You are to design a four-room house. It can have as many storeys as you like, but every room must have a room underneath it or be on the ground. There are costs for building the house: each square of roof costs $3000 to tile, and each square of outside wall costs $1000 to paint. Design some houses and work out how much they cost to build.
To limit the scope of the problem, assume every room is a cube of the same size. Then you can make models of the houses using blocks.
How many different houses can you design? Which is the most expensive house to build and which is the cheapest?
Extension problem: What if you had a five-room or six-room house?