### 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

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

Thank you to Samuel and Sakunthala who sent separate solutions to this problem. Samuel recorded his solution in a very clear way:

B x x x G
x B x x G
x B x G x
x x B G x
x G B x x
x G x B x
G x x B x
G x x x B

Samuel explains that they have both swapped places without getting wet. He says that at school they continued the problem up to 11 pads with 5 frogs of each colour. I wonder whether you noticed any patterns in the numbers of jumps it took each time, Samuel?

Sakunthala did it in exactly the same way but started with the green frog.

Well done both of you!