269.Twenty-Five Horses
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You have 25 horses and a track that races exactly 5 at a time. You have no stopwatch, so a race tells you only the finishing order of those 5. Assuming every horse runs at a consistent speed and there are no ties, what is the minimum number of races needed to identify the fastest three horses in order?
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Five races split the field into ranked groups. After a sixth race between the group winners, most of the 25 can be eliminated on logic alone — count how many genuine candidates remain.
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