4
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8 competitors (A-H) participated in 2 races. The first was the practice race, and the second being the final one. No 2 people got the same rank.

A and B improved their ranks in the final race by 5 spaces each. C did worse than G in the final race. G became worse by 5 spaces in the final race. C did better than E and F in the practice race. D came first in the practice race, but became 4th in the final race. E and F swapped ranks in the final race.

How did the winner of the final race fare in the practice one?

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The winner of the final race was

H, who placed 3rd or 4th in the practice race.

Explanation:

You have 8 possible places in each race. We know that D was 1st in the practice, 4th in the final, so we can fill him in.

   P  F
1  D
2
3
4     D
5
6
7
8

Next we know G got worse by 5 spaces, which means he was either 1,2, or 3 in the practice race and 6,7, or 8 in the final race. However, D was 1 in practice, and C was worse than G in the final, so G must have gotten 2 and 7 in the respective races.

   P  F
1  D
2  G
3
4     D
5
6
7     G
8     C

E and F switched spots in the final race, so they can't be in spots 4,7, or 8 in the practice race. C did better than E and F in the practice race, so they must be in slots 5 and 6 in both races (doesn't matter which order).

   P  F
1  D
2  G
3  
4     D
5  E  F
6  F  E
7     G
8     C

A and B moved up five spaces in the final race, so they must be in slots 7 and 8 in the practice race and 2 and 3 in the final race (doesn't matter which order).

   P  F
1  D
2  G  A
3     B
4     D
5  E  F
6  F  E
7  A  G
8  B  C

That leaves H in the remaining places: 3rd or 4th in the practice race, 1st in the final race.

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  • $\begingroup$ Why can't H be 3rd and C be 4th in the practice race? $\endgroup$ – Bailey M Jul 7 '15 at 18:15
  • $\begingroup$ Well, you even got the explanation before I did! :-) Question though: how do you know C came 3rd and not 4th in the practice race? $\endgroup$ – Rand al'Thor Jul 7 '15 at 18:16
  • $\begingroup$ That was an error on my part, for some reason I was filling C, E and F into spots 3, 5, and 6 in the third step, but of course C could be in 3 or 4. $\endgroup$ – VictorHenry Jul 7 '15 at 18:19
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In the practice race:

  • D came first (given)
  • G came second or third, since he has room to become worse by 5 spaces; also C did worse than G in the final race, so G came second
  • A and B were both in the last three, since they had room to improve by 5 spaces
  • C came third or fourth, since E, F, A, B must all be worse than C

In the final race:

  • D came fourth (given)
  • A and B were both in the top three, since they improved by 5 spaces
  • G came seventh, since he became worse by 5 spaces
  • C came eighth, since she did worse than G
  • one of H, E, F was in the top three and the other two were fifth and sixth

Since E and F swapped places, the only possibility is now that they were fifth and sixth in both races. That means A and B were seventh and eighth in the practice race and therefore second and third in the final race. So:

H won the final race, and came third or fourth in the practice race.

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