Finding Horses For Courses

There are 25 horses among which you need to find out the fastest 3 horses. You can conduct race among at most 5 to find out their relative speed. At no point you can find out the actual speed of the horse in a race. Find out how many races are required to get the top 3 horses. 

Click here for logical answer! 

Source 

Races To Find Horses For Courses

What was the task? 

First we need to make 5 groups of 5 horses each. Let's put each group on race & note down rank of each horse & corresponding group. This requires 5 races.

Taking out winner of each group aside. In a next race, winner of each group run & fastest winner is found. Total 6 races are conducted till now.

Now let's name group of fastest winner as A, second fastest winner as B & so on as C, D, E. Each horse would be identified by it's group name & rank as Group.Rank. For example, B.3 means the horse that came 3rd in group B & D.5 is horse that came last in group D.

For next race, we can eliminate few. Let's remind we have to find 3 fastest horses. Now let's logically eliminate few horses. Those horse for which we are sure that at least other 3 are faster than those will be eliminated.

1. Now A.1, B.1 & C.1 are faster than D.1 & E.1. So D.1 & E.1 & respective groups eliminated straightaway.

2. The C.2 (& other members of C) eliminated as A.1, B.1, C.1 are faster ones.

3. The B.3 (& other member of B) eliminated as at least A.1, B.1, B.2 are faster ones.

4. Similarly, A.4 & A.5 have 3 horses ahead as A.1, A.2 & A.3.

5. A.1 is already proved it's fastest among all, so no need to re race by taking it.