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Hanging by a thread

By David, 27 November 2017 Activity

a picture hanging from two pinsYou’ll find yourself going a little loopy with this puzzle, but it’s worth unravelling the secret.

You will need

  • A cork noticeboard
  • Two corkboard pins
  • 40 cm piece of string
  • Sticky tape
  • 20 cm x 20 cm piece of card

Preparation

  1. A piece of string sticky taped to the corner of a peice of cardboardPlace one end of the string on one corner of the card and stick it in place.
  2. Connect the other end of the string to the opposite corner and stick it in place. This is your ‘picture’ you will need to hang.
  3. A cork board with two pins in it. a string goes around them.Insert both pins into your cork noticeboard roughly 5cm apart.

The puzzle

Loop the string around the pins in such a way that you can pull either pin from the board to let the picture fall to the ground.

To help explain, here’s an example. Loop the string over one pin but not the other. If you remove that pin, the picture falls. But if you remove the other pin instead, the picture stays up. You need to make sure the picture falls no matter which pin you pull.

A solution

click here to reveal a solution

Click to reveal a solution

Wind the string around Pin A at once fully in a clockwise fashion. Run the string over to Pin B and loop it in a clockwise fashion there as well. Return to Pin A, and now loop it in an anti-clockwise fashion. Return to Pin B and do the same.

What’s happening?

If you read through the solution, you might notice something interesting – you go around each nail clockwise once, and anticlockwise once. That’s no coincidence – the balance of clockwise and anticlockwise turns is the key to the puzzle.

If you wind the string around a pin clockwise and then straight away anticlockwise, the two loops cancel out. Pull the string tight and it won’t catch on the pin.

So how does the picture stay hanging? In between the clockwise and anticlockwise loops on the first pin, the string visits the second pin. And in between the two loops on the second pin, it visits the first pin. These detours stop the clockwise and anticlockwise loops from cancelling each other out.

When you pull one pin out, the loops around that pin disappear. That lets the clockwise and anticlockwise loops on the other pin meet and unravel each other.

This puzzle is from a part of mathematics called topology. Topology is often referred to as ‘rubber sheet geometry’ and it explores the properties of shapes that stay the same even when you can bend and stretch those shapes. Since string is very bendy, topology is often a good way of exploring string puzzles.

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