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28march

Horse Race Problem

Ok, so there are 25 horses and the race track only allows 5 horses to race at a given time. Given that there is no stop watch available your task is to determine the fastest 3 horses. Assume that each horses speed is constant in different races, what is the minimum number of races to determine the fastest 3?

1. 6
arrange arrange 5 races for all 25, 5 distinct in eacg race.
pick up winning horses for 5 races and make these 5 winners in 6th race and pickup top 3
;)

2. 6 races are required ...

3. 5+3+2+1+1=12
============
divide 5 grp of 5 horses first. and then select top 3 from each race (to make sure we don't loosed topmost 3, our final winner).
[5 races done]
now we have 15 horse. divide again into 3 gro of 5 each. and again select top 3.
[3 more races done]
now we have 9 horse. Now run 5 and 4. select top 3.
[2 more races done]
now we have 6. run any 5. select top 3.
[1 more race is done]
now we have 4 horses. run them and select top 3.
[1 more race is done]

The key here is to keep the search space to only those horses which can be the top 3 horses.
Initially all 25 can be the required horses. So divide among groups of 5 and perform the race. Let the result 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

Now perform the race for winners of each group to reduce the search space. Let the result be:

A1 B1 C1 D1 E1
This implies A1 is the best. Also, the search space for top 3 horses reduces to:

A1 A2 A3 B1 B2 C1

Now conduct the last race for A2 A3 B1 B2 C1. Select top 2 from this race which will be overall runner-up and second runner-up.

Total race count = 7.

5. Agree with Shishir. That's the solution I had worked out as well. 6 races wouldn't give the correct answer.

6. This is a really nice problem. Indeed, 7 is the answer.

7. 7
make goup of 5 each, take the winner of all five gp hav a race, therefore no of race = 6(5+1)
now from the winner take 2nd n third horse n 2nd hrs frm horse gp which came 2nd in fifth race..now the final race of these 5 will gave the top 3 horse.. :)

8. i think the answer is 6
5 races for distinguishing the faster horse in each group and 1 race for distinguishing the fastest 3 so the answer is 6

9. we have 25 horses.at first we have (5) group with 5 member.each race have 3 winner.[we choose 3 winners in each race, because maybe these are the 3 fastest horses!]
now we have 5*3=15 horses. now we have (3) group with 5 member... so at the end we have 3*3=9 horses.
now we must have (2) group with 5 and 4 member... so at end we have 3*2=6 horses.
now (1) race for any 5 and choose best 3.
at the last (one) race with these 3 and the rest one (4 horse) we choose 3 best!!

if u add the nubers in parantese we have:
5+3+2+1+1=12

10. 7 is the best option
12 is a waste

11. 11 would be minimum number of race to depict first 3 fastest horses.

12. only 6 will be needed divide into group of 5 horses . choose fastest horse from each group and race between them and choose top 3 horse ....

13. Now perform the race for winners of each group to reduce the search space. Let the result be:

A1 B1 C1 D1 E1
This implies A1 is the best. Also, the search space for top 3 horses reduces to:

How did u decide A1 is best, when u don't have stopwatch to measure the time .....

14. only 7 race

15. wow, at first also thought of 6 races
but after i read the explanation of 7 races, it all make sense...wow...complicated simple things

16. The answer is 11... the answer 6 or 7 is horse shit.... you dont have anystop watch and so you dont know if the fastest horse of second race is faster than the 2nd fastest horse of 1st race.....

Races shall be like this
25 horses, 5 races - pick 15 fastest horses...
15 horses, 3 races - pick 9 fastest horses....
9 horses, 1 race and pick three fatest and other 4 who havnt been put in race... total 7
7 horses, 1 race and two left... pick fastest 3 and plus two total 5...
5 horses, 1 race --- you are done....

total races - 5+3+1+1+1 = 11....

17. I disagree with you all. The answer definately is NOT 7.
Why did u assume (for example) that A2 or B2 is faster than E1, D1or C1? How did u come up with this conclusion????