# Ranks in 2 races

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?

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.

• Why can't H be 3rd and C be 4th in the practice race? – Bailey M Jul 7 '15 at 18:15
• 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? – Rand al'Thor Jul 7 '15 at 18:16
• 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. – VictorHenry Jul 7 '15 at 18:19

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.