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Australian AMC 2009 - Intermediate Question 17

AMC AUSTRALIA · Australian AMC 2009 - Intermediate

Question 17

An eyebrow is an arrangement of the numbers 1, 2, 3, 4 and 5 such that the second and fourth numbers are each bigger than both their immediate neighbours. For example, $(1,3,2,5,4)$ is an eyebrow and $(1,3,4,5,2)$ is not.

The number of eyebrows is
  1. 16
  2. 12
  3. 15
  4. 24
  5. 18