find the fastest second fastest and third fastest horses out

find the fastest, second fastest and third fastest horses out of 25 horses in the minimum number of races, each race has 5 lanes and any 2 horses always finish in the same order (no stopwatch)

Solution

Give horses number as H1, H2,..., H24, H25.

Race 1: H1, H2, H3, H4, H5

Race 2: H6, H7, H8, H9, H10

Race 3: H11, H12, H13, H14, H15

Race 4: H16, H17, H18, H19, H20

Race 5: H21, H22, H23, H24, H25

Here they are arrranged in order of position they come in race.

Now do race between winners between above races:
Race 6: H1, H6, H11, H16, H21

Here also they are arranged in position of race outcome.

We can notice from race 6:

1)As H16 is 4th ,hence there is no chance that H17, H18, H19, H20 get in top 3 horses.

2)Same for H21.H21 is 5th ,hence there is no chance that H22, H23, H24, H25 get in top 3 horses.

3)As H11 comes third in the race, so we can be sure that horses (H12, H13, H14, H15) cannot acquire top 3 positions also.

4)As H6 is 2nd then there can be chance that H7 can become 3rd horse but H8, H9, H10 cannot be in first 3 positions.

5)As H1 wins race between all winner we get fastest horse.

6)As H1 wins, we can take H2,H3 for possibility of  second fastest and third fastest horses.So in our final race we will have H2, H3, H6, H7, and H11

Race 7:In this race,let H2 comes fiirst and H3 second then we have our  second fastest and third fastest horse.

Hence minimum number of races is 7.