There are 25 horses and five tracks. There is no stop clock
and we have to find the top 5 horses in the bunch. What is
the minimum possible races ?
Answers were Sorted based on User's Feedback
Answer / niraj singh
Answer = 10 races ....
Divide the horses in 5 group a,b,c,d,e. Since there are 5 tracks and assuming only one horse can run on one track hence one group of 5 can run at a time
1. Make each group race once and mark the position of each horse in the group as 1,2,3,4,5. So we have total of 5 races in this way.
2. Take the top horses of all the groups and make them run. The winner of this race is fastest horse of all. Promote the second horse of the winner group to 1. This constitute of 6th race.
3. Now take the first of all groups and do a race. This gives you horse for 2nd position. Again promote the next horse from the winner group. This constitutes of 7th race.
4. Now take the first of all groups and do a race. This gives you horse for 3rd position. Again promote the next horse from the winner group. This constitutes of 8th race.
5. Now take the first of all groups and do a race. This gives you horse for 4th position. Again promote the next horse from the winner group. This constitutes of 9th race.
6. Now take the first of all groups and do a race. This gives you horse for 5th position. Again promote the next horse from the winner group. This constitutes of 10th race.
So total of ten races is required to find the top 5 horses
Is This Answer Correct ? | 41 Yes | 17 No |
Answer / mohini
there will be 7 races.
let divide 25 horses into 5 groups a,b,c,d,e.
after 5 races, let their ranks 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
total races =5
now 1 race between a1,b1,c1,d1,e1
let a1 wins with the ranking a1,b1,c1,d1,e1
that means a1 is the winner
now a2 can be on the second position since it is after a1
in one race also b1 can also be second because in second race it was after a1.
similarly a3 can be third due to frst race and also b2 can be third if a1,b1 wins
likeise c1 was also on third number.
hence the 6 selected horse are
a1,a2,a3
b1,b2
c1 in which a1 is the first.
now there b race btween a2,a3,b1,b2,c3 that will decide 2nd,, 3rd, 4th n 5th winner.
hence total race= 5+1+1=7
Is This Answer Correct ? | 3 Yes | 1 No |
Answer / sai krishna
Total races = 10
Firstly divide the horses into five groups
A,B,C,D and E
Those are 5 races. In these five races we get
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
Assume 6th race is between
A1 B1 C1 D1 E1
here we get one horse as winner.It is 6 th race
If A1 is winner in that position A2 will be placed and again raced. It is 7th race
LIke that another 3 horses to be placed to get top 5.So 3 races will occur.
So totally 5 + 1 + 1 + 1 + 1 + 1 = 10 races.
Is This Answer Correct ? | 0 Yes | 0 No |
Answer / kaustubh
Bragaadeesh Can u explain How can u achive this in 8 races.?
Is This Answer Correct ? | 3 Yes | 4 No |
Answer / dharshanah n
The above one was one easier answer. But there is one more efficient answer. It can be done in 7 races
First 5 rounds for 25 horses ( 5 sets A, B, C, D ,E) - Each set 5 horses.
you can eliminate the 4th and 5th position horses from all the 5 sets because they already have 3 horses before them. So now 10 horses eliminated 15 remaining. that is 3 horses each in the sets A , B, C , D, E
6th round - race all the fastest horses from the first 5 rounds. The winner will be the fastest of all the horses. So now we have found the top horse. The horses in the 4rth and 5th positions can be eliminated along with the remaining 2 in their respective sets . So now 6 are eliminated - 9 remaining of which 3 are from first set, 3 from second set and 3 from third set
Now you can eliminate the last two from 3rd set as they have more than 3 horses faster than them - so now 7 remaining - 3 from first set, 3 from second set, 1 from third set.
Similarly you can eliminate the last horse from the second set as it has more than three horses faster than it. So now 6 remaining - 3 from first set, 2 from second set, 1 from third set. The first horse from the first set is the fastest as proved earlier. So now we have to find the 2nd and 3rd position among five horses remaining - two from first set, one from second and third set each
7th round - race the five horses to find the 2nd top and 3rd top horse
Is This Answer Correct ? | 9 Yes | 11 No |
Answer / rajesh
I naming the groups as A, B, C, D, E and the position of the horses in the races as 1,2,3,4,5.
Horse that came first is denoted as A1, B1 etc.
Assume: A1, E1, C1, D1 and D2 are the horses that we have to find.
