There are 5 racing tracks and 25 horses At a time you can conduct race for 5 horses in the five available tracks What will be the minimum number of trials needed to find out the ultimate winner run?

Answer 1

Let's take an assumption, each horse runs at uniform speed every time. They all have different but fixed speed tag.

Step 1) Divide the 25 horses into 5 groups. Each group will have 5 horses each.

Step 2) Conduct 5 races for the 5 groups.

Step 3) Conduct an another race with each group winners. (i.e. Fastest from Group 1, Fastest from Group 2, ... , and Fastest from Group 5)

Step 4) Choose the winner from the Step 3. That will be fastest horse. (So, it needs only 6 races to find out the fastest horse of all the 25 horses)

Additionally,

Step 5) Name the horses as below:

{a1,a2,..., a5}--> For the group which has the fastest horse after Step 3 (6th Race)

{b1,b2,...,b5}---> For the group which has the 2nd fastest horse after Step 3

{c1,c2,...,c5}----> For the group which has the 3rd fastest horse after Step 3

{d1,d2,...,d5}---> For the group which has the 4th fastest horse after Step 3

{e1,e2,...,e5}---> For the group which has the 5th fastest horse after Step 3

Where according to their speed, a1>a2>..>a5; b1>b2>..>b5; c1>c2>..>c5; d1>d2>..>d5 and e1>e2>..>e5, also, a1>b1>c1>d1>e1, but not necessarily, b1>a2, c1>b2 etc. [Clearly a1 is the fastest horse]

Step 6) Conduct a race with a2, a3, b1, b2 and c1 to find out the 2nd fastest and 3rd fastest of all the 25 horses.

So, we need to conduct only 7 races to find out the top 3 fastest horses!