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hello I wonder whether this puzzle is possible to solve.

if possible, what kind of thing should I learn to solve this?

the problem is make left one to right one without cut the rope only stretch and bending are allowed I found out this puzzle here->(www.ocf.berkeley.edu/~wwu/riddles/hard.shtml/)

from here to here

I wish this problem lead me to learn math intuitively.

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This puzzle can be found here. It's labeled "topological rings". –  littleO Nov 15 '12 at 11:47
    
The puzzle description: "Imagine the object above in the figure to the left made from perfectly elastic material. Can you transform it so as to unlink the two rings as in the figure on the right? One possible way is to cut one ring, move the other ring through the gap, and rejoin the the first ring exactly as it was. That would be a legitimate topological transformation. However, it is also possible to transform the first shape into the second without any cutting, simply by manipulating the objects in the appropriate manner (stretching, bending, but not breaking). Can you see how to do it?" –  littleO Nov 15 '12 at 11:52
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There's a nice diagram showing how this is done in Keith Devlin's Mathematics: A New Golden Age. –  Peter Phipps Nov 15 '12 at 15:20
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1 Answer

This is a classical topological problem and magic trick.

The concept is fairly simple and the diagram is misleading. If you manufacturer latex or plastic loops as per the diagram, it is an impossible task.

However, if you take a string then to create the loops, you need to tie 2 knots. That's the key. The idea is basically to pass one loop through the other's knot.

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