Perplexing Packing from Pelikan

Minima Ronde

333 & 444 cubes

Apteek

The pressure is on! I managed to dismantle 4 burrs by Alfons coming up soon from Pelikan last week and had 3 left to solve for this week's blog post. I knew this was going to be a hell of a challenge as 2 of them were by the amazing Dr Volker Latussek and one by Lucie Pauwels. Packing puzzles are definitely not my strong point and these two designers are particularly skilled.

Minima Ronde

Minima Ronde by Volker Latussek

I had to start with the Minima - I adore this whole series and actually think I have almost every one made. Considering Volker had not been certain about designing Minima puzzles initially, he has taken the idea to new heights with some incredible designs and this one is definitely one of the most fun ones I have ever played with. Jakub and team have made this one with a wonderful set of accurately cut Wenge pieces and a beautifully grained Oak box.

The basic premise of the Minima series is to have a 2x2x3 box to be packed with relatively simple pieces in such a way that the holes in the walls always end up filled. The interior may not be and the need for interesting rotations is often part of the fun but not always. Volker has taken this simple idea here with packing pieces that are just 2 voxels in volume but spread over a 3 voxel space with the use of diagonal cuts across one of them. Here is what Volker said about this design:

"MINIMA FOR FREDERIC was actually meant to mark the end of my foray into the world of MINIMAs. Over the last few months, I’ve been playing once again with one of my favourite building blocks: this is the complete set of fourteen building blocks, each consisting of a cube and a second cube that is cut diagonally into two parts, with each half glued across its entire surface to the cube. Accordingly, the building blocks in this set each have the volume of a bicube. Twelve of these blocks uniquely fill a 3x4x2 box (TOUR), nine fill a 3x3x2 box (GIRO) and six fill a MINIMA box (3x2x2). Years ago, I designed a ‘put-together’ puzzle for Pelikan’s RONDE using five pieces. Naturally, I now wanted to find out which building blocks could be used to fill a MINIMA box and provide it with suitable openings."

Oh boy! He has really provided us with a puzzle where the openings are crucial and used in different ways. It arrives in a special configuration (as almost all of his puzzles do) which gives a tiny hint of what might be coming up for the intrepid puzzler. Most of the pieces come out through the large 2x1½ voxel hole in the top surface but one of them is blocked and needs a bit of rotational fiddling to be released.

As usual, the initial challenge is to make the cuboid shape that will fit (this time the cavity will be completely filled. The handedness of the pieces means that you have to be careful which position they are placed in. I quickly realised that the arrival position had the 4 pieces with bevels at 90º to each other would form a cube and then the straight-line pieces would have to be used as a sort of length extender. 

The straight-line pieces lengthen the sides

Having realised this I made a cuboid of the correct size and then discovered that I could make 2 of them with mirror configurations. Time to pick one and then work out which of the 8 possible positions it could possibly be paced inside. I started with a brute force trial and error approach and very quickly realised that, due to the needed rotation(s) I was going to have to be more systematic and actually apply logic and thought©. The 4 single voxel holes in the box were going to have to be there for a purpose - Volker NEVER places anything unnecessarily - everything has a use. Working backwards, I Started with a shape that would allow the last(first) piece to be removed(placed). I searched for orientations of the cuboid that then had the possibility of either a second piece removal straight away or would utilise the holes for movements. At this point I had a fabulous Aha! moment and found a wonderful sequence that made lots of space inside the box. Now, it was time to work out how to place the pieces sequentially to allow that wonderful sequence to occur. Here is the challenge - the pieces don't just fit inside easily, there are multiple rotations involved (one in particular is absolutely incredible - Ronde means a round dance and that is exactly what you will have to do with this one. I don't think I have seen a Minima do that before. It took me an hour or so to find the required moves but eventually I reversed all my earlier moves and packed the pieces inside.

Absolutely incredible!

This is one of the most fun and rewarding Minima puzzles that I have ever worked on. The solution is completely unique, totally logical and beautiful to perform. A little dexterity is needed to control all the moves but it is fun. 

BUY IT! IT'S AMAZING!

333 & 444 Cubes

333 & 444 Cubes by Lucie Pauwels

This lovely little challenge by Lucie arrives as an interlocked set of pieces that form a cube with a lump on the top - obviously this is not the final placement of the pieces. This has been made using Maple and a brilliantly vibrant Jatoba. The precision is perfect. I removed the pieces to examine them and realised that the name of the puzzle came from the fact that the pieces could all fit together to form a 4x4x4 cube or the Maple pieces alone would form a 3x3x3 cube. I made the simpler assembly first and enjoyed that - a nice little warmup for the main puzzling.

4x4x4 and a 3x3x3

Creating the fully packed 4x4x4 is a clever challenge which reminded me a little of the Swan Cube from an earlier Pelikan release - the holes in the faces of the larger cube would need to be filled and this would need careful planning as they got blocked off quite quickly if the wrong piece was placed first. It's not too difficult and is a lot of fun. It could probably be solved by brute force but is better solved by noticing what the shapes will allow you to do and then thinking© about how this should be used in sequence to fill the void in the frame. Assembled shape hidden behind a spoiler button.

444 shape complete

Apteek

Apteek by Volker Latussek

Apteek and Farmacia

This incredible creation has been made from a deep Purpleheart wood for the box and an incredibly dark and fabulously grained Acacia. It is simply gorgeous. It arrives in a special configuration that Volker deliberately designed - the pieces seem to fit inside the 3x3x3 cavity but the central row is protruding above the surface. Obviously, this needs to be remedied and the pieces rearranged so that the pieces fit flush with the top surface. It's not going to be an easy process as the pieces (five L-triominoes and three L-tetrominoes) each have either a dowel protruding from one of the voxels and a reciprocal hole for accepting them. The box has a single dowel protruding into the top row of the puzzle. This reminded me a lot of a puzzle that I still haven't managed to solve from last year, Farmacia - this is still sitting on my desk waiting for me to complete it.

Volker wrote this about it:

"As promised, here it is APTEEK. When working with the usual v’s and developing FARMACIA, I had to learn that some very nice moves are not possible. However, from my experience with FILLING V, I know how powerful L’s are. So what could be more obvious than turning four v’s into three L’s and filling the 3x3x3 box together with the remaining five v’s? And suddenly, the previously impossible moves become possible. I really hope that you too will see that the price of losing the simple and clean construction principle of the 9 v’s of FARMACIA is not too high and that the beauty of the APTEEK solution - just as in APOTHECA - justifies the mixture of eight v’s and L’s."

Unlike the Farmacia there is no hole in the box to accept a dowel and with the dowel positioned in the top row, I had a funny feeling that this puzzle was going to require rotations to solve it. I spent a good few days trying to make at least a cube shape with the interlocking dowels and holes all fitting together. Interestingly, after many hours I had completely failed to find one. This didn't bode well for solving the puzzle in the box! 😱

Eventually, I resorted to Burrtools. Initially I looked for cube shapes and was slightly horrified to see that there were 7 cubic assemblies and 3 had a single hole that occurred in the correct place were it to be placed inside the box. I will need to assemble each of these cubes and then try the disassembly to see whether I can put one of them in the box. I did recreate the file with the box and found that there are 8 possible assemblies but no solutions. OMG! It will need rotational moves to assemble. Burrtools can only be used to give you a hint as to how it might possibly be assembled but not the actual solution.

I have spent several days on this and gotten nowhere so far and also to my horror, I cannot put it back into the transport position either.

This is an incredible challenge and best suited to the hardcore packing/interlocking puzzle solver amongst you.

Hopefully these will be going on sale within the next week or so.