The houses in Mathsland are all 3 storeys tall. Each storey is painted using one colour.

How many ways can the houses be painted if you have:

2 colours; 3 colours; 4 colours.......

[See also Cube Construction and Combinations and Permutations]

Investigate further.....

A mathematical investigation is quite different to other mathematical activities. The best investigations are open ended and allow students to choose the way they work and how they record their findings. It is one of the few occasions when 'going off on a tangent' is not only acceptable but actively encouraged (within reason).

Students may ask for 'the answers' but this supposes that the activity is
closed. Investigations can always be extended by varying the initial
instructions or asking the question 'what if...?'. Sometimes students point out
that the instructions are ambiguous and can be interpreted in different ways.
This is fine and the students are encouraged to explain how they interpreted the
instructions in their report.

Some students may benefit from a writing frame when producing the reports
of their investigations. Teachers may suggest sections or headings such as
Introduction, Interpretation, Research, Working and Conclusion or something
similar.

Teacher's notes for this investigation and solutions to Transum puzzles, exercises and activities are available when you are signed in to your Transum subscription account. If you do not yet have an account and you are a teacher, tutor or parent you can apply for one by completing the form on the Sign Up page.

A Transum subscription also gives you access to the 'Class Admin' student management system, downloadable worksheets, many more teaching resources and opens up ad-free access to the Transum website for you and your pupils.