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Australian AMC 2016 - Intermediate Question 24

AMC AUSTRALIA · Australian AMC 2016 - Intermediate

Question 24

You have an unlimited supply of five different coloured pop-sticks, and want to make as many different coloured equilateral triangles as possible, using three sticks. One example is shown here.

Two triangles are not considered different if they are rotations or reflections of each other.

How many different triangles are possible?

Question illustration
  1. 35
  2. 5
  3. 20
  4. 56
  5. 10