**Question:**

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.

**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

POST YOUR OPINION IF YOU HAVE BETTER SOLUTION

## 1 comment

Wow...very good problem....

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