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IMAS 2012 Junior First Round Question 8

IMAS · IMAS 2012 Junior First Round

Question 8

Cups labelled 1, 2, 3, 4 and 5 with mouth upwards line in row, as shown below. Initially a ball is put into cup #3. In each move, the ball is transferred to an adjacent cup. If the ball is in cup #1, it can only be moved to cup #2. If the ball is in cup #5, it can only be moved to cup #4. After $2^{10}+3^8$ moves, which of the following statements about the ball is correct?

Question illustration
  1. It cannot be in cup #3, cannot be in cup #4 and cannot be in cup #5
  2. It cannot be in cup #2, cannot be in cup #4 and cannot be in cup #5
  3. It cannot be in cup #1, cannot be in cup #4 and cannot be in cup #5
  4. It cannot be in cup #1, cannot be in cup #3 and cannot be in cup #5
  5. It cannot be in cup #2 and cannot be in cup #4