The three pillars puzzle

You will need

  • A block of wood, about 200 mm long
  • 1.25 mm wide solid copper wire
  • Wire cutters
  • Claw hammer
  • 1.3 mm wide (metric) or 2d (imperial) nail
  • String
  • Scissors
  • Hot melt glue and glue gun
  • Ruler
  • Pen or pencil
  • Small, round bottle, about 40 mm wide (optional)

What to do

  1. Measure and draw a line down the length of the middle of your piece of wood.
  2. Mark three points on the line, 25 mm apart.
  3. Hammer the nail into each point, and then pull it out to leave a hole.
  4. Make a loop in the end of the copper wire. The diameter of this loop should be about 40 mm across. You can wrap the wire around a small round bottle to help get the shape. Twist the ends of the loop together to hold its shape.
  5. Measure 50 mm along the wire from the loop, and cut the wire. Put the wire into the first hole on your piece of wood.
  6. Bend the loop so it lies horizontal, but the rest of the wire stays vertical. It should look a bit like a netball hoop. Turn the hoop so it is directly over the second hole in the piece of wood.
  7. Make the same sized loop on a second piece of wire. Cut the wire 75 mm away from the loop. Put the end of the wire down through the first loop, into the second hole. Bend the loop horizontally like before, and make sure it is over the third hole.
  8. Cut a piece of wire about 150 mm long. At one end, bend 25 mm of wire back on itself, and twist it together. Stick this wire through the second loop, and into the third hole.
  9. To make everything stronger, put hot melt glue on the base of all three pieces of wire to hold them in their holes.
  10. Cut a piece of string about 400 mm long. Tie the ends together into a loop.

The three pillars puzzle

  1. Try to get the string to encircle the base of the shortest wire. It’s not as easy as you might think!
  2. Once you’ve mastered this puzzle you can try the five pillars puzzle. To make a ‘five pillars puzzle’, you’ll need to make five holes, four loops and a straight pole. Follow the same pattern, where each loop goes through the next shortest loop. But beware! The five pillars is a lot harder than the three pillars.

What’s happening?

It’s easy to get the string around the base of the tallest pillar. From here, you should be able to get the string onto the middle pillar. However, it won’t go straight from the middle pillar to the shortest one – you’ll need to get it around the base of both the larger pillars first.

This puzzle might look impossible at first glance, but we can use a special branch of mathematics called topology to investigate the problem. Topology is sometimes called ‘rubber sheet geometry’ and it’s all about what happens if you’re allowed to bend shapes. In topology, a sphere is the same shape as a cube – you just need to bend it a little. You’re allowed to stretch things as much as you like, but you aren’t allowed to rip them, punch holes in them, or get rid of holes that already exist.

If they were made of very stretchy rubber, you could bend the tallest pillar so it didn’t go through the second tallest, and then the second tallest so it didn’t go through the shortest. Topologically speaking, the pillars are all separate from each other. Since you can solve the puzzle by bending the poles, it should be possible by just bending the string.

step1

Hammer the nail into the point, and then pull it out to leave a hole.

step2

You can wrap the wire around a small bottle to help get the right shape.

step3

Cut the wire so the loop has a 50mm stalk.

step4

Try to get the string around only the base of the shortest pillar.

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