1. Julia is an architect with a construction company in Auckland.
She is designing a new development of stand alone townhouses.

2. The townhouses will have four levels and the exterior cladding will be made from only two colours, light and dark.
Each townhouse will have it’s own unique combination of the two colours. Here are three possible designs.
How many different townhouses are possible?

3. One possible strategy: Try a simpler problem
Are any other two storey townhouses possible?
If so, what is the colour scheme?
What three storey townhouses are possible?

4. Is this a full set of three storey townhouses?
How do you know?
What system has been used here?

5. One possible strategy: Look for a pattern

6. Number of
storeys
Number of possible townhouses 1 2 3 4 ? 1 2 4 8 ?
How many different townhouses are possible with no storeys?
What is happening to the number of possible townhouses as you scan to the left?
What is happening to the number of possible townhouses as you scan to the right? Why does this happen?

7. What does this tree diagram show?