Two Colours Game

Task 23 ... Years K - 12


Played on a 5x5 grid this is an easy game to get started, but not so easy to analyse. Take turns placing counters of different colour one at a time so that counters next to each other horizontally and vertically are not the same. Is there a winning strategy?


  • Thirteen counters in each of two colours and a 5x5 playing board


  • 2D spatial perception
  • concept of horizontal and vertical
  • logical reasoning, in particular 'break a problem into smaller parts'
Two Colours Game


A task is the tip of a learning iceberg. There is always more to a task than is recorded on the card.

3x3 Board
A Poly Plug board
can easily change size.

Investigating the game with a view to finding a winning strategy against 'the world's best opponent' is the iceberg of this task. Perhaps the strategy of breaking the problem into smaller parts might help. For example try the game on a 3 x 3 board.

  • The most powerful place is the centre.
  • The second most powerful places are the corners.
  • The next most powerful places are the middles of the sides.
  • Is it a winning strategy to play the most powerful place available?
  • Is it a winning strategy to play the least powerful place available?
  • Is there a better strategy than either of these?
  • How do you explain your strategy?

Whole Class Investigation

Tasks are an invitation for two students to work like a mathematician. Tasks can also be modified to become whole class investigations which model how a mathematician works.

Use circular margarine lids (because they look different on each side) to play the game on the floor where everyone can see. Perhaps the teacher can challenge one or two students to start things off. Children love to return to this game, so perhaps the large version can remain on the floor for a while as a focus for conversation.

Following the introduction, supply each pair of students with a 5x5 grid and counters so they can play the game at their tables. If you have Poly Plug it is easy to set up a table top version of the game. Students could be encouraged to try out strategies on the table top version then demonstrate and discuss them around the floorboard version.

At this stage, Two Colours Game does not have a matching lesson on Maths300.

Visit Two Colours Game on Poly Plug & Tasks.

Is it in Maths With Attitude?

Maths With Attitude is a set of hands-on learning kits available from Years 3-10 which structure the use of tasks and whole class investigations into a week by week planner.

The Two Colours Game task is an integral part of:

  • MWA Space & Logic Years 3 & 4

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