**There are 25 horses. We have to find out the fastest 3 horses. In one race maximum 5 horses can run. How many such r****aces are required in minimum to get the result ?**

Check your answer:-

Click here to See SolutionLets say it looks like this

O1,O2,O3,O4,O5

T1,T2,T3,T4,T5

TH1,TH2,TH3,TH4,TH5

F1,F2,F3,F4,F5

FV1,FV2,FV3,FV4,FV5

Here O1 > O2 > O3 > O4 > O5 same way for others.

Now lets take fastest horse in each race and then have one race between them, so have race in O1, T1, TH1, F1 and FV1.

Lets say O1, TH1 and F1 comes in top three(and O1 > TH1 > F1), then there are no chances that horses slower than T1 and FV1 can come in top 3 and we can also say that O1 is fastest horse and also F2-F5 horses are not among top 3.

Now we need to find second and third fastest horses

they can be from O2,O3,TH1,TH2 and F1, So we will have once more race among them to determine second and third position.

Thus a total of minimum 7 races are needed to find top 3 horses from 25 horses.

Vishal Singh Chauhan says

We need fastest 3 horses…

First divide the 25 horses in five groups.. Having 5 horses in each group…

Race the 5 groups (each seperately)..

So 5 races…

And we got top 5 horses in this way…

Now race these 5 horses together….

And select the first three horses finishing the finish line…

So total of #six race…

Hardik Patel says

Surely 7 is 100% correct answer.

Harshit Anand says

step1: Compete in 5 random groups and get results as:

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

step2: Compete the top runners and say results obtained are:

a1 b1 c1

clearly we get a1 is fastest and whole group d and e are eliminated.

step3: Now race is for second position. a2 and a3 can be faster than b1 and c1 as a1 is faster, b1 and b2 can be faster than c1.

We don’t consider other participants as we need three places only.

Race a2 a3 b1 b2 c1 and select top 2.

So, 7 races.

Aashirwad Khaitan says

11

Take any 5 horses for 1st race.(1 race)

Now divide the rest 20 horses into groups of 2 i.e. 10 groups.

Take any group and join them with the top 3 of the 1st race.(2 races)

Now, again take the top 3 of the 2nd race and join them with any other of the remaining 9 groups.

Thus, in total 10+1 = 11 races will be required.

Vijay Kumar says

step 1: 7 Races, 5 races we will rank top 3 in all Races

step 2: Take all the first horse in 5 races and conduct a race and mark there rankings in 6 Race

step 3: Horse which were ranked 4 and 5 are eliminated and horses which were ranked 2 and 3 in the same group of Horses which are ranked 4 and 5 are also eliminated as they are inefficent

Step 4: Horse which ranked 3 has chance to be in top 3, but horses which got 2 and 3 in step 1 of gorup of rank 3 horse in step 2 has no chance of being in top 3 so they are also eliminated

step 5: Horse which ranked 2 in step 2 has chance to be in top three, and horse which ranked 2 in step 1 of this horse group also chance to be in 3 position, but horse ranked 3 in step 1 of this horse group will be eliminated as it has chance to be in 4 overall, now we got 2 horses of this group

step 6: Horse which ranked 1 in step 2 will always be the top horse whose rank will be 1, horse ranked 2 and 3 in the group which rank 1 horse of step 2 ran will have chances to be in 2 and 3 overall, so we will take all the 3 horses

step 7: now we have total 6 horses

3 horses from group of a horse which came first in step 2(best of best horses)

2 horses from group of a horse which came second in step 2

1 horse from a group of a horse which came third in step 2

now we have total of 6 horses

Horse which came first in step 2 is always best of best horses so it is ranked 1

now we have 5 horses and we will conduct a race to all the five, and select first and second and they will be 2nd rank and 3rd rank(as we already got first rank horse)

Total ************* 7 races *****************

Ganesh VishnuPriya says

first conduct 25/5=5 races

take 1st position horses in that 5 races and conduct another race

so that top 3 horses is select… i think so it is crt….

finally 6 races….is it crt guys…

Vijay Kumar says

No It is not correct because 2 and 3 horse in first race, can be faster than first horse in second race

Ramesh Chandra says

first make of group of 5 and make 5 race

take top 5 and make one more race…

select which are top three and take two more horse which group has fastest horse…and make one more race too

total race = 7

Anurag Pushpam says

Lets have a different solution…

Divide the track in two equal halves. Now we can get 10 horses to run in a go i.e from both sides. after first run we keep the top three and replace the other seven . We do this process again until no horse left.

In this way we get only three attempts 🙂 🙂 . ASSUMPTION :THERE IS NO COLLISION/HARM TO HORSES

puzzlersworld says

And you are assuming track is equal, as some horses might perform better than other in particular condition.

Anurag Pushpam says

if you talkin about condition then …all horses at one go fits most … condition of tracks may change with every race ….

Shyam Vijay says

11 races are required and the explanation is here :

1st race – any 5 horses — get 3 fastest horses

2nd race – above 3 fastest horses + 2 from remaining 20 — get 3 fastest horses (18 remain)

3rd race – repeat the 2nd step (16 remain)

4th race – repeat the 2nd step (14 remain)

5th race – repeat the 2nd step (12 remain)

6th race – repeat the 2nd step (10 remain)

7th race – repeat the 2nd step (8 remain)

8th race – repeat the 2nd step (6 remain)

9th race – repeat the 2nd step (4 remain)

10th race – repeat the 2nd step (2 remain)

11th race – repeat the 2nd step (0 remain)

We will get the 3 fastest horses among all 25 horses.

