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In this trick, you’ll wrap a shoelace around a pencil and a strip of cardboard. The string seems to pass straight through both, tearing the cardboard, but leaving the pencil untouched!

You will need

• Pencil
• 2 rubber bands
• Thin cardboard
• Scissors
• Shoelace
• Some friends to impress

What to do

1. Cut a thin strip of cardboard as long as the pencil.
2. Put the strip of card and pencil next to each other. Put a rubber band around one end of the pencil and card to hold them together.
3. Fold the cardboard strip away from the pencil.
4. Tie a knot in one end of the shoelace. In this activity, whenever the shoelace crosses itself, the knotted end always goes on top.

   

5. Lie the middle of the shoelace across the pencil.
6. Bring the two ends behind the pencil, making sure to cross the knotted end over the unknotted end.
7. Now, cross the ends of the shoelace on the front side of the pencil. Once again, make sure the knotted string is on top.

   

8. Fold the cardboard strip back over the top of the shoelace, so it runs along the pencil. Put a rubber band at the other end of the pencil to hold the cardboard in place.
9. Back to the shoelace. Cross the two ends over the front of the cardboard strip. Then cross them again behind the pencil, and finally, cross them a third time over the paper strip. Each time, remember to cross the knotted end over the unknotted end.

   

10. It’s time for the big reveal. Get a friend to hold the pencil. Then pull hard on the two ends of the shoelace. It will come free of the pencil, but break the cardboard!

What’s happening?

Take a pencil, wrap string around and around, pull it tight, and usually nothing special happens. But this time, the string seems to magically unwrap itself. So what’s happening?

Try following the instructions a second time, but leave out the cardboard strip. You’ll find that the second half of the activity is doing the exact opposite of the first half. It unties the wrapping you’ve already done.

If you’re not looking for it, there is very little difference between the early wrapping loops and the later unwrapping ones. But keep an eye on the knotted end of the string and you might notice the difference – for half of this activity it’s going clockwise around the pencil, and in the other half it goes anticlockwise.

For some of you, this trick might not have worked at all! This trick isn’t just about clockwise and anticlockwise. It’s also about over and under. If you put the wrong end of the string on top of a crossing, the twists won’t untie each other properly. There’s a whole field of mathematics to do with this, called knot theory. You can add knots together, or subtract them, but it’s harder than simple arithmetic!

If you’re after more maths activities for kids, subscribe to Double Helix magazine!