0809.4: Prof. Inscrutable

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Puzzle #4: Professor Inscrutable **(February 2009**)

Professor Inscrutable had three students in his contemporary meta-metaphysics course: Amie, Matthew, and Sven. Each student had to write the same number of papers for the course. Professor Inscrutable graded on a curve, such that the best of the three papers got p points, the second-best got q points, and the third-best got r points, where p, q, and r are distinct integers such that p > q > r > 0. There were no ties, and all students handed in all the required papers.

At the end of the term, Amie had earned 22 points, and Matthew and Sven each had 9 points. Matthew had the best grade on the first paper.

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Questions

1. How many papers were there?

2. What are the values of p, q, and r?

3. Who had the second-best grade on the second paper?

Solutions must contain explanations!