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Australian AMC 2015 - Senior Question 22

AMC AUSTRALIA · Australian AMC 2015 - Senior

Question 22

This list

Question illustration

was made by Norm and Zoltan, starting with 3 and 5 and then taking turns to add one number to the list. Norm went first.

Whenever it is his turn, Norm’s new number (shown circled) is the product of the last two numbers in the list. Whenever it is his turn, Zoltan’s new number (shown boxed) is found by dividing the second-last number by the last number.

What is the 2015th number in this list?
  1. $\frac1{15}$
  2. 3
  3. 5
  4. $\frac13$
  5. $\frac15$