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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?


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?

Four-triangle Arrangements

Age 5 to 7 Challenge Level:

Starting with good squares and getting them cut in half from corner to corner as best as you can is really helpful. If necessary get someone to help.
You can record these by simply drawing around them, but find whatever suits you best. A digital camera may be good - or even a computer drawing program.
How will you know when you have got them all?