25 Horses Puzzle

Question:

This is a classic puzzle which can look simple.
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 challange is how we can do it in 7 races.

Solution

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 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 abd 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

a2,a3,
b1,b2,b3,
c1,c2,c3,

Race 7

Race a2,a3,b1,b2 and c1
The first and second will be second and third of the whole set