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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?

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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?

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Let's Investigate Triangles

Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?

Four-triangle Arrangements

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.