Puzzle time - Rating the Horses
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Just to have a quick baseline, which I'm certain isn't optimal:
The naive strategy would be the "keep the best three so far" strategy, which in this case would require 11 races.
Another suboptimal strategy would presumably be "reject 2/5th of the candidates in each round", i.e. 5 races for the first round (leaving 15), 3 for the second (leaving 9), 2 for the third (leaving 5, with a little trick), and then a final round. Which also adds up to 11.
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Testing all 25 in 5 groups to start seems reasonable. From there you can test the five heat winners, which will give you the fastest. You can disregard the groups led by the two slowest. That leaves six horses which might be the next two fastest, which are the two fastest horses from each of the three remaining groups. You don't have to race the second fastest from the group led by the third fastest in the semi-final though, because you know it's at best fourth fastest. So there are only five left. Total 7 races.
