Colouring Curves Game

Age
7 to 14
Challenge level
filled star empty star empty star

In this game, try not to colour two adjacent regions the same colour. Can you work out a strategy?

Thinking mathematically

Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Explaining, convincing and proving

Mathematical mindsets

Being curious Being resourceful Being resilient Being collaborative



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:

 

Colouring curves game
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:

 

Colouring curves game
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:



 

Colouring curves game