What is the minimum number of races required to pick the best three horses from 25 horses if each race has maximum of 5 horses ?



What is the minimum number of races required to pick the best three horses from 25 horses if each race has maximum of 5 horses ?

We will only need 7 races to get the best three out of 25.

Let us Name horses as H1, H2, H3...H25.

Now,

Race 1 - H1 - H5
Race 2 - H6 - H10
Race 3 - H11 - H15
Race 4 - H16 - H20
Race 5 - H21 - H21

Let us now assume

First Rank of Race 1 - W11
Second Rank of Race 1 - W12
.
.
First Rank of Race 2 - W21
.
Third Rank of Race 2 - W23

Fifth Rank Of Race 5 - W55

Race 6 - W11 , W21 , W31, W41, W51 ( toppers from first five races)

Race 7 - 2nd from Race 6, 3rd from Race 6, X, Y , Z where

X= 2nd winner from the team of winner of race 6
Y= 3rd winner from the team of winner of race 6
Z= 2nd winner from the team of 2nd winner of race 6

So the three best horses will be , Winner of Race 6 and Winner and Second Winner of Race 7.


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