Sunday, 27 February 2022

You Cannot Rush A Good Puzzle

Or...Failure Again!

Swiss Cheese and Grape
A couple of weeks ago I showed of Bruno's Caffe Latte packing puzzle and have to say that despite it being a packing puzzle, I absolutely adored the process of solving it (I hope that all of you have gone out and bought your copy?) He had sent me his Swiss Cheese and Grape puzzle as well which was really admired by the very discerning Michel and I just needed to find time to play. I had actually expected to have some time this week but something went badly wrong. My week rapidly filled up with work and my puzzling time disappeared. I even failed to attend the virtual MPP yesterday due to work (bloody virus!!!) and the last puzzling opportunity passed by.

I decided to give it a go this morning and early afternoon in the hope that I would have a tale of rapid success for you today. How foolish am I? 

The standard maze plates
The premise of this wonderful design is to place your 6 cheese slices into the frame in such a way as to allow the holes that run through will allow the ball bearing/grape to drop all the way through from one face to the other and out. I am not sure where this falls in the puzzle classification - I wonder if it straddles two classifications? It is certainly a Maze but this is one where the maze has to be created by the puzzler.

The slices have the letters from the words "SWISS CHEESE" spread across them. Each slice has multiple holes...some blind ending and at least 3 passing obliquely through to the other side. Therefore it is a simple matter of stacking them so that the exit hole of one matches up with an entry hole of the next and so on. Easy peasy? Sigh! Maybe for Michel (or you) but definitely not for me. I really thought that an hour or so experimenting would get me to the end and a success story. Alas in answer to my question above...I am VERY foolish - or really really dense!

Creating stacks of 3 or even 4 of these slices is pretty easy. It just needs a bit of fiddling about and this works - the grape slides through with a very satisfying rattle (I am not sure grapes should be that hard). Adding a 5th slice is a bit problematic...quite often none of the 2 remaining slices have holes that will line up with either entry or exit holes at each end. There are 4 orientations to try with each slice and when it doesn't work (which is often the case), it is time to start trying to interleave those remaining two slices between the ones that I had already assembled. This usually mucked the whole thing up and led to me starting afresh. My maths abilities are not great but I think that if I just try random picking of slices and orienting them randomly one after another then there are 96,909,120 different possibilities. Maybe one of you mathematicians could correct me if you think that I am wrong (it has been a VERY long time since I studied Combinatoric theory). Whatever the true number is, I am highly unlikely to find the solution by randomly picking pieces and placing them. It needs the old Think© trick - nooooo!

The Thinking© was where I fell down. I realised quite early that 2 of the slices have one side that does not line up well with the other pieces - I need to improve my odds first by positioning these two and then later working on the more freely placeable slices. Even with the letters on them, I struggled to keep track of what I was trying in my head and began to take some notes on a piece of paper. After an hour or so, my notes were completely incomprehensible to anyone and I had quite a headache brewing. Wow! this is one tough puzzle! 

I have spent a good 3 hours on this today and so far gotten absolutely nowhere! Maybe I am rushing it to try and get a blog post? All this has shown me is the title of the post - "You Cannot Rush a Good Puzzle". I will continue working on this one and hopefully get some time to solve it during the week.


4 comments:

  1. Your estimate is way high. As a rough estimate, there are 6! ways to order the plates and each has 4 orientations, this gives (6!*4^6) ~ 3 million stackings. But this is an overestimate because the same stack flipped over or turned around isn't really different.

    In any case, I think the key would be to explore the topology of the holes. Which holes on one plate can connect to holes on another plate? It is not clear from the photos which holes go all the way through.

    Finally, if the ball goes down at all times, then it must pass through one hole in each plate. This might help reduce the number of possibilities. On the other hand, maybe the ball reverses at some level and has to go back up through some plates. If so there must be at least one plate that the ball passes through three times (or more). Is there such a plate, or combination of plates that would allow this?

    Finally is the frame useful, or does it just get in the way?

    ReplyDelete
    Replies
    1. I knew that I would get a reply from you George! I love your logic and I’m sure that you are right. As for your suggestion of a possible solution approach - I’ve come to the same conclusion but not had any time to try it out.

      Delete
  2. Look for plates where the ball can enter a hole in the top, and come out of another hole in the top (as opposed to going through the plate). Are there any such holes? This would be the only way the path of the ball could reverse, if I understand the geometry.

    ReplyDelete
    Replies
    1. There are indeed such holes in 2 of the plates! I has an idea…
      Need to find some time soon!

      Delete

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