Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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->(

from here to here

I wish this problem lead me to learn math intuitively.

share|cite|improve this question
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
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

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.

share|cite|improve this answer

Here's one way to think of it.

Call the loops $L_1$ and $L_2$, joined by the stem which attaches to $L_1$ at $S_1$ and $L_2$ at $S_2$. You will notice there is a point $A$ where $L_1$ crosses and is above $L_2$ and another point $B$ where $L_1$ crosses and is below $L_2$.

Now contract the stem until it vanishes so that $S_1$ and $S_2$ become a single point $S$ and you will see that one of the points $A$ or $B$ will also move to $S$ under this deformation.

If you try to draw the two rings now joined at the single point $S$ you will see they are no longer linked - there is only one crossing point now so you simply have two rings sitting on top of one another joined at a point.

All you need to do now is stretch out the stem again and the rings will look like the second picture.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.