June 1–June 7, 2010
Problem
In Mathland, players Thomas, Freddy and Walter competed against each other to win the Golden Disk. There were X tests: in each of them, an integer amount of points were awarded to the first, some less points were awarded to the second, and even less (but still positive) to the third. All tests were rated with the same scale.
At the end of the day, Walter won the Golden Disk with 22 points, Thomas
was second with 15 points, and Freddy was third with a total of 14
points. If Freddy won the Geometry test,
a) How many tests were there?
b) Who was second in Algebra?
Solution
List of solvers
Lloyd Sakazaki, Eric Bensley, Jason Uanon, David Aaronson, Neal Johnson, Peiyush Jain, Jason Shaw, Tristram Bogart, Congpa You, Jonathan Cross, Crispin Pereira, Jonathan Shi, Chaitanya Rachabattuni, Mohammad Hamza Mufti, Gary Mager.
Tristram Bogart wins the prize!