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Problem of the Week 886

Ultimate Round Robin

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Twenty teams entered a "round robin" ultimate frisbee tournament (meaning: each team played each other team once). Each game resulted in a win for one of the teams, and at the end of the tournament each team's score was the number of games won (that is, teams received one point for each win and zero points for each loss). Each score turned out to be a perfect square, and more teams scored 16 than scored 9. How many games went against form, in the sense that the winner turned out to have a lower score than the loser?

SOURCE: Suggested by Dan Velleman, as adapted from The London Times.

© Copyright 1999 Rob Leduc. Reproduced with permission.

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31 March 1999