Answer / dileep p g

Answer : 7 races

PERFECT SOLUTION is already there from Jason Mitchell !!!

Detailed Explanation
--------------------
First 5 races => all 25 different horses
Race 6 => 5 winners from 1st 5 races

let r1,r2,r3,r4,r5 represent the 1st 5 races sorted
according to the results of race 6.

Race 6 results
---------------
1st : winner of r1
2nd : winner of r2
.......
.......
5th : winner of r5

Position after 6 races:
-----------------------
r1 r2 r3 r4 r5

1a 1b 1c 1d 1e (1st places)
2a 2b 2c 2d 2e (2nd places)
3a 3b 3c 3d 3e (3rd places)

Race 7:
-------
1a is the overall champion => Race 7 is to decide who comes
overall 2nd & 3rd.
To decide the participants of race 7, we start elimination

1a obviously cant b 2nd or 3rd as it is 1st !!
1d & 1e are not good enough to be 2nd or 3rd even in Race 6

proceeding along similar lines, we can see that

2nd can be 1b, 2a or 3a
3rd can be 2a, 3a, 1b, 2b or 1c

=> a total of 5 possibile contenders - 2a, 3a, 1b, 2b, 1c

=> run Race 7 with these horses

RESULT
------
overall 1nd = winner of Race 6
overall 2nd = winner of Race 7
overall 3rd = 2nd in Race 7

_________________________________
=================================

Answer / pravalika

answer is 9.

Answer / bharath.p

when we calculate the race according to the 'TIME' , then
spilt it to 5 groups and contect the race then calculate
time of arrivial of each hourse. Then we easily select the
BEST 5 OF 25

Answer / viral avalani

10 races are needed. as in 1st 5 races we ill identify best
horse in each group. than make race between all best 5
horses. that is 6th race. now we have no.1 race. we need to
find no. 2,3,4 &5 horse. for that from group of no.1 horse
select second horse. makes race b/w that second horse and
remaining best horse of 4 groups. from which we will have
2nd best horse. this will be 7th race. soe now at 8th race
in same way will give 3rd horse. 9th will give 4th best and
10th will give 5th best.

Answer / jayesh pakhale

We cannot choose best five. Answer is not possible. Because
we need to choose best 5 out of 25 not an accumulation of
best 5 one from each group. Why answe is not possible: Here
from the 1st group we cannot select any one or we cannot
select all 5, becasue this group may be fastest group from
all 25 hourses or may be a slowest group or may be a
intermideate. We don't know from this first group how may
houses are best among 25.

Answer / jayasree

it is 26.
divide 25 into 5 groups and select one from each group and
conduct race among them and select one ( first fastest one).
and the remaining 4 horses are named as A1, A2,A3,A4.
now divide 20 horses into 4 groups and conduct race
between them then select one from each group. now conduct
race between these 4 horses + A1 and select one ( second
fastest one).
now divide 20 horses into 4 groups and conduct race
between them then select one from each group & conduct race
between these 4 horses + A2 and select one ( third fastest one).
likewise select other two fastest horses. totally five

Answer / rajendra sikaria

First randomly select five horses and grade them by racing
(1,2,3,4,5). Now select four horses from the remaining
twenty and add graded 5 of the first race. Now run the
second race and grade them. If grade is 5,6,7,8,9 five is
selected and other four horses stand eliminated. If grade is
4A,5,7,8,9 the horse graded 4A is selected and rest of the
four horses eliminated. If grade is 4A,4B,5,8,9 the horse
graded 4A,4B is selected and other three horses eliminated.
and so on. Since further grouping is now depends on the
outcome of this race we can not have a unique answer.
Maximum selection from this race could be four horses i.e.
4A,4B,4C,4D where 5 is eliminated. (i.e from each race now
onwards their will be at least one elimination) Now we have
third race consisting of one of the combination
4,4D,10,11,12 or 4,4C,10,11,12,13 or 4,4B,10,11,12 or
4,4A,10,11,12 or 5,10,11,12,13. Each combination will have
five possibility of with respect to 4 or 5. The last
combination is same as second race and we will not discuss.
The first option if result is 4,4D,10,11,12 the horse 4 is
selected and rest eliminated. If the result is
4,4DA,4D,11,12 the horse 4 and 4DA is selected and rest
three is eliminated. And so on.

Answer / tarun

i wud like to correct my ans above
the ans is 29
as to find d last best horse only 5 races are required
so total races=6*4+5=29
to find 1st best horse
total=25
eleminated horse=4+4+4+4+4+4=24
total races=6

to find 2nd best horse
total=24
eleminated horse=4+4+4+4+4+3=23
total races=6


to find 3rd best horse
total=23
eleminated horse=4+4+4+4+4+2=22
total races=6


to find 4th best horse
total=22
eleminated horse=4+4+4+4+4+1=21
total races=6


to find 5th best horse
total=21
eleminated horse=4+4+4+4+4=20
total races=5

Answer / sunil902

6

Answer / jayasree

it is 10.
first divide 25 horses into 5 of each group. then conduct
the race for each group and select best two of each. now 10
horses will be there. now conduct the race among 10 horses
and select best five from them.

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