The diagram below shows four types of tile, each of which is made up of one or more equilateral triangles.

For how many of these types of tile can we place three identical copies of the tile together, without gaps or overlaps, to make an equilateral triangle?

If you liked this problem, here is an NRICH task that 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.