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I'll make him look. Without reading the spoiler,
If I do five races of five horses as follows:
A1 A2 A3 A4 A5
B1 B2 B3 B4 B5
C1 C2 C3 C4 C5
D1 D2 D3 D4 D5
E1 E2 E3 E4 E5
Then I know that all the 4th and 5th finishers are not in the three fastest. So I have the following left:
A1 A2 A3
B1 B2 B3
C1 C2 C3
D1 D2 D3
E1 E2 E3
If I race the winners and get
A1 B1 C1 D1 E1 as the finishing then all of E is dead and all of D is dead and all of the ones behind C1 are dead as well, leaving me with
A1 A2 A3
B1 B2 B3
C1
I know A1 is the fastest so I have
A1 ? ?
A2 A3
B1 B2 B3
C1
I just need to figure out if I know anything else. A1 was faster than B1, but if B1 is the second fastest than B3 cannot be, and if B1 isn't the second fastest than B2 and B3 are both dead. So toss B3 out and I can race the rest to determine second and third.
Here is the final race (race number 7) and the winner and runner up are second and third fastest.
A2 A3 B1 B2 C1
7 races.
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