A tecup with 3 houses drawn on it. there are 3 different whiteboard markers inside the cup

See if you can connect these houses into the grid!

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

  • A plain mug or teacup that you can mark
  • Permanent marker
  • 3 whiteboard markers in different colours

Making the puzzle

  1. someone is drawing little houses on a tea cupWith your permanent marker, draw 3 small separate houses on the mug. Make sure you spread them out, so there’s space to draw between them.
  2. someone is drawing little factories on a tea cupNow draw 3 separate small factories on the same mug. Label one factory ‘E’ for electricity, one ‘W’ for water and one ‘G’ for gas.


The 3 utilities puzzle

  1. 3 houses, each with a red, a blue and a black line leading out of themThe 3 houses must each be connected to electricity, gas and water. Unfortunately, the 3 utility companies are having a dispute – they won’t let their lines cross.
  2. 3 factories – one has 3 red lines coming from it, another 3 blue lines and the third 3 black linesDraw 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?

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 2 factories and 3 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 2 regions with your connections. One fence goes – factory 1, house 1, factory 2, house 2 and back to factory 1. The other fence goes – factory 1, house 2, factory 2, house 3 and back to factory 1.

If you try to add a third factory, you must put it in one of the 2 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.

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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