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: Horse race.  ( 3987 )
« : September 07, 2007, 11:11:29 AM From Sudeep»

Horse race.

There.. are 25 horses.. and only 5 tracks. so only 5 horses can run the race at a time. How many minimum no of races should be conducted to find the 3 best horses..?

note: the answer is surely not 5;

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« #1 : September 07, 2007, 02:26:20 PM From Poonam»

Take 3 top horses from each race.
Hence after first 5 event, select 15.
3 races among the 15. Select 9.
2 races among the 9. Select 6.
2 races again with the best 3 and the remaining one.

Totally 12 races.

I am sure there will be a shorter way.
« #2 : September 07, 2007, 04:19:32 PM From PSM»

it can be done in small way........ 8)
tht is 9 races

Take 3 top horses from each race - 5 races
now take all the horses those were at no. 3 in the races....
and have their one race...- and select the winner out of them......
select winner only because two better than tht horse are already their and we need 3 horses........

now have race between the horses those were at 2nd place..select top 2 out of them....
because one is already better than them.....

now have a race between al the horses those were at 1st position and take best three from it .....

total no. race till now=5+3=8

now we have 6 horses and in which is the best we know....it is the one tht topped the race between all the horses those were 1st in the first five matches..

so he is the winner now remain 5 horses...have a race between them and take the best 2...
in this way we get best 3 horses...
and no. of races = 8+1=9  ;)

well reply if answer better than this is their
and also i'm not gud at explaining so srry  :-\
« #3 : September 07, 2007, 11:10:42 PM From Shrinidhi»

Race 1: H11 H12 H13 H14 H15

Race 2: H21 H22 H23 H24 H25

Race 3: H31 H32 H33 H34 H35

Race 4: H41 H42 H43 H44 H45

Race 5: H51 H52 H53 H54 H55

Now assume the blue ones are the winners of their respective races.

To decide the first winner, lets have a race among the top 5.

Race 6: H11 H21 H31 H41 H51

Assume the first 3 are top 3 in this race in that order. So H11 is the clear first winner.

Now, contenders for the second and third place are

H21 H31 H12 H13 H22

The reason for this is as follows. Obviously, the second and third best horses of race 6 are the among the contenders. Since H11 is the first winner, H12 and H13 are contenders. Since H21 is the second best in race 6, H22 is also a contender for the 3rd place. Now, since H31 is a contender for 3rd place no one else from race 3 is a contender except H31.

Race 7: H21 H31 H12 H13 H22

The top 2 of the race 7 decides the second and the third best horses.
« #4 : September 07, 2007, 11:14:26 PM From PSM»

ya u are right ....shrinidhi...
i did the same but did it with quite long way....
« #5 : September 10, 2007, 05:05:55 PM From Sudeep»

ya... he is right!!
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