Here is a different version of the problem but the answer is here - http://www.programmerinterview.com/index.php/puzzles/25-horses-3-fastest-5-races-puzzle/
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6
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I think 5. Split the horses into 5 groups of 5 then compare the time of the winners of each group. If time comparison is not allowed, then I'd say 6 races i.e. get all the winners to run one last race.