VeritasPrepKarishma wrote:
I3igDmsu wrote:
I am struggling with this one, it may be that I don't understand the question and information given.
If there are 3 teams of 3 members each (9 people total), wouldn't the possible finishes for each member of the teams be 1st, 2nd, 3rd,..., 9th?
How is it that 1 <= n <= 5 when there are 9 racers? Do racers 6 through 9 just get 0 points?
Yes, a racer gets points only when he/she ranks 1 - 5.
Break down the question to get a handle on it:
For a certain race, 3 teams were allowed to enter 3 members each. This means 9 racers.
A team earned 6-n points whenever one of its members finished in nth place, where 1<= n<=5, there were no ties, or withdraw. Since n varies from 1 to 5, only when a member finishes in one of those positions, does he score something. That something is 6 - n. So person who finishes first, gets 5 points, person who finishes 2nd gets 4 points and so on till the person who finishes 5th gets 1 point. So in all, 5+4+3+2+1 = 15 points were given
If no team earned more than 6 points, what is the least possible score a team could have owned? No team got more than 6 points. We have to find the minimum score of a team. Since the total is 15 and one score has to be minimized, we should try to maximize the other two scores. Maximum score is 6 so other two teams get 6 points each maximum (e.g. One team gets 5 + 1, another gets 4+2). Then the third team will get a minimum score of 15 - 2*6 = 3
Responding to a pm:
Quote:
may i ask you a question about this problem: would it be correct to assume that the least nr of points that team could possibly earn in a race is 1 point (disregarding the case when no racer from a team scores any points), and so much as a result of each race, which yields 3*1=3 points?
I do understand your reasoning, but mine is a bit more straightforward, and I wonder if I am lucky to hit the correct answer with wrong assumption, or is it a valid reasoning?
No, this reasoning is not correct.
Look, there is only ONE race. The rankings in that race are the only points the racers get. The reason some points get added up is that the racers belong to a team.
Team A has three racers: A1, A2, A3.
Similarly, team B and team C.
If A1 gets 4 points and A3 gets 2 points, team A gets 4 + 2 = 6 points.
No team got more than 6 points. So say team A got 6 points and team B got 6 points. This means team C must have got 3 points.
That is the reason 3 points is the minimum any team would have got.
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Karishma
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