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Logic Level 3

Professor McGonagall digs up some history and brings out a rather intriguing example of a House Cup when only three houses competed, namely Gryffindor, Ravenclaw and Slytherin. The three houses participated in a series of events.

Points were awarded for 1st, 2nd, and 3rd places in each event (the same points for each event, that is 1st always gets \(x\) points, 2nd always gets \(y\) points, and 3rd always gets \(z\) points), with \(x>y>z>0\), and all point values being integers.

In that House Cup,

  • Gryffindor finished first overall with 22 points.
  • Slytherin won the Quidditch event and finished with 9 points overall.
  • Ravenclaw also finished with 9 points overall.

Which house finished second in the OWL (Ordinary Wizarding Level Examinations, it was one of the events in the House Cup that year)?

Source: Technothlon 2017

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