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?

Graphic shows two pairs of mathematical knots labeled “pair 1” and “pair 2.” The knots within each pair are identical except for one difference in the looping configuration.

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.

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