The Half Voxel Confuses Me!

Marble Cake +

The last few weeks have been rather poor puzzling weeks for me. The case mix at work has become rather challenging as I have been presented with quite a lot of really challenging cases. For 3 weeks in a row, I have been up to my eyeballs in blood which has a marked tendency to leave you just a little fatigued by the time you get home. At one point, was also a connection on a pice of equipment that had not been tightened adequately and when some salvaged blood was connected, there was a ...erm... leak. I have to tell you that a little blood goes a long way! Especially when it trickles up your arm inside your clothing! Aargh! 

One puzzle that I have been carrying around with me for a few weeks has been another packing puzzle from Frederic Boucher, produced by the amazing Tye Stahly, is the Marble Cake+. It is currently sold out but, again, if enough of you make enquiries, Tye might be convinced to make it again. In this one, Frederic proves his mastery of 3D puzzle design - he abandons the usual 2x2x3 container to be packed and uses a 2x4x4 box which has a giant 2x2 hole in the top (plus a small 1 voxel hole in the front. No rotations are allowed. So what makes it a challenge? 3 of the pieces have ½ voxel overlaps which effectively means that it is not a 2x4x4 packing puzzle - it is, in reality a 2x8x8 puzzle and my brain doesn't work well at that scale.

I have spent at least a month searching for a way to assemble the pieces that fit the space (there were going to be gaps) and I really struggled. Having the ½ voxel pieces messed with my head. In fear that I would need to work my way through dozens of assemblies to pack, I entered the pieces into Burrtools and, much to my relief, I saw that there was only one way to assemble the pieces in the 2x4x4 space. All that I needed to do was find it and then work through 16 possible orientations with the box to find one that worked and finally, work out the order and move sequence of the pieces. I deliberately did not memorise the position of all the pieces but had a vague memory of where 3 of them went with respect to each other. I know it is sort of cheating but I was getting desperate for some success. 

Even knowing the start positions of these pieces did not make it easy. I really struggled to assemble my shape and after a month, I finally found it. Next, place it inside the box. Easy peasy? Nope! I always start by trying to see whether I can remove the pieces from the box rather than put them in. Here this was made a little easier by the fact that the front wall of the box was detachable. I don't know whether this was deliberate but it really helped me! I pulled off the front and stuffed the assembly inside and attempted to take the pieces out.

Make sure you take your photo of the assembly because you will forget it almost immediately after you take it apart to place individual pieces in the box! Quite a few of the orientations of the shape can immediately be discarded because there is absolutely no way to get even a single piece out.

I spent all morning today with my assembled cuboid and systematically worked until I found which one was possible and with great relief, just before it was time to write a blog post I had my solved puzzle. Talk about cutting it to the wire! It's a brilliant design by the absolute master of packing puzzles. A slight spoiler in the next picture so I have hidden it behind a button.

Finally after a month!

This is a huge challenge for such a simple idea and with no rotations. The half voxel pieces seemed to confuse me so much. Maybe you will be better at it than me? Ask Tye about making more and hopefully you can try it yourself.