Question

For a certain race, 3 teams were allowed to enter 3 members each. A team earned 6 – 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?

Answer 1

The least possible score a team could have earned is 3.

Explanation:

From the given information it is clear that the total number of teams is 3.

Total number of members in each team is 3.

A team earned 6 – n points whenever one of its members finished in nth place, where 1 ≤ n ≤ 5.

It means the points for 1st, 2nd, 3rd, 4th, and 5th place are 5, 4, 3, 2 and 1 respectively.

Total points that can be earned all teams together = 5+4+3+2+1=15

There were no ties, disqualifications, or withdrawals.

To minimize the score of a team, we have to maximize the score of the other two teams.

It is given that no team earned more than 6 points,

Let two teams earn there maximum score. i.e. 6. So the score of third team is

`15-6-6=3`

Therefore, the least possible score a team could have earned is 3.