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North American Swim Meet (Posted on 2009-04-29) Difficulty: 2 of 5
Canada, Mexico and the United States each sent three swimmers to a North American swim meet. The scoring was that the first place finisher would get 8 points, the second place finisher 7 points, and so forth, down to no points for ninth (last) place.

The first two Mexican swimmers to finish were the two swimmers whose times were closest to each other among all the contestants, and last place, with no points, was one of the Canadians.

When the three nations' scores were totaled, it was found that each team had the same total score.

What was the order of finish, by team?

See The Solution Submitted by Charlie    
Rating: 2.0000 (2 votes)

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Solution Solution Comment 3 of 3 |
The total number of points divided among the 9 swimmers is 8+7+6+5+4+3+2+1+0 = 36.
As each team ended with the same total score, each team scored 36/3 = 12 points.
One of Canada's contestants is given as having scored 0, therefore the other two Canadian contestants scored the 12 points, thus Canada would have one of the following:
  • 8+4+0 (first, fifth, ninth)
  • 7+5+0 (second, fourth, ninth)
If Canada had the first, fifth and ninth places, the other places that would total 12 would be the following:
  • 7+3+2 (second, sixth, seventh)
  • 6+5+1 (third, fourth, eighth)
If Canada had the second, forth and ninth places, the other places that would total 12 would be the following:
  • 8+3+1 (first, sixth, eighth)
  • 6+4+2 (third, fifth, seventh)
Of the four possible places, the only one that fits the condition that Mexico's first two places were consecutive is the third, fourth and eighth places...

    ...thus, the order of finish, by team, must be:

  1. Canada
  2. United States
  3. Mexico
  4. Mexico
  5. Canada
  6. United States
  7. United States
  8. Mexico
  9. Canada

  Posted by Dej Mar on 2009-04-29 18:43:45
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