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There are $n$ horses. At a time only $k$ horses can run in the single race. How many minimum races are required to find the top $m$ fastest horses? Please explain your answer.

PS: There is no timer.

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    @RossMillikan Now the [Math Horizons article of Morris, Stong and Wagon](http://www.jstor.org/stable/10.4169/mathhorizons.20.4.20) has been published, but is not available for free.2013-09-11

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