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OPM 1995 Problem 5

  • Final day 2

Rosa dos Ventos, Aurora Boreal and Manuela do Norte organized a competition between them last weekend, consisting of several athletics events. The winner in each test obtained xx points, the second placed yy points and the third placed zz points ( x,y,z∈Nx,y,z \in N and x>y>zx >y>z ). The final result of the competition, obtained by adding up the scores in each event, was Rosa had 2222 points, Manuela had 99 points, Aurora had 99 points. In how many tests did they compete and who came second in the high jump knowing that the Manuela won the 100100 meters and no one gave up in any race?

Dataset text AI-MO AoPS. Quoted with source.

Official text: Portuguese Mathematical Olympiad 1995 official paper, page 1.

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