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A picture of a flag is to be completed by shading two squares that do not share an edge. The diagram shows one way in which this can be done.

Flag

How many different possible completed pictures are there (including the one shown)?

 

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

 

 

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