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In how many ways can you fit all three pieces together to make shapes with line symmetry?

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Shady Symmetry

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Doubly Symmetric

Age 11 to 14 Short Challenge Level:

What is the smallest number of additional squares that must be shaded so that this figure has at least one line of symmetry and rotational symmetry of order $2$?

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.