25 horses Puzzle

Puzzle Problem :
Given 25 horses, find the best 3 horses with minimum number of races. Each race can have only 5 horses. You don't have a timer.
Now the challenge is how we can do it in 7 races.

Answer:

We will have 5 races with all 25 horses.

 Let the results be

 a1,a2,a3,a4,a5
 b1,b2,b3,b4,b5
 c1,c2,c3,c4,c5
 d1,d2,d3,d4,d5
 e1,e2,e3,e4,e5

Where a1 is faster than a2 , a2 faster than a3 etc and We need to consider only the following set of horses
a1,a2,a3,
b1,b2,b3,
c1,c2,c3,
d1,d2,d3,
e1,e2,e3,


Race 6
We race a1,b1,c1,d1 and e1
 Let speed(a1)>speed(b1)>speed(c1)>speed(d1)>speed(e1)

We get a1 as the fastest horse .

We can ignore
d1,d2,d3, e1,e2 and e3 
also c2 and c3 can be ignored as c1 is already 3rd in the race and is faster than c2 and c3.
similarly b3 will also be ignored as a1 is fastest and b1 and b2 are faster than b3.

The set left for the last race

a2,a3,
b1,b2
c1

 Race 7
 Race a2,a3,b1,b2 and c1

 The first and second will be second and third of the whole set