I suppose this best goes in the discussion rather than the solution space.
This question confuses me a bit, and I'll go into why and then hopefully someone can come along and clarify.
1) Why can't we just take the top 3 from the 6th race?
- Initial thinking: So of course we have 5 groups to race all 5 horses. Now in the 6th race we should be able to determine 1, 2, and 3rd.
- Second thought: I think I understand why this can't be done. This would clearly be inaccurate in the case that others in group 1 are faster than those in groups 2, 3, 4, and 5.
- Third thought: But then, if that is the case, what happens if all the horses in group 1 are faster than everyone in the other groups. Clearly 6 or 7 races would not find the 1, 2, and 3rd ranked horses
- Final thought: If I go back to the beginning and state that the 5 winners were the horses with the fastest times no matter what heat they were in, then 6 races would be the most needed to determine the fastest horse. Right?