# Time to train!

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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