In looking at Paul's proposed solution he would require a total of nine races. The five races [first round] to race all horses. Select top three from each of the first races to compete in three second round races. One more race to determine the second and third fastest horse. So his total number of races is nine, not eight. There is still a solution that requires fewer than eight races total though. Paul is onto the crucial logic, he just has not made the most possible out of it. Let's see what Paul or anyone else can come up with over the next 12 hours or so.