Not the Fool's problem of the day,

There are 25 horses. At a time only 5 horse can run in the single race. How many minimum races are required to find the top 3 fastest horses? Please explain your answer.

PS: Not much difficult; I am sure that any Fool can do it in a jiffy.

Enjoy!

Question

Not the Fool's problem of the day,

There are 25 horses. At a time only 5 horse can run in the single race. How many minimum races are required to find the top 3 fastest horses? Please explain your answer.

PS: Not much difficult; I am sure that any Fool can do it in a jiffy.

Enjoy!

anonymous · Answer

maybe:
$$NR=C_{25}^{5}$$

anonymous · Answer

NR=number of races

anonymous · Answer

$  \binom{5} {25} = 0 $and $\binom{25}{5}$ is not the right answer.

anonymous · Answer

ups, my bad.

anonymous · Answer

but this way each horce would race with every other.

anonymous · Answer

all possible combinations

anonymous · Answer

Minimum no of races = 6

anonymous · Answer

Can you expalin your answer Raghu?

anonymous · Answer

In a single race 5 can run so in total we can have 5 separate races and one winner from each so in the end we have 5 winners which will race again from where we can get the top 3  fastest horses... Hope it helps...

callisto · Answer

This question is quite tricky.. @raghu04 gives the no. of min. races, but it just asks how many races. What if the top 3 fastest horses are in the same group?

anonymous · Answer

@Callisto U have a  good point.... but then we can proceed like this : in each of 5 races we can eliminate last two...so in total we have 15 horses left (3 from each race).. now again 3 races can be done and top 3 can be chosen so we have 9 horses left...again two races possible  Top 3 from each race will give six eligible horses however 1st from each cannot be loser so we have Top 2 fastest horses and last 4 horses can be raced again to have the last fastest horse... so intotal we can have: 11 races however i think if more brain can be involved in this many races can be clubbed.

callisto · Answer

Now, you have a point :)

anonymous · Answer

@Callisto :-)

callisto · Answer

'' 1st from each cannot be loser'' :D

anonymous · Answer

the problem is that the horse that comes last in one race, may still be fastest of all the horses that rase in other race. @raghu04

anonymous · Answer

so your method will not work

callisto · Answer

But we just select the top 3..
Assume the top 3 fastest horses are all in group 1.
There are 5 horses in group 1, the last in group 1 can't be the top 3 (among the 25 horses)!

hba · Answer

To find the fastest we have to track time.

callisto · Answer

lol, time of the race isn't recorded

hba · Answer

^ How do you say that ?