There are 25 horses. We have to find out the fastest 3 horses. In one race maximum 5 horses can run. How many such races are required in minimum to get the result ?

The Answer is 7 races. Lets discuss each race in detail.

**Races 1 to 5**

We can first go for 5 races by taking 5 horses each and get top horse in each race.

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

Here A1 finished 1st in first race, A2 finished 2nd and same way for others.

**Race 6**

Now lets take fastest horse in each race and then have one race between them, so have the race between A1, B1, C1, D1, E1

Take top 3 from the race. Lets say A1 > C1 > D1 comes in top three.

B1 and E1 came in last 2 positions in the race and from this we can conclude that all horses in B and E group are slower than A1,C1 and D1

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

Also horses D2,D3,D4,D5 cannot come on top 3 positions as these 4 horses are slower than D1 and D1 finished 3rd in the race.

A4,A5,C3,C4,C5 also cannot come on top 3 positions.

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

**Race 7**

A1 > A2 > A3

C1 > C2

D1

Now we need to find second and third fastest horses

They can be from A2,A3,C1,C2,D1. So we will have one more race among them to determine second and third position.

Thus a total of minimum 7 races are needed to find top 3 horses from 25 horses.

I thought the minimum number of races is 5. I would just write down the time it took each horse to finish each race, then compare the times.

Please put in the explanation for why A4 A5 C3 etc are eliminated. It took me some time to figure that out

7 races are required to get the top 3

One race

One race