Welcome to the Transum Club; here is your badge:

You can click on a square in the badge to change its colour to either red, blue or yellow, but no two adjacent squares can be the same colour.

Each member of the Transum Club has a different combination of colours in their 'T' badge. What is the largest number of members this club can have?

Use the badges below to help you find the answer.

Click on the squares in the badges above to change their colours. No two squares which meet each other edge to edge can be the same colour. How many different 'T' badges can you make?

Click a yellow square to make it red.

Click a red square to make it blue

Click a blue square to make it yellow.

You can drag the badges to put them in a logical order.

Now extend this idea to investigate different badge designs and a different number of available colours.

If you liked this activity you might also like Striped Sweets, Ice-cream Combinations and Misfits.

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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.