Two Half Voxels Make All The Difference

Sukiyaki by Frederic Boucher

I am catching up today with a puzzle from the Pelikan workshop that I did not manage to solve within the time frame that I had been given before they went on sale. Unbelievably, there are still 7 of these left available for sale. Stop reading now and go buy one - it is an amazing puzzle. 

This puzzle is one of three designed by Frederic Boucher named after Japanese foods (Frederic lives in Japan). Frederic wrote this about it:

“SUKIYAKI is the first in a series of 3 packing puzzles I created some years ago, named after famous Japanese foods (SUKIYAKI, TAKOYAKI and TAIYAKI). The box size is 2x3x4 units, with 3 openings on the sides plus the entrance on the top. At first glance the pieces seem identical, but there are actually 3 kinds of pieces. No rotation is required to solve this puzzle, but that doesn’t mean it’s easy. To solve this puzzle you’ll have to think “outside the box” to find the right configuration and then how to make the pieces interact with each other. I hope you will have as much fun solving it as I had creating it!”

Having failed to solve it for the sale, I have carried it with me for several weeks and have been playing with it intermittently for 3 weeks. It looks like a fairly straightforward packing puzzle with 6 identical S-shaped tetrominoes (made from Maple) to place in the 2x3x4 unit box (made from a rather lovely American Walnut). The opening seems quite large and there are 3 holes in the box for manoeuvring pieces out of the way to allow more to be placed inside. I genuinely didn't think it would be too much of a challenge (one reason, I had saved it to last in that batch) but, oh boy, I was very wrong!

Looking closely, you can see that whilst there are 6 S-shaped pieces, 2 of them have a half voxel removed from it and, for each of those, it is the opposite side of the piece. The obvious question to ask is, why? My initial thought was that these two pieces would interlock inside the box to form a whole voxel. As advised by Frederic, I set to "thinking outside the box" and created some shapes with the 2 odd pieces interlocked. Much to the amusement of several orthopaedic colleagues, I began swearing at myself under my breath and had to deny their urge to do the orthopaedic thing and hit it with a hammer. Let's just say that particular surgical specialty is better known for their brawn and not their brains, unlike my Urologist friend who is better at solving things down a long tube and surrounded by rather smelly liquid - hence his preference for copious amounts of alcohol!

Needless to say, I resisted the urge to use force and decided to use thought©. I worked out quite quickly that the 2 half voxels are not interlocking with each other and they must be present to make space for internal moves to happen in the box. I struggle to think© in terms of whole voxels and so half ones are really going to confuse me! This is why it took me 3 weeks to solve this fabulous puzzle. It was useful to know ahead of time that there were no rotations involved as there was a huge temptation to start turning pieces about inside or in the entry hole. Despite the relatively large entry hole in the top of the box, the pieces are quite restricted in how they can be inserted if rotations are not allowed. Having thunk outside of the box, and using the position of those single holes, I had found what I thought was the likely assembly and none of the gaps formed by the half voxels would be visible through the holes in the box. Of course the 2 odd pieces could be placed in several possible positions and I just needed to decide where so they would be useful. 

Interestingly, this ended up being solved as an assembly puzzle outside the box followed by a disassembly puzzle before actually packing the pieces inside. It really took a whole lot of logic and thought before I had my sequence and packed the pieces away for this photo:

Sukiyaki solved at last

The assembly sequence for this is absolutely stunning! It really cannot be solved by random movements unless you are willing to be completely exhaustive. The proper way to solve it is by genuinely applying multiple steps of logic. There was a huge grin on my face when the last piece went inside and a complete look of disbelief on my orthopaedic friend's face when it was done. In retrospect, I actually think this might be the pick of the bunch from Jakub and Jaroslav's last release.

There are 7 of these left in stock as I type this. Go buy it now! You really will not be disappointed!

I have been in discussion with Frederic about the Minima puzzle series and he has written a wonderful article on the whole series including additions by other designers. It is a wonderful, large and comprehensive document which is downloadable here. If you have any comments on this series which you would like me to pass on to Frederic then please get in touch and I will pass on your thoughts.