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BEBRAS 2018 Grade 9-10 Round 2 Ext Question 9

BEBRAS · BEBRAS 2018 Grade 9-10 Round 2 Ext

Question 9

Seven beavers walk around seven chairs while music plays, and sit on the nearest chair when it stops. A chair may hold several beavers. Initially A is at chair 1, E at 2, D at 3, C at 4, G at 5, B at 6 and F at 7, as shown; chair numbers increase clockwise.

Question illustration

In each music round, adults A,B move 3 chairs counterclockwise, teenagers C,D move 2 counterclockwise, and children E,G,F move 1 clockwise. Which chairs are empty after three rounds?
  1. 2 and 7
  2. 3 and 7
  3. 1 and 2
  4. 1 and 4