Grab a partner and work together to try and solve this tangled web math puzzle. A fun activity to help primary school students to learn why knots are important in mathematics.

You will need

  • two pieces of string, about one metre each
  • at least two people.

What to do

  1. Challenge yourself to seperate from the other person

    Divide the people into pairs.
  2. Have each person tie the ends of a piece of string to their wrists, with the string looped around their partner's string, so they are tied together. The loop tying around the wrist should be tight enough so it doesn't easily slip off the person's hand, but loose enough you can fit a finger under it while it is around the wrist (there's a hint for you!).
  3. A prize goes to the first pair to unlink themselves without cutting or untying the string. 

What's happening

To solve the puzzle, pass the centre of one string under the string around the other person's wrist (between the string and their skin), then over their hand and then back under the string again. This is hard to visualise, and even harder to work out, so have a look at the picture.

Hand with rope cuff tied around wrist with loop of joining rope to other cuff being pushed through hole between hand and rope

Tangled web solution

You have just participated in a maths puzzle. This puzzle has been known about since at least 1747. Mathematics doesn't always involve numbers. The study of knots and linkages, such as this puzzle, belongs to a branch of geometry called topology.

Mathematical puzzles vary from simple through to very complex problems which are still unsolved. History is filled with mathematical games which have led to the study of many areas of mathematics. Number games, geometrical puzzles, network problems and combination problems are among the best known types of puzzles.

Leonhard Euler's 1736 paper on the Seven Bridges of Königsberg is regarded as one of the first results in geometry that does not depend on any measurements.

Can you name something that only has one side? The Möbius strip, also part of topology, has only one side and one edge. It consists of a strip of paper connected at its ends with a half-twist in the middle.

There is also a one-person version of this puzzle. Tie a knot in the middle of a piece of string, then tie the ends to your wrists. Can you untie the knot without cutting the string or untying the string at your wrists.

Topology has many complex scientific applications, such as in the study of turbulence in flowing fluids. It is also used in computer science, engineering and even magic tricks, although most people would be most familiar with its use in the everyday knot.

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