and depth of the box (created to avoid 'in and out' attempts (as called by Bill and John) which eliminates reaching in and out and easier to slide pieces around). There are 76 doubly-unique solutions to the packing ranging from the 10/11 piece CRUMB (which is relatively easy) to several 13/14 piece ones, which are very difficult to solve manually. Whilst I really appreciate the beauty of the craftsmanship and the incredible variety of puzzling provided by this amazing multi-puzzle, I commented that I am not a huge fan of packing puzzles with so many pieces in them as there is far too much random trial and error and not enough deduction in the solution process. A wonderful and far more eloquent follow up comment from George Syriaque stated it beautifully:
"The issue is that ‘figuring out where the pieces should go’ requires far more effort than ‘figuring out how to get them there’"
This sums me up with packing puzzles entirely. I did eventually solve and review the Melting block a long time ago but have seldom attempted such a complex packing challenge since. I definitely prefer my packing puzzles to be about getting the pieces into position rather than finding where they should go - this sort of follows on from my love of interlocking puzzles. One example of this is the Box Rebellion pictured at the top of the post.

I was very proud to get a copy of the Box Rebellion puzzle (Coffin #195) from Tom Lensch quite recently. Tom had made a bunch after some discussion with my friend John Rausch who had reminisced that the 4L puzzle had been getting a lot of attention recently and that he had exchanged Stewart Coffin's Box Rebellion (#195) at IPP24 in Tokyo which had a number of similarities. I had absolutely adored the 4L puzzle back in 2016 and would always seek out something similar if it came up for sale. By the way, if you don't yet have a copy of 4L then get one NOW - Eric has them for sale here - they are an ESSENTIAL purchase.

John's original exchange puzzle had been made by Walt Hoppe. Like 4L, it has 4 L-shaped pieces that must fit into a restricted-entry box. Unlike the 4L, the acrylic top is not fixed in place, it can slide back and forth 5/32" (Lord, why can't the US embrace the present and the future and go Metric?),  which is enough to allow an L piece to fit on one end, and enough for one cube of an L piece to raise up on the other. Unlike 4L, the L pieces for this puzzle are made from three cubes.

Tom's lovely version is made with a Walnut box (complete with small finger sized holes in the ends to allow manipulation inside and an oddly shaped acrylic top which has a little movement to it. The 4 L shaped pieces are beautifully made from Yellowheart. The premise is very simple and with only a little thought, it is obvious how the pieces are to be positioned in the box. Getting them there is another thing altogether. If you have done the 4L before then you will not be overly troubled by this one because the thought processes are similar. But it still takes a bit of planning and a fun little struggle with moving the pieces around using just the little holes and gravity.

Very clever - I will be storing it unpacked though, to allow torture of colleagues at work
If you have never solved 4L then this is will be a much greater challenge but still possible without spending weeks on it and it may be a nice work out for when 4L finally comes your way.

Next up os another packing puzzle with very few pieces and a placement challenge:

Petit Ring
Of course, I cannot buy just one simple little packing puzzle from Tom and have it shipped 1000s of miles! He also offered me the opportunity to buy one of Osanori Yamamoto's latest designs, Petit Ring. Made from the same woods as the Box Rebellion it is another "simple" packing puzzle with just 3 relatively simple pieces to be put into a 3x3x2 box with oddly restrictive but wide open holes in opposite corners of the top and bottom. The fact that there are holes in both sides gives an idea that this is going to be quite a challenge. Again, it is more interlocking puzzle than packing and I love the challenge. It looks at first that the holes are wide open and that this will be easy but that diagonal half voxel is a real problem - the end result of it is that the entry holes are L shaped which is seriously restrictive.

These 3 pieces do not completely fill the cavity of the box but I assumed that the final result should have the entry holes completely filled and any gaps are concealed inside. The similarity to Pack 012 (also by Osanori) and the false solution to that one made me quite wary. There are a few ways that the pieces can slot together in a 3x3x2 shape and it is a fun challenge to work out which of those are physically possible to get inside the box.

I came up with a very promising way to put the pieces together quite quickly and then moved the puzzle to the box packing part and quickly ran into trouble. The larger shape will only go into the box in a few orientations and needs a lot of manoeuvring space to get it in. As soon as the other pieces are introduced that manoeuvring space disappears very quickly. After a bit of thought, getting 2 pieces in is achieved and then the final challenge is how to get that final piece inside. I could find 2 possible orientations for it but it was terribly blocked. Changes to the entry order were no help and I struggled with it for a few evenings.

Eventually, I had a thought© which is an unusual event for me but as is more common, that thought had an error! Many of Osanori's puzzles have very ingenious rotations in them and I wondered whether that was required for the Petit ring? The tolerances in Tom's craftsmanship are fabulous and rotations are almost impossible. After another evening of experimentation I had finally achieved the final puzzle state:

Solved it! This photo was taken after a rotation
I was really pleased with myself for solving it and then I had a look at the page on PuzzleWillBePlayed only to see that I had solved it but in the incorrect way. It states that there are 72 assemblies of which only one is achievable and, crucially, it makes no mention of the need for rotations. Now Ishino san is very meticulous in his maintenance of the pwbp pages...if a solution needs rotations in the solution then it is always described (have a look at the listing for Osanori's Galette puzzle here - it clearly states that rotations are required).

The lack of this mention forced me to go back to my puzzle and spend another few hours on it. Finally, I got it! That is a wonderful design - not really one for trial and error but requiring planning and thought©.

If you have a copy of Petit Ring then your challenge is now to solve it both ways. Can you find the correct solution and then do it all over again with rotations? It is brilliant and I cannot wait to get more of his fabulous "low number of pieces" designs.


  1. I am still struggling with Petit Ring and Lychee. It will be great once I suss it out

    1. Still not found out if Lychee needs rotations though

    2. I don't think I've ever heard of Lychee. If it has not got rotations then Burrtools can solve it.

    3. Yeah I couldn’t find it on PWPB. Come to think of it I think I did put it into BT and no rotations. I will have to double check

  2. You included a quote from little ol’ me???? I feel honored!

    Although I still suffer the nasty habit of generally thinking and speaking in standard imperial measurement most of my fellow primitive American brethren ;-), it may please you to know that i’ve actually used & targeted metric dimensions for all but 2 of the 150-ish puzzles I’ve crafted since getting into the hobby several years ago, as I’ve found it alot easier to be precise in terms of whole millimeters units than in fractions of an inch.

    Lastly, the 4L is the perfect example of a really fun and challenging packing puzzle that meets our apparently mutual criteria. If you or any one else can recommend others I might similarly regard/appreciate, like the 4L and others mentioned above, please do. Thanks, George.

  3. Can't agree more with this statment! "I definitely prefer my packing puzzles to be about getting the pieces into position rather than finding where they should go." Like George, I too would be interested in a list of packing puzzles similar to 4L (not same solution, but design/# of pieces/etc). Thanks!

  4. Well, the Cubic Dissections Pin Block Case and Stumbling Blocks are DEFINITELY in that same class, but I'd be surprised if you don't already know this.

    1. Yes, both are awesome puzzles. I have both and am looking forward to more.