What is the minimum number of races required to pick the
best three horses from 25 horses if each race has maximum of
5 horses?
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Answer Posted / alok chandra
I m sorry for the wrong answer I posted earlier. So the
answer is definitely not 11. At the same time Anjali, it is
not even 6. It would be wrong to assume that the horses
which came second and third in the first set of five races
cannot come second and third overall. So let me provide the
correct answer now.
We conduct the 5 races. Choose the top 3 from all the 5
races. Now conduct a race of the top horses of all the
races. Choose the top 3 of the last race. They could
probably be the top 3 of the horses. We discard the horses
which came 4th and 5th along with all the horses of their
group. Let me explain it pictorially.
The top represents the standing of the 6th race. The race
among the top horses of each group. Now we can discard all
the horses which came 4th and 5th in their respective
groups. So we are left with the top 3 horses of each
group.Now consider the horses which came 4th and 5th in the
6th race. They cannot fall in the top 3. Nor can any of
their group members. So we get rid of all the remaining
horses of group 4 and group 5. So we are left with 9 horses
to choose from.
Now consider the horse which came 3rd in the 6th race and
its group memebers. We call it group 3. Now the 2nd and 3rd
horses of group 3 cannot come even 3rd overall. Hence they
can be discarded. SO we consider only the horse which came
first(1 selected for the final race). Consider group 2. We
can discard the horse which came 3rd in the group. And we
select the horses which came 1st and 2nd( 1+2 selected for
the final race). Similarly we consider all the top three
horses from group 1. But we can safely ignore the horse
which came first overall.( 1+2+2 selected for the final
race). So we have 5 horses to choose the best two from. We
already have the horse which came 1st overall. No need to
put that in the race. So the minimum number of races
required is 7 and 11 or 6.
1 2 3 4 5
1 1 1 1 1
2 2 2 2 2
3 3 3 3 3
4 4 4 4 4
5 5 5 5 5
| Is This Answer Correct ? | 20 Yes | 12 No |
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