Then following would be the races
Race 1: All 25 horses in groupsof 5. A,B,C,D,E
Race 2: A1, B1, C1, D1, E1 - Say A1 is first - First horse
Race 3: A2, B1, C1, D1, E1 - Say E1 is first - Second horse
Race 4: A2, B1, C1, D1, E2 - Say C1 is first - Third horse
Race 5: A2, B1, C2, D1, E2 - Say D1 is first - Forth horse
Race 6: A2, B1, C2, D2, E2 - Say D2 is first - Fith horse
Assume: A1, A2, A3, A4, A5 are the horses that we have to find.
Then following would be the races.
Race 1: All 25 horses in groupsof 5. A,B,C,D,E
Race 2: A1, B1, C1, D1, E1 - Say A1 is first - First horse
Race 3: A2, B1, C1, D1, E1 - Say A2 is first - Second horse
Race 4: A3, B1, C1, D1, E1 - Say A3 is first - Third horse
Race 5: A4, B1, C1, D1, E1 - Say A4 is first - Forth horse
Race 6: A5, B1, C1, D1, E1 - Say A5 is first - Fifth horse.
So for picking up any 5 out of 25 we always need only 6 races.
Is This Answer Correct ? | 1 Yes | 5 No |
Answer / dharshanah n
Totally there are 25 horses.
First round:-
Race 5 horses. Take the top 3. So totally 5 horses raced
Second round:-
Race the top 3 from 1st round + another 2 . So now totally 5+2=7 horses raced. Take the top 3 from this race too
Third round:-
Race the top 3 from second round + another 2 . So now 7+3=10 horses raced
If you keep going like this , in every round you get the top 3 of pervious round and add 2 more horses and race them together
So the number of rounds would be
first - 5
second - 2
third- 2
fourth - 2
fifth - 2
sixth - 2
seventh - 2
eighth - 2
ninth - 2
tenth - 2
eleventh - 2
Totally all 25horses raced. So in the eleventh round , the top 3 horses will be the top 3 among them all
Is This Answer Correct ? | 2 Yes | 9 No |
Answer / tony
you guys are dumb! It only takes on race. Just use one track and race all the horses. The fastest horse wins.
Is This Answer Correct ? | 0 Yes | 10 No |
Answer / munesh
25 horses can be grouped in to A,B,C,D,E groups.
1st Round:
One race for each group. (5 races)
Total Races=5
2nd Round
1 race for the horses came first in 5 races.(1 race)
The horse came first in this race is ranked 1st can
be removed for further races
Select the group of the horse came 5th in this race and the
last 4 with in the group in the 1st round can be eliminated
as already there are 5 horses ahead of those.(4)
Select the group of the horse came 4th in this race and the
last 3 with in the group in the 1st round can be eliminated.
(3)
Select the group of the horse came 3rd in this race and the
last 2 with in the group in the 1st round can be eliminated.
(2)
Select the group of the horse came 2nd in this race and the
last 1 with in the group in the 1st round can be eliminated.
(1)
Total horses taken aside are
1 -------Horse came first in the 2nd round
4+3+2+1 -------Horses came last in the first round
Total horses taken aside are 11.
Remaining horses= 14.
Total Races=6.
3rd Round
Take 10 horses out of 14 horses.
2 races for 10 horses.
The horse came last in each race can be eliminated.
(2)
Total horses taken aside are 11+2=13.
Remaining horses= 12
Total Races=8.
4th Round
Take 10 horses out of 12 horses
2 races for 10 horses.
The horse came last in each race can be eliminated.
(2)
Total horses taken aside are 13+2=15.
Remaining horses= 10
Total Races=10.
5th Round
2 Races for 10 horses.
The horse came last in each race can be eliminated.(2)
Total horses taken aside are 15+2=17.
Remaining horses= 8
Total Races=12.
6th Round
Take 5 horses out of 8 horses.
1 race for 5 horses.
The horse came last in the race can be eliminated.
(1)
Total horses taken aside are 17+1=18.
Remaining horses= 7
Total Races=13.
7th Round
Take 5 horses out of 7 horses.
1 race for 5 horses.
The horse came last in the race can be eliminated.
(1)
Total horses taken aside are 18+1=19.
Remaining horses= 6
Total Races=14.
8th Round
Take 5 horses out of 6 horses
1 race for 5 horses.
The horse came last in the race can be eliminated.
(1)
Total horses taken aside are 19+1=20.
Remaining horses= 5
Total Races=15.
9th round
1 race for 5 horses.
The horse came last in the race can be eliminated.
(1)
Total horses taken aside are 20+1=21.
Remaining horses= 4
Total Races=16.
The horse came 1st in this race can be ranked 2nd.
The horse came 2nd in this race can be ranked 3rd.
The horse came 3rd in this race can be ranked 4th.
The horse came 4th in this race can be ranked 5th.
Is This Answer Correct ? | 7 Yes | 22 No |
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