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Connection conniption!

By David, 2 July 2013 Activity

Do you have a favourite mug? This is my favourite. Not only does it hold my hot chocolate, it has a wicked tricky puzzle on it!

You will need

Mug and green marker.

You will need these items.

  • A plain mug that you can mark
  • Permanent marker
  • Three whiteboard markers in different colours

Making the puzzle

  1. With your permanent marker, draw three small separate houses on the mug. Make sure you spread them out, so there’s space to draw between them.
  2. Now draw three separate small factories on the same mug. Label one factory ‘E’ for electricity, one ‘W’ for water and one ‘G’ for gas.

The three utilities puzzle

White mug with green houses drawn on it.

Draw three houses and three factories on the mug.

  • Three houses each want to be connected to electricity, gas and water. Unfortunately, the three utility companies are having a dispute – they won’t let their lines cross.
  • Draw a line from each factory to each house. You can’t let lines from different utilities touch. Use one colour whiteboard marker for each utility.

Hint: This puzzle is possible on a mug, but you can’t do it on a bowl. What makes a mug different from a bowl?

What’s happening?

Three factories drawn on a white mug.

Use different coloured markers for each utility.

This is a tricky puzzle. If you’re having difficulty, it might help to try a much simpler version. Grab a piece of paper and draw two factories and three houses. Then draw a line from each house to the first factory and another to the second factory.

If you look carefully, you’ll notice you’ve fenced off two regions with your connections. One fence goes – factory 1, house 1, factory 2, house 2. The other fence goes – factory 1, house 2, factory 2, house 3.

If you try to add a third factory, you must put it in one of the two regions, or somewhere on the rest of the paper. Wherever you put the extra factory, there will be one house you can’t get to.

Blue pen held by a hand drawing on a white mug.

Try to connect each house to all three utilities. Remember, you can draw on ANY PART of the mug!

In order to solve this puzzle, you’ll need to find a way of getting over a line without crossing it!

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