Math Puzzle: Find the Unknot


One string in each of the following pairs can be unraveled into a circle—the so-­called unknot. Which one is it?

The knots at the top left and the bottom right can be unraveled into circles:

Graphic shows how to undo the first knot from pair 1 in four steps and the second knot from pair 2 in seven steps.

Challenge problem: The other two knots, which can’t be completely unraveled, can each be made to look like one of the four most basic knots. Identify them!

Graphic shows four basic knots: trefoil, figure eight, cinquefoil and three-twist.

The top right knot is equivalent to knot 2, and the bottom left one is equivalent to knot 4.

Graphic highlights the second knot from pair 1 alongside the three-twist knot and the first knot from pair 2 alongside the figure eight knot.

We’d love to hear from you! E-mail us at games@sciam.com to share your experience.


Leave a Reply

Your email address will not be published. Required fields are marked *

Back To Top