Answer / jason mitchell

It is 7. You race all the horses in batches of five. Now
you take all the first place houses and race them in a '6th
race'. Now this will tell us the fastest horses and we also
know that the horses that finished 4th and 5th in
this 'sixth race' cannot be in the top 3. So we have a 7th
race which we race 2nd and 3rd from the '6th race', but we
also have to add in the 2nd and 3rd places horses from the
overall winners original group and then we add 2nd place
horse from the original group of the 2nd place horse in the
6th race.

Answer / sonali jayale

first race between 5 will give 1 best, then chose another
4 and make race between this 4&1 will give 1 best
again.this 1 will carry race with other 4 i.e it is 3 race
will give 1 best,now from 4 race 1 ,from 5 race 1,& 6 , 7
&8 rce give 1 .all 25 have completed running we get 1
best.now in 8 races horses in second position are present
so carry out same process for second best and in all 40
races will be carried out for best five.
40 races

Answer / tarun

the ans is 30
how-
step 1-
first best horse can be found by having 6 races
every time a race is made,4 horses are eleminated and the
best is to race with other 4.
likewise 4+4+4+4+4+4=24 horses eleminated
total horses=24(eleminated)+1(best).

now likewise we find the the other best horses removing the
best horses obtained earlier from d group.
for second best horse
4+4+4+4+4+3=23 horses eleminated
total horses=23(eleminated)+1(best).

hence total races required will be=6*5=30

Answer / jayesh pakhale

Hi,
As per given problem, we need to choose best 5 horses among 25.
after first race we get 1 best among 5.
in second race we will include winner of first race and other 4 horses and get one winner. So now we have best one out of nine.
3rd race 1-winner from 2nd +4 new ->judged 13 horses
4th race " 3rd " -> " 17 "
5th " " 4th " -> " 21 "
6th " " 5th " -> " 25 "
put this best horse a side.
Now we need to choose 2nd best among 24 horses
7th race 1-winner ->judged 5 horses
8th race 1-winner from 7ht +4 new ->judged 9 horses
9th race 1-winner from 8th +4 new ->judged 13 horses
10th race1-winner from 9th +4 new ->judged 17 horses
11th race1-winner from 10th +4 new ->judged 21 horses
12th race1-winner from 11th +3 new ->judged 24 horses
put this best horse a side.
Now we need to choose 3rd best among 23 horses
13th race 1-winner ->judged 5 horses
14th race 1-winner from 13ht +4 new ->judged 9 horses
15th race 1-winner from 14th +4 new ->judged 13 horses
16th race1-winner from 15th +4 new ->judged 17 horses
17th race1-winner from 16th +4 new ->judged 21 horses
18th race1-winner from 17th +2 new ->judged 23 horses
put this best horse a side.
Now we need to choose 4th best among 22 horses
19th race 1-winner ->judged 5 horses
20th race 1-winner from 19ht +4 new ->judged 9 horses
21th race 1-winner from 20th +4 new ->judged 13 horses
22th race1-winner from 21th +4 new ->judged 17 horses
23th race1-winner from 22th +4 new ->judged 21 horses
24th race1-winner from 23th +1 new ->judged 22 horses
put this best horse a side.
Now we need to choose 5th best among 21 horses
25th race 1-winner ->judged 5 horses
26th race 1-winner from 25ht +4 new ->judged 9 horses
27th race 1-winner from 26th +4 new ->judged 13 horses
28th race1-winner from 27th +4 new ->judged 17 horses
29th race1-winner from 28th +4 new ->judged 21 horses
thus we got our 5th best horse after 29 race.
such every horse has been compared with each one.

Answer / krishnaveni

5 horses at a time are made to participate
the first & second are selected
thus initial races =5*5=25
so selecting in such a way 10 horses are remaining
again 2 tests are heid
thus total 12 races are required

Answer / sandhya

37 races

Answer / sachin

5 races capture time of all 25 horses sort them the first
five are the top five

Answer / jaspreet

the answer is 53130...........
acc. to the permutation and combination
25!/5!*(25-20)!=25*24*23*22*21*20!/5!*20!
=53130..........

Answer / siddharth

answer is 25!

Answer / konstantin

Just got this question during interview.
The only difference was to determine 3 best horses.

The RIGHT answer is 10.

Just abstract your brain from horses and racing track.
This is INSERTION sort algorithm.
You have an array of 25 elements and you need do determine
5 elements that have greater values among others elements.

Divide the array down to 5 non overlapping ranges.
Sort each of those ranges (5 RACES) and as a result you will
have maximum value element for the whole array somewhere
among top value elements of each individual range.
Compare them against each other(+1 RACE). Determine maximal
value element, remove this element and replace it for second
in order for this range.
Perform latest 2 steps for whatever number elements you need.


So, to determine 1 best horse you need 5+1=6 races,
best 2 horses will require 7 races and so on.
Obviously determination of 5 best horses will require
5+5 = 10 races.

16*2/3*7*3/43*1/3=?

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