Satya says

Answer is 6

25 horses => 5 groups (5 in each group)

5 group=> 5 race=>5 winner horse=> group no. 6

now give one race and get 3 winner

sandeep says

this is exact answer 11

krisN says

Answer is 7.Without any duobt

Anshul Rajvanshi says

I think its 6. 5 races would give top 5 racers. Sixth race can give the top 3 racers? Isin’t?

Tejaswi Tejas says

6 races gives three top fastest horses….its simple. ..

Pankaj Kumar says

ans will b 10….devide in 5*5 and get best 3 of each…now again devide into 5*3 and get 9 best of them..now run any 5 of them eleminate last 2..now we have 7 remaining again run 5 n eleminate now we have 5…….run them all n get best 5…..

5+3+1+1+1=11 ans

puzzlersworld says

Think if you can avoid some races, we need to find minimum number of races needed

Srivaths says

Ans is 12

Make 5 horses in 5 groups

The fourth and fifth place of each race can’t be the top three… Which eliminates 10 horses… 15 horses remain… Split them into three groups… Again the last two are removed…. So 9 horses remain… Split into 5 and 4… We get 5-2 and 4-1…so 6 horses remain… Let the first four run… And eliminate one…. Let the remaining 5 run….. And u get the top three….

5+3+2+1+1

dj says

that’s seems exact..

puzzlersworld says

That does not give minimum number of races required

dj says

oh, right! Thankyou

Raizel says

No the answer should be 6 cause if you took a winner from each group of five horses then you again can make a team of five and after their racing you can get top 3 fastest horse 😀

Jason says

This is a worst case scenario and gives the upper bound on the problem; however, it is a valid solution.

Alok Raghuvanshi says

only 5 race required .

1 ) make 5 groups having 5 horse in each group

2) let the 1st group run for certain distance and note down the time taken by all the horses.

3) repeat step 2 with all groups for the same distance and note down the time taken by each horse.

Now you have time taken by all the 25 horses to complete the race and easy to decide the best 3 of them.

puzzlersworld says

you can not note down the times, as the fastest horse might have slowed down as his opponents were slow, but he might have tried harder if required, you know the last minute stint…

Amit says

Only 6 race will be required to determine fastest horse.

5 to determine fastest from group of five and one to determine fastest from fast five

Saubi says

I think 8 is the answer..

12345 ABCDE LMNOP PQRST UVXYZ = 5 races

Here’s the order:

123 ABC LMN PQR UVX

1 A L P U = 6th race

1 is clear winner.. Now,

Here are the relationships between these horses ( “>” : may be faster, “>>” is definitely faster)

1 >> 2,3,A,B,C,L,M, N

2,3 > A

2 >> 3

A >> B, C

A >> L

B, C > L

So, we have 6 (2,3,A,B,C,L) horses to find the fastest 2 horses now.

2, 3, A, B, C = 7th race

If, 2 comes first then 3 can come 2nd and A is 3rd fastest.

If, A comes 1st and any1 else comes second then we cannot determine if L is faster or othr 4 horses are faster.

Therefore, in case 2 we will need 1 more race, i.e. total 8 races in worst case.

Alok Raghuvanshi says

only 5 race required ….

1 ) make 5 groups having 5 horse in each group

2) let the 1st group run for certain distance and note down the time taken by all the horses.

3) repeat step 2 with all groups for the same distance and note down the time taken by each horse.

Now you have time taken by all the 25 horses to complete the race and easy to decide the best 3 of them.

saandy says

that is absolutely correct…

damii says

I think this is the best answer

Zakeer Belthangady says

11 races my dear

First five group of five horse means 5 race

Result 5×3 15

3 group of 5 horse = 3 race

Result 3×3 =9

1 set race = 1 race

Found best three + 4 from above= 7

1 set race 1 race

Found 3

3+ remaining 2 from 7 means 5

Another race = 1 race

now we found finalist means 11 race

rohit says

its simple..and ans is 7

loki says

7 races

loki says

5 races

Giriraj Mulay says

How???

Anonymous says

We can do 5-5 race for total 25 horses. Now we have 5 top horses.

Out of 5 we need to find 3.

For 5 top horses, we can have another race.So we found 1st faster running horse.

Now for 4 top horses we can have another race -> Condition is maximum 5 can include but there is no restriction for minimum. -> Found 2nd faster running horse

Now for remaining 3 horses, we can have another race -> Will get the 3rd faster running horse.

So total 8 races required to find the faster running horses.

Vijay says

here u think wrong. because in first race, line 1 -> second horse can be fast from other 4

naman says

What should be the answer?

Harish Kotkar says

11

Saran MK says

This in not fair. After the final race, those came top 3 is correct, as it went throuh. But again making a race for 2nd of every group is disturbing the logic ? so correct answer should be 6 as i think

puzzlersworld says

There is a chance that horse which is beaten by fastest horse in earlier races can be better than other 4 horses.

Anil says

correct ans will be 7………………………think again……..

crazyforstudy it says

well explained @puzzlesworld…..answer is 7 only

lion says

hi dude…