25 Horses Puzzle

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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

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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