Brain Teaser

Question

Magnus, Garry, and Fabiano are playing in a badminton event. In this event, after two players face off for a set, the winner stays on the court to play the player who was sitting out.

At the end of the event, Magnus played 9 sets, Garry played 14 sets, and Fabiano played 15 sets.

What pair played set number 13?


Answer

Since each set involves two players, the total number of sets played will be the sum of the sets played by each player divided by 2, which is 19.

Now no player can sit out more than one set in a row, so with 19 sets played, the fewest sets a player can be involved in is 9, which can only occur if such a player is involved in every other set starting from the 2nd set. As Magnus fits this criteria, we know that he is involved in only the even-numbered sets, and so Garry and Fabiano must have played the 13th set.

  • Problem by Michael Huang
  • Solution by Brian Charlesworth
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