### 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?

# Briefcase Lock

### Why do this problem?

This problem is a good context in which to encourage children to work systematically to find all possibilities.

### Key questions

If $8$ is the first digit, what numbers are possible?
What could be the first digit instead of $8$?
How do you know you have all the possibilities?

### Possible support

If children are struggling to find a system, invite them to write down different possible numbers on separate pieces of paper. Once they have thought of as many as they can, work with them to sort the numbers so that a pattern emerges and a structure is imposed. In this way, learners will be able to spot any gaps for themselves.