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 into 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 the 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 the 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 gives us the second and third fastest horse after A.
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