# Fastest Horse Puzzle

## Find the Fastest Horse Puzzle

Solve the Fastest Horse Puzzle here.
There are 25 horses, among which you have to find the fastest 3 horses. At one time you can conduct a race with five horses, but you have no way to time them.

What is the least number of races required to find the three fastest horses?  ## Find the Fastest Horse

There are 25 horses, among which you have to find the fastest 3 horses. At one time you can conduct a race with five horses, but you have no way to time them. What is the least number of races required to find the three fastest horses?

## Solution

The minimum number of races we can conduct is 7.

#### Step 1:-

• First we randomly group the 25 horses in 5 groups  and conduct a race for each group. (in total 5 races are conducted here)
• Let the winners of the five races be A, B, C, D and E respectively.  #### Step 2:-

• From the above 5 races, we take the winners of each race and conduct a 6th race amongst them.
• The winner of this race is the fastest horse among the 25.
• Say horse A wins this race.

#### Step 3:-

• Conduct a 7th race among B, C, the horses that placed second and third in A’s group, and the horse that placed second in B’s group.
• In this race the horses that will place first and second, are the second and third fastest horses among the 25. #### Inference:-

• From the first 5 races we get 5 horses.
• From the 6th race between the 5 horses, we get the fastest horse.
• Now, we select the probable fastest horse by such:
• since we assume A to be the fastest horse, w can see that, the horses that came second and third in A’s first race have the potential to beat B and C in speed.
• Similarly the horse that came second in B’s race, has the potential to beat C in speed.
• Therefore the race among the last five horses give us the second and third fastest horse after A.

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