**Category:** 3D Objects & 2D Shapes and Patterns**Suitable for Grade Level:** Elementary and Secondary

**The Math in this Problem:**

Using red, blue, and yellow circles, students are challenged to fill in various shapes made up of circle units. The test of Touching Circles is to not have a circle next to another one of the same colour. Since the different colours can be applied one by one, this makes for a fun two-player game, with the winner being the last one able to make a move.

Fill the following triangle with red, yellow and blue circles so that no circles of the same color are next to each other.

#### Extensions:

- Is your answer unique?
- Can you fill a larger triangle with red, yellow and blue circles so that no circles of the same color are next to each other?
- Can you fill the following hexagon with red, yellow and blue circles so that no circles of the same color are next to each other?

- How many circles of each of the three colours are needed for a triangle with N chairs per side?
- Find a shape which is not possible to fill using the three colours.
- Mathew, Desirée and Cade of Alice M. Curtis Campus ask you to fill the following square with four colours, so that no connected circles share the same colour.

- Can four colors also be used to fill this triangle? (Remember, no connected circles can share the same color.)

#### Two person game:

Each player takes turns tossing a circles into the small hexagon below. A player may not toss a circle so that two touch that have the same colour. The winner is the last player able to move.