### 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?

# Late Again

##### Age 5 to 7 Challenge Level:

Here is a picture of Moira's school which has a paved playground at the front:

If Moira was sitting on the bench nearest the school gate, to get to the climbing frame she could:
Go forward $2$ squares to the pond.
Turn to the right and go $1$ square forward.
Turn to the left and go $2$ squares forward.

This morning, Moira is late for school.
What is the shortest route she can take from the school gate to the school door?
Is there more than one way she could go?