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## 'Colouring Curves Game' printed from http://nrich.maths.org/

This game is for two players, and you will need paper and a
pencil.

Start by drawing a curve on the paper. The curve can cross over
itself as many times as you like, but must join back to where you
started (this is called a closed curve).

Here is an example of the sort of curve you might draw:

Now take it in turns to
choose a region and colour it in. The only rule is that shaded
regions can't share an edge, although it's ok for them to meet at a
corner or vertex.

This is what the curve above might look like after each player has
had two turns:

Eventually, you will run
out of regions to shade without shading regions which share an
edge. The last person who can shade a region is the winner!

#### Here are some ideas to
think about as you play:

- Is it better to go first or second? Does it depend on the
curve?
- Can you design some simple curves where you can guarantee that
you will win?
- What do you notice about the number of regions that meet at
each vertex?
- Can you come up with any strategies to help you to win?

Another way to play the
game is to take it in turns to shade regions each using a different
colour, without shading adjacent regions in your own colour, so the
game might look a bit like this: