# Rank the 25 horses puzzle

Rank the 25 horses puzzle

You are given 25 horses, you need to rank them on the basis of their speed. They all run at the same speed everytime. Given that you can run only 5 of them at a time.

1: What do you think how many races to will it take to rank all of them from 1 to 25

2: how many races will it take to find out the fastest one?

3: how many races will it take find the top 5 fastest?—

tell me if im wrong. 25 horses can be arranged in order in 25! ways

and the actual ranking of the horses can be any 1 of these 25!

now , in one race , we are able to determine the relative ranking of 5 horses. they could have occurred in any order

so , after 1 race , we are able to divide all the 25! arrangements into 5! classes , and we know which class contains the actual order.

so , number of arrangements reduce to 25! / 5!

the next race will again give us 5! classes provided we choose our horses to race in such a way that we always learn new information.

so , i think the number of races required should be log( 25!) to the base 5!

or : ln (25!) / ln( 5!)

any ideas as to what extent this argument seems valid ?

Divide into 5 groups(h1-h5). Race them. u will get first 5 horses(for ex. h11,h21,h31,h41,h51). race them. u will get fastest one in tat(let us assume h11 is 1st, h21 is 2nd, h31 is 3rd). leave all horses those came in 4th and 5th places. now we need only two. we have now h12, h13, h22, h23, h32, h33. so, take the h21 & h31 (those are 2nd & 3rd in 6th race) and h12, h13, h21. Race them. which ever come first and second is the 2nd and 3rd fastest respectively.

I m confused, when they all run at the same speed every time, how can then it be found out which runs faster!

u are getting it wrong.. they run at their own individual speed which is constant through different runs

But each horse has a different speed.

For example :

horse 1 : speed A km/h everytime he runs

horse 2 : B km/h

horse 3 : C kmph …… and so on

where A,B,C….. may or may not be equal

1. 29

2. 6

3. 5

Let me see the answers now!!

a cheeky answer could be measure time for each horse and get it compelted in 5 races

🙂

I think ans shud be:

1. 18

2. 6

3. 8

Hey, I could fine topper in 6 races, all ranks I could find in 26 races, and top five in 10 races… Tell if it’s right?