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Australian AMC 2019 - Intermediate Question 24

AMC AUSTRALIA · Australian AMC 2019 - Intermediate

Question 24

Out of modern musical theory comes the following question.
Twelve points are equally spaced around a circle. Three points are to be joined to make a triangle.
We count two triangles as being the same only if they match perfectly after rotating, but not reflecting. For instance, the two triangles shown are the same.
How many different triangles can be made?

Question illustration
  1. 10
  2. 14
  3. 19
  4. 20
  5. 22