Fastest 3 Horse Puzzle

puzzle : you have 25 horses and a racetrack with 5 lanes which means that at 5 horses can race at a time on that track . you don't have any stopwatch. find the three fastest horses among them

solution

It can be done in 7 races

let the horses by h1,h2,.., h25
h1 h2 h3 h4 h5
h6 h7 h8 h9 h10
h11 h12 h13 h14 h15
h16 h17 h18 h19 h20
h21 h22 h23 h24 h25

make groups of 5 and race them , so we'll have 5 races

1) Remember that the winners are not necessarily containing the fastest three

2) we can eliminate the last 2 horses in each race as in no possible way that can be the fastest three. that eliminates 10 horses. so we have 15 horses left

h1 h2 h3
h6 h7 h8
h11 h12 h13
h16 h17 h18
h21 h22 h23

3) again race the winners of the first five races , let the winners be in the same order as above by chance as this will not affect the answer. ;-)

4) again eliminate the last 2 horses and the horses beaten by them in first 5 races .
that eliminates 2+ 4 = 6 horses , so we are left with 9 more horses

h1 h2 h3
h6 h7 h8
h11 h12 h13

5) we are sure that the winner of 6th race (h1) is the fastest horse. so we can eliminate the horse that came that came third in the other races . that leaves only 5 horses

6) race the last batch of horses and select the first and second horse. they will be the second and third fastest in all