MathDB

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

x

points, the second placed

y

points and the third placed

z

points (

x,y,z \in N

and

x >y>z

). The final result of the competition, obtained by adding up the scores in each event, was Rosa had

22

points, Manuela had

9

points, Aurora had

9

points. In how many tests did they compete and who came second in the high jump knowing that the Manuela won the

100

meters and no one gave up in any race?
[hide=official wording]Rosa dos Ventos, a Aurora Boreal e a Manuela do Norte organizaram no passado fim de semana uma competi¸c˜ao entre elas, consistindo em v´arias provas de atletismo. A vencedora em cada prova obteve x pontos, a segunda classificada y pontos e a terceira classificada z pontos (x,y,z ∈ IN e x >y>z). O resultado final da competi¸c˜ao, obtido por soma das pontua¸c˜oes em cada prova, foi Rosa 22 pontos Manuela 9 pontos Aurora 9 pontos Em quantas provas competiram e quem ficou em segundo lugar no salto em altura sabendo que a Manuela ganhou os 100 metros e que ningu´em desistiu em nenhuma prova?

Problem Statement