Solution
Twenty-Five Horses
Show the problem again
You have 25 horses and a track that races exactly 5 at a time, with no timer; you learn only the finishing order of each race. What is the minimum number of races needed to guarantee finding the fastest three horses, in order?
Worked solution
The answer is 7. Race five groups of five (races 1–5), then race the five winners (race 6); the winner of race 6 is fastest overall. Only five other horses can still be 2nd or 3rd: the runner-up and third from the champion's original group, the second-place winner of race 6 and its group's runner-up, and the third-place winner of race 6. Race those five (race 7); its top two are the overall 2nd and 3rd. Six races provably cannot suffice.
Source: Classic tournament-sorting puzzle in wide circulation, long used as an interview question. Statement written for AxiomIQ.