Monday, March 4, 2013

A Harry Potter Puzzler

I recently had occasion to put together a bit of a puzzle for a fellow math fiend on the occasion of his birthday.  If you enjoy Harry Potter and recreational mathI know that's a limited bunch, but it occurred to me this blog readership might just select a little for thatyou may well like this small offering:
Gryffindor and Slytherin played a Quidditch match.
  1. Alicia Spinnet scored the first goal of the match, giving Gryffindor its one and only lead of the match until the moment that Harry caught the Snitch, winning the match for Gryffindor. The match was, however, tied three times (other than at 0-0).
  2. Gryffindor never scored two goals in succession; Slytherin always scored at least one goal in between. Furthermore, each pair of Gryffindor goals was separated by a different number of Slytherin goals.
  3. Ginny Weasley and Katie Bell each scored a hat trick (three goals) for Gryffindor.
  4. Each Gryffindor score was assisted by the Chaser who scored the previous Gryffindor goal. Each Slytherin score was also assisted by the Chaser who scored the previous Slytherin goal.
  5. Katie Bell's second goal came one hour into the match. Slytherin scored twice as many goals after that point than they did before it. Interestingly, Graham Montague scored all of his goals before that point, Cassius Warrington scored all of his after that point, and Adrian Pucey scored more than the other two combined.
Who scored the last goal of the match, and what was the final score after Harry ended it?

(Muggles—non-magical folk—may find it helpful to know that in Quidditch, goals are worth 10 points apiece.  Play continues until a player catches the Golden Snitch, which is worth 150 points and ends the match.  There are no other ways to score points.  The team with more points at the end of the match wins.  Assists are passes from one player to a different player leading directly to that second player scoring a goal.  Finally, each team has three and only three Chasers, who score all the goals; the other players are two Beaters, a Keeper, and a Seeker.)

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