What will be the minimum number of sprints required to find the fastest 3 runners out of 25 olympic runners, if one can race a maximum of 5 runners at a time?
What will be the minimum number of sprints required to find the fastest 3 runners out of 25 olympic runners, if one can race a maximum of 5 runners at a time?
The correct option is D 7
We need the first 5 sprints to ensure that each of the 25 runners complete a sprint once.
We are going to call these five sprints as preliminary sprints. From these 5 preliminary sprints, we get 5 winners.
The sixth sprint will be a sprint among these runners, who are the winners of the preliminary sprints. The winner of the sixth sprint is clearly the fastest runner. This way we have identified the fastest runner (runner A in the figure).
We need to identify the second and the third best runners. This is where the real trick in