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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:

These are the ones we found for the first rule.

These are some extra ones we found for the second:

Again we worked in a system just moving one triangle and keeping the other three fixed. So there are many, many more to find for this second rule.