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  • Horse Race

    pradeep_agrawal

    pradeep_agrawal

    @pradeep-agrawal-rhdX5z
    Updated: Oct 25, 2024
    Views: 1.1K
    There are 25 horses. Given that only five horses can run at a time in a race, how many races do you need to find top three horses? Also explain the logic behind the answer.

    Note:
    1. A horse runs all the races with same speed.
    2. You can't measure time but you know the outcome of the races.
    3. The outcome of any race is never conflicting (i.e., it never happens that there are two or more horses that hold same position).

    -Pradeep
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  • Saandeep Sreerambatla

    Member • Jun 30, 2009

    The number of races required are 7

    Explanation:

    Divide 25 into 5 groups of 5 horses each.
    Name them as a1 ,a2 ,a3,a4 ,a5
    b1 ,....,b5 ; c1,...c5 ,d1....d5 ,e1....,e5
    Now 5 races in these 5 groups which gives 5 winners , assume the winners are in the order i gave the names .
    i.e., In the first race a1 is first , a2 is second and so on.

    Now conduct a 6th race between a1 ,b1,c1,d1,e1 who are the winners of 5 races.
    This race results in 3 toppers.
    consider a1 ,b1,c1.

    Now a1 is the fastest put aside.
    We can neglect the teams d and e and c2 to c5.
    b2 can get atmost 3rd position so he is in the race neglecting b3-b5.
    a2 and a3 are included as they probably can get 2 or 3.

    So the seventh race is between a2 ,a3 ,b1,b2,c1

    we can get the winners !!!
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  • pradeep_agrawal

    Member • Jun 30, 2009

    That was quick. It's a correct answer with correct and good explanation.

    Good going English-Scared.

    -Pradeep
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