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For a certain race, 3 teams were allowed to enter 3 members [#permalink]
28 Aug 2004, 10:18
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For a certain race, 3 teams were allowed to enter 3 members each.
A team earned 6 â€“ n points whenever one of its members finished in nth place, where 1 ≤ n ≤ 5. There were no ties, disqualifications, or withdrawals.
If no team earned more than 6 points, what is the least possible score a team could have earned?
This question came from the OG, but I think it was a DS questions.
Anyway, there are 3 teams and 9 members altogether.
So if a team finish first, it gets 6 points, second, 5 points, third 4 points and so on.. there's no points for coming in last.
The least possible points a team can get is when the other 2 teams pick up the maximum points. So assuming 2 teams got the maximum of 6 points, then there's still (5+4+3+2+1)-12 = 3 points left for the last team.
Combination of possible points that the three teams can score (given the condition that it cannot exceed 6 points)
(5,0), (5,1)
(4,1), (4,2), (4,0)
(3,2), (3,1), (3,0)
Considering points beyond this would mean scores of
(2,4), (2,3), (2,0) and
(1,0), (1,5), (1,4), (1,3)
However if scores were (2,0) and (1,0) this would mean that there is a possibility that in the total points score other two teams can have distributions exceeding 6 total points.