answer:Without giving you the answer, I can tell you how I’d approach the problem that you presented, namely: “How can I determine the three fastest horses out of 25, when I can only race five at a time together?” In the first place, because you’ve asked for “the three fastest”, then it’s not just “which ones can win their heats?” (when I race five at a time), because some horses, like some humans, won’t necessarily run their fastest in a heat if all they have to do is beat four other relatively slow competitors to win. You only race as fast as you need to in order to win, which won’t tell you much about “who is fastest overall”. So I’d definitely race five heats of five horses each, but I’d time both the winners and the second-place finishers (at least), because if you have a heat made up of your five fastest horses and only take the winner from that heat, plus the winners from your other four heats, and have a final race, then you may have unknowingly left out the second and third fastest horses from the finals. The races have to be timed, in other words, so that you know (at least within heats) which are the fastest horses. You may not necessarily want to have a final composed of only the winners of the five heats.