What A Mammoth N-ary Effort!

Brass side

Steel side with monkey

The Blind Panic puzzle was Ali's IPP exchange. I received a copy at the MPP

It ooks and feels wonderful and is effectively a Panex (with one difference discussed later).

First of all, a little note to inform you that the OPUP remains packed and the Dovetail bar 2 remains a single piece! maybe I need another hobby?

I am having to work this weekend yet again and so only have a quick update on last week's challenge. I do maintain that I definitely am an eejit! I decided to finally work on the two puzzles that I own that are effectively Panex puzzles. I had thought for a while that the Panex was a "simple" N-ary puzzle and it "just" needed me to work out the pattern and then slog through.

Damn! That wasn't very bright! I should have realised that any so called N-ary puzzle that is more complex than the basic Chinese rings is not necessarily going to be straightforward. The clue should have come from the incredible puzzles sent to me by Aaron Wang over the years. I don't buy everything he has to sell because a. I can't really afford to buy them all and 2. some of them look impossible for human beings to solve! However, I have bought quite a few of his fancy N-ary designs and have solved very very few of them! Even the ones that are "just" N-ary have some very complex sequences that I often seem to get lost in and most of them remain unsolved and in my pile of puzzles reminding me of how rubbish I am at puzzling and, more importantly and dangerously, they are annoying Mrs S and tempting the cats into string swallowing. 😱

Street Lamp

Golden Gate Bridge

Both of these were bought last summer and both have ended up with me completely stuck.Thank heavens for the quick reset that Aaron installed. This should remind the unwary puzzler that many N-ary puzzles have rather a lot more to them than one might expect.

The Bell
Unsolved for several years!

How does that relate to the Panex? Well, I am not certain but I think the Panex is sort of N-ary but with patterns within patterns and the challenge is to find an approach in stages. It is not a simple thing to do and took me a week to complete a level 5 version. The Bell from Siebenstein Spiele is a very similar puzzle but has the advantage that the 3rd column is visible. I decided to solve the two puzzles in stages side by side. I started on the level 3 solve. It is trivial to move 3 disks from one arm to the empty arm like a Tower of Hanoi puzzle and then move the ano0ther one to where they came from:

⅔ of the way

Done it!

This was done fairly trivially on the Bell and then also on the Blind Panic. Success! I think must have taken me about 60 moves. Time to move to level 4 and OMG! it was not trivial. It can no longer be solved by using simple Tower of Hanoi sequences.

The first sequence is Tower of Hanoi and transfers one arm to the gap

It looks as if being able to do the sequence above is possible then all that is required is to do it again with the dark set of disks. But and it's an enormous BUT the way the Bell and Panex is constructed requires to use the top pathway as temporary storage as the disks are slid from one leg to the other. The problem when attempting a level 4 is that having moved the first sequence across to the middle leg the temporary storage that would be used is above that middle leg and it subsequently blocks movement of disks across the top to the other leg. It took me absolutely ages to realise that the Tower of Hanoi approach is impossible with this puzzle. The interesting thing with Ali's Blind Panic is that the path at the top of the puzzle is circular and also that the temporary storage is above the pile of pieces in an arm and not in the top path! 

This end result of this is that the two puzzles are not actually the same. They are almost equivalent but the crucial difference makes the Blind Panic much more approachable and more like a multi-layer  Hanoi puzzle. After a couple of days of play I solved the level 4 on the Bell and convinced myself I had a reasonable approach. A level 4 Panex should take 174 moves - I must have been several times that many:

Level 4 solved - this almost killed me!

Time to strat on the level 5 Bell and simultaneously solve the Blind Panic. It was more of the same but to me did not feel very logical. It took me a lot of back and forth, getting it wrong and starting again. I did the Blind Panic at the same time. My hands were rather sore but the end of another few days of work:

Level 5 solved!

Brass above the monkey

Apparently the level 5 Panex takes 461 moves as a minimum to solve but for me it must have been thousands and thousands as I made mistakes and had to backtrack or got lost and had to start sections again. I was mentally and physically exhausted after doing that and despite being elated, I have absolutely no plan to undo it and go back to the beginning using the same approach - I think it would kill me! The Bell puzzle can be unscrewed and this is exactly what I will be doing! Then there is the thought of completing the entire Bell puzzle (level 6) - OMG! NO! It should take a minimum of 1170 moves but I suspect it would be 10's of thousands for me and most of the rest of my remaining hair and my life! I'm afraid that the final solution to the Bell will never happen.

There has been quite a lot of mathematical analysis on the minimum number of moves that are required to solve the Panex puzzle and I don't really understand any of it. I do know that it is a LOT more moves than you would expect and the logic is really not obvious! Have a look at the papers linked from Nick Baxter's site - I did and it didn't help me much at all! 🤣

What about resetting the Blind Panic puzzle? There is a screw on top which I suspect can be undone and the puzzle pieces removed and replaced back in the start position. BUT, I am fairly convinced that that a simple Tower of Hanoi approach is possible for this puzzle because of the circular top pathway and the extra storage position in the top of each column. I am going to work on that for the next day or so and will report back to you next week!

Wish me luck!