Cast Cake

No Fiddling! It's Time to Think©

Hanayama Cast Cake

Last weekend I blogged about 2 of the latest Hanayama cast puzzles which have yet to be generally available outside of Japan. I am sure they will be available from all the usual puzzle suppliers soon. I began my odyssey with the easiest of them (a level 1), the Cast Diamond and decided that it was a fun little puzzle with little challenge for the experienced puzzler but a really nice one to give to friends to watch them attempt. Then I moved on to the hardest of them (level 6 out of 6), the Cast Infinity which I actually found relatively easy but I have been told by other puzzlers that it actually isn't as easy as I think it is and many people may find it a reasonable challenge.

I had seen on Facebook that quite a few puzzlers had really struggled with the supposedly easier challenge of the Cast Cake. The Cake is rated as a level 4 on Hanayama's 6 point scale putting it at the same difficulty level as the Cast Möbius which Mike reviewed for me here. He was not very impressed with it and rated it much easier than a 4 (as would I) and it certainly would not be in the same league as others rated as level 4 like the Cast Marble, Cast Radix, Cast Donuts and others. All of those have been reviewed by me (Marble, Radix, Donuts) and I have thoroughly enjoyed them but consistently thought of them as considerably harder than the level 4 they had been given. I have to say that the Cast Cake also should be rated as a level 5 or maybe 5½. This puzzle was designed by the incredibly talented Bram Cohen who is responsible for quite a few puzzles in my collection, many of which are incredibly challenging.

The puzzle is cast, like many of the series, from Zinc alloy and made to look like an aged copper. The name is beautifully inscribed in the top and the Hanayama name is on the back. The outer compartment has a ¼ circle cut out from the front and back making the puzzle resemble a rather large coppery Pacman - this cutout is extended in the centre to a ½ circle which would apparently give a nice easy slot for removal of the contained pieces. Unfortunately (actually that should be fortunately!) easy removal is definitely NOT what you will find! The contents of the shell consists of another 3 identical plates each of which has a ¼ segment removed (1 large Pacman has swallowed 3 smaller ones). None of the inner plates can slide out because they slot together and are held by the indentation in the front of one interacting with a bulge in the back of the other. All 3 plates slide into each other and they also interact with the outer case - this results in a construction in which it is only possible to rotate them in situ.

Like many new puzzles I start of by idly fiddling, hoping to either fluke the solution or to at least notice something crucial whilst I move pieces about. With this one, the only thing to notice is that nothing is possible except rotation, that the pieces are fiddly to rotate due to friction with the plates above or below. Also after a while of rotating pieces around and around you realise they are all identical and there is no maze or key piece inside. At this point it was clear to me that I was stumped and I was going to need to borrow one of Allard's skills and Think© - something I am not particularly good at!

This is NOT a puzzle anyone is likely to solve by accident - you do need to fiddle with it to make a number of discoveries and then you need to stop and think how to use these discoveries. I played with the Cast Cake in the evenings for a week before I finally had my epiphany and after moving the disks around for a few minutes into the precise positions I had calculated I completely failed! Back to the drawing board! I thunk again and the following day tried a new variant of my original idea and Bingo!

3 baby Pacmen came out of the mother

2 have been flipped over to show how the reverse

Here it can be seen how the pieces interact

Having scrambled the pieces from the orientations they had been in on removal, I was slightly horrified to realise that I couldn't get them back inside. I knew what my initial thoughts had been and had to work it out from scratch to allow the reinsertion. The reinsertion is a bit less fiddly than the extraction but definitely a fun process. I did find that I had spent so long devising my thoughts that I was able to repeat the process after that without too much difficulty. I am aware, however, that a few puzzlers (including my friend and VERY experienced puzzler, Michel van Ipenburg) have had to spend a few days after the initial solution before they could say that they had truly mastered the puzzle.

This puzzle is right up there with the Cast Marble, Cast Donuts and Cast Radix as one of the best - it needs a proper understanding of how the pieces fit together and then thought and planning to solve it. Random fiddling is not going to get you anywhere at all. Derek (yes the genius) has been playing with his copy for a week now and so far has not managed to solve it which should give you some idea of the difficulty level. I think I will need to take it to work for a few weeks before my poor anaesthetic assistant, David, manages it - he certainly has had one or two reasonable thoughts but not yet put them together into a coherent whole yet.