Trisected Triangle

Weekly Problem 34 - 2015
Four tiles are given. For which of them can three be placed together to form an equilateral triangle?
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Problem



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

Image
Trisected Triangle


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.