So by request, maths . . .


You have 25 horses and want to know which are the three fastest. Whenever you race horses, the order of finish accurately reflects the relative speeds of the horses but you can only race five at a time. What’s the minimum number of races required to determine the three fastest, and how do you do it?

To be clear you have no measure of absolute speed, that is no race times. To forestall any similar questions you are sitting in a room without a view of the track and are only handed slips of paper with the names of the horses and the relative positions of finish after each race. You may select any five horses to participate in each race.

Provide your reasoning with the answer for any credit.