Better way to solve it ?

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Better way to solve it ?

by sapuna » Sun Aug 10, 2014 12:40 am
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Ok , that type of questions are super easy for me because I`m smart and know I should to that would be enough ( for example I have no idea of the formula but know that if a square is inscribed in a circle and we know the radius , we can find everything about the square because there is only 1 square with 1 particular size that would be inscribed in that circle ).

So , back to this : since we need the least number , I thought the first and secodn team both got a total of 6 points.

Team 1 got - First place , fifth place , ninth place ( 5 + 1 + 0 = 6)
Team 2 got - second place , fourth place, eight place ( 4 + 2 + 0 = 6 )
Team 3 got - third place , sixth place , seventh place ( 3 + 0 + 0 = 3 )

So , any other cool idea ?
Source: — Problem Solving |

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by [email protected] » Sun Aug 10, 2014 12:55 am
Hi sapuna,

This is essentially a "limit" question; to figure out the LEAST number of points that any team could score, we have to MAXIMIZE what the other 2 teams scored.

Since a team score 6-N points for each racer who finishes in Nth place (1 <= N <= 5). This means that ONLY 5 racers get points:
1st = 5 points
2nd = 4 points
3rd = 3 points
4th = 2 points
5th = 1 point
Total = 15 possible points

We're told that none of the 3 teams scored more than 6 points.

IF we can find a way for two of the teams to score 6 points each, then the third team would have the remaining 3 points. There IS a way for that to occur (which you figured out).

Final Answer: D

You actually do have to go to the trouble of proving this though; in other types of limit questions, there might be restrictions that would change the answer.

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