### Homes

There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?

### Stairs

This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.

### Train Carriages

Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?

# Teddy Bear Line-up

##### Stage: 1 Challenge Level:

Lachlan was playing with his bear counters.

He had four blue, then four red followed by four yellow and finally four green bears.

"What are you doing now?" Jenni asked.

"I want to arrange them so that no two bears of the same colour are next to each other", he said.

"That's easy!" cried Jenni.

"Ah, but you have to do it in the least number of moves possible", replied Lachlan.

What's the least number of moves you can take to rearrange the bears?