Interview Question for Associate Software Engineer at JDA Software:

Yes, the answer is seven races, in three rounds. Round 1 (5 races) is raced by a 5 sets of different horses. Round 2 (1 race) is raced between the 5 first place finishers in round 1. Round 2's winner is the fastest. Round 3 is a race between the five remaining horses that have not already been beaten by three horses. First and second place of round three are the 2nd and 3rd fastest horses.

The winner of round 2 is clearly the #1 fastest horse. The fourth and fifth place finishers of round two are clearly not in the top three, neither are the horses they beat in round 1. Similarly, all four of the horses that were beat in round 1 by the horse that took third place in round 2 can be eliminated. And so on for the three slowest horses in round 1 that were beat by the 2nd place horse in round 2. finally the two slowest horses in round 1 that were beat by the winner of round 2 can also be eliminated.

Finally round 3 is raced by the remaining 5 horses to determine the 2nd and 3rd fastest horses. The remaining horses are
* Round 2 2nd place
* Round 2 3rd place
* Round 1 2nd place behind round 2 winner
* Round 1 3rd place behind round 2 winner
* Round 1 2nd place behind round 2 second place