Thursday, November 3, 2011

25 Horses Puzzle

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

7 comments:

Mohammad Shamsi said...

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

shouldn't it be "The FIRST and SECOND will be second and third of the whole set" ?

Syama Prasad S said...

Thanks Shamsi,
I have corrected it.

jr mangulabnan said...

RACE#1 - 1 2 3 4 5

RACE#2 - R1 6 7 8 9

RACE#3 - R2 R2 10 11 12

RACE#7 - R3 R3 R6 R6 15

RACE#6 - R5 R5 14 15 javascript:void(0)16

RACE#5 - R4 17 18 19 20

RACE#4 - 21 22 23 24 25

The R#(Race#) represent the winner of the previous race.

in race 1 - 3 we get the 2 best horse

in race 3 - 6 we also get the 2 best horse

so in race 7, 2 best horse in round 1-3 + 2 best horse in 4-6 + the one that did not yet compete

Akshay Dabholkar said...

Why didn't you consider b3 too as the b3 < c1 relationship is not established yet??

Bijay Rungta (rungss) said...

@Akshay,
Why didn't you consider b3 too as the b3 < c1 relationship is not established yet??

Because b3 is slower than a1, b1 and b2 so it can never be in the top 3.

Social Anchorite said...
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Tarun Sharma said...

another link on technical forum: http://www.writeulearn.com/5-horse-track-25-horses-puzzle/