### 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?

# Leap Frog

### Why do this problem?

This problem encourages children to work in a systematic way and is a good context in which to share different ways of recording solutions. It can be done practically with pupils being the frogs which makes it an appealing and intriguing problem.

### Key questions

What move can you make first?
How will you remember what you have done?
Is there only one way that the frogs can swap places?

### Possible extension

The interactivity in this extended version of the challenge can be used to introduce more frogs and to find the minimum number of moves for them to swap places.

### Possible support

Using counters to represent the frogs with five circles drawn on a sheet of paper for the lily pads will help some children make a start on this problem.