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Australian AMC 2024 - Junior Question 21

AMC AUSTRALIA · Australian AMC 2024 - Junior

Question 21

A long line of ping-pong balls numbered 1, 2, 3, … is sitting in order in a tilted chute, as shown below. Xavier, Yasmin and Zebedee take turns removing balls from the chute. When a ball is removed, the rest roll down to fill the gap. When Zebedee has taken his ball, it is Xavier’s turn again and they continue in the same order for as long as there are balls remaining. Xavier always takes the second available ball. Yasmin always takes the third available ball. Zebedee always takes the first available ball. Which statement is true?

Question illustration
  1. Xavier takes ball 48.
  2. Yasmin takes ball 49.
  3. Zebedee takes ball 50.
  4. Yasmin takes ball 51.
  5. Xavier takes ball 52.