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This is a simplified version of this physical puzzle. I believe it captures the essence at much reduced complexity.

A piece of string with a blue ball at each end. The string runs through a flattened elongated orange torus and a similar red double torus.

Please, forgive my poor drawing skills.

The goal is disentangling the orange torus from the other stuff. The other stuff being the red double torus and the grey string with balls at its ends.

Rules: The torus fits through either aperture of the double torus and vice versa the double torus fits through the torus. The balls do not. The string can go anywhere, you may assume it's long or elastic enough.

Note that I do not know the solution nor whether a solution actually exists, though I assume it does.

Your task is therefore to either describe a solution or prove there is none.

loopy walt
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    It looks similar to this one https://puzzling.stackexchange.com/questions/77679/solution-or-name-to-a-mechanical-puzzle-two-rings-three-balls-wooden-centerp – Florian F May 12 '22 at 06:14
  • Very similar, indeed. Nice find, @FlorianF! I'm not sure, though, whether it's 100% equivalent. The fact that one end of the string fits through the double torus looks crucial for the solution they give. – loopy walt May 12 '22 at 07:13
  • I think that in the original puzzle it might well be possible to pass the spectacles through the donut hole. I don't know if that is in any way useful. – Jaap Scherphuis May 12 '22 at 07:57
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    @JaapScherphuis I was actually just assuming it is possible. That's what I mean by "vice versa". Do you feel I should make it clearer? EDIT: I clarified it. – loopy walt May 12 '22 at 08:24
  • I overlooked it, but it's certainly clear enough now, thanks. – Jaap Scherphuis May 12 '22 at 08:27

1 Answers1

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I also believe your puzzle is impossible.

Let's simplify the puzzle a bit more. If you rotate the left red (elongated) torus half a turn and merge the holes of the red tori you get something like below. It removes constraints on the string so, if anything, it should be easier. (These are chain links. On link easily goes thru the other link.)

Puzzle with straight loop

I have been playing with it and there really isn't much you can do. It can't be separated. It is not a proof, well, you have to trust me on that.

Note that if you join the balls the puzzle becomes equivalent to Borromean rings. They become inseparable.

So does it matter whether the balls are joined or not? I think not. The balls are large enough that you cannot pass the chain links over them. So they might as well be huge. If they are huge they might be considered connected to infinity for all practical purposes and therefore connected to each other. One difference is that the string cannot pass over a ball any more. But by this can be replaced by allowing the string to cross itself. This doesn't change the "Borromean rings" nature of the puzzle.

OK, it is a bit intuitive I agree. But I don't know how to explain it better.

This being said I wanted to challenge your initial statement that the puzzle captures the essence of the one you link to.

For instance, my version above is not solvable, at least by experience, but the following version is not difficult to separate.

puzzle with U-shaped loops

So it does matter what shape the metal loop is. A straight loop is not equivalent to a U-shaped loop.

Spoiler on 2nd puzzle

Pass the U-shaped loop over the chain link. You get a similar position with U on the right and the string passing thru the large loops of the U. Then stick one side of the U in the chain link and pass one ball thru both large loops releasing the string.

Florian F
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  • Can you briefly describe the solution to the second puzzle you show? – 2012rcampion May 14 '22 at 13:41
  • As I said it is an easy one. But OK. – Florian F May 14 '22 at 14:00
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    Very nice and I essentially believe all your statements. And the trick with the bent loop is exactly what I was missing. If you do the same move with a straight ring it looks like nothing changes. Ir is easy to miss that the sides of the ring are changed which makes all the difference with the bent ring. I wouldn't be surprised if your solution could somehow be adapted to the original puzzle. This all leaves one problem: While I believe your statement regarding my "simplification" it really isn't proof.so I'm not sure I can accept your answer however insightful it may be. – loopy walt May 14 '22 at 15:10
  • I believe puzzle 2 holds the ingredients to solve the linked puzzle. The crucial part that applies also to the linked puzzle is that you must pass the chain link thru the U in order to reorient the U. The other move which is to stick half of the U in a hole and pass a ball in the double loop is also a key move in the linked puzzle. – Florian F May 15 '22 at 10:08