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'Colourful Tiles' printed from https://nrich.maths.org/

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A tile is fixed to a wall and then painted with four different colours, one for each quarter. One way of doing this is 
 
How many other ways can the tile be painted?
 
 
 

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.