25 Horses puzzle

Puzzle Level :- Moderate

PUZZLE

         You have 25 horses, among these you need to pickup 3 fastest horses for an upcoming competition. Unfortunately you forgotten stop watch at home and there are only 5 tracks to test these horses. (i.e at a time only 5 horses can race)
What is the minimum number of races required to find the 3 fastest horses?

ANSWER

7

SOLUTION

         Since there are 5 tracks we can group these horses into 5 groups, with 5 horses in each group.

and now find the fastest three in each group.

let's number these horses based on fastness in each race. Here A1 is fastest and A5 is slowest in first group and this is same for all other groups.

Race-1 :-  A1  > A2  >   A3  > A4  >  A5  

Race-2 :-  B1  >  B2  >  B3  >  B4  >  B5

Race-3 :-  C1  >  C2  > C3  >  C4  >  C5

Race-4 :-  D1  >  D2  > D3  >  D4  >  D5

Race-5 :-  E1  >  E2  >  E3  >  E4  >  E5

      You might get doubt why we need to pick 3 fastest one in each group, instead of picking the top one from each group and find fastest 3 in these horses (i.e A1,B1,C1,D1,E1).

      This is because second or third fastest one in a group can be faster than top ones from other groups.  i.e for example A2 can be faster than B1,C1,D1,E1 , then we need to pick A2 instead of top one from other groups.

So we can eliminate A4, A5, B4, B5, C4, C5, D4, D5, E4, E5 from all 25 horses

Now conduct Race-6 between fastest one from each group (A1, B1, C1, D1, E1) to find overall fastest one.

Who ever wins this race is the fastest one among all 25 horses

Now let's assume C1 won the race and  the order of finishing race is as below.

Race-6 :- C1 > D1 > B1 > A1 > E1

Keep C1 aside since it is fastest one among all horses.

Since A1 and E1 are slowest in Race-6 we can eliminate these and obviously we can also eliminate A2,A3 and E2, E3.

Since we only need two more fastest horses , we can eliminate B2, B3 because D1,B1 are faster than these two.

And also we can eliminate D3 since D1,D2 are faster than these.

So now remaining horses are

C2, C3, D1, D2, B1

Now conduct Race-7 with these horses (C2, C3, D1, D2, B1).

Which one come in first two places are second and third fastest one among all 25 horses

So in 7 races we can find fastest three horses.

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