R Hansen says: >Assuming that we do not know the time and assuming that "top 3" means that they have beaten everyone else directly or indirectly...
I think that's what intended - you either beat someone in a race or beat someone who beat someone, etc., in a direct race. You have to rule out ties by fiat as well. I think that's the intention, though allowing ties just makes it a slightly different problem. I'll also just note that if we allow two people to race each other more than once that complicates the whole ranking scheme.
R Hansen says: >That would be 8 races. In each race the original racers are advancing up one as a member in their original group wins. Basically a merge sort with 5 groups.
I think your fondness for canned "strategy" has done you in again. It only takes 7.
Given the "intended" constraints as above, prove it cannot be done in 6.