Find three fastest horses

 Q We have 25 horses we need to find fastest 3 horses.We can race 5 horses together. How many minimum races we require?

We have 25 horses and can race only five. Let’s Divide horses in groups of five horses each. Now we have five groups and each group has five horses.

Next, let us name our groups as A, B, C, D, E with horses 

• 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

Next, let us suppose we have following winners from the 5 races of above groups.

• A1, A2, A3
• B1, B2,B3
• C1,C2,C3
• D1,D2,D3
• E1,E2,E3

Next, we will have a 6th race of all the winners, and we will have a fastest horse among all. So now we have the horse at first position which is A1.Let the outcome of the 6th race be as follows.

• A1,B1,C1

Since B1 lost to A1, also A2 lost to A1 so we need to have a race between 2 to find third fastest horse. Also for the 3rd fastest horse we have choices B2, A3, C1, A2,B1 since C1 , A3, B2 came in second and third positions have a race among these horse’s to find the second and third fastest horse. This will be our seventh and final race.

So we require 7 races in total.