Imagine that each of the ropes in the two sets of links in Figure 1 are solid (with thickness) and made of very flexible and stretchy rubber.

Question: is it possible to deform one set of links into the other in a continuous motion (without tearing or cutting)? In other words, can you get the purple pretzel off the red ring?

Surprise answer: Yes!!

**Presentation Suggestions:**

Students (as well as you) may find this very hard to believe!

**The Math Behind the Fact:**

The transformation can best be explained by a sequence of pictures that demonstrate the transformation, since it is not easy to describe in words! It is important here that the ropes are solid, with thickness, and very stretchy; it wouldn’t be possible otherwise. See Unbelievable Unlinking for a hint on how it can be done. The reference contains a solution.

A course in *topology* is the best place to learn about links and knots and continuous deformations.

**How to Cite this Page:**

Su, Francis E., et al. “Pretzel Unlinking.” *Math Fun Facts*. <https://www.math.hmc.edu/funfacts>.

**References:**

V.V. Prasalov, *Intuitive Topology*.

**Fun Fact suggested by: **

Francis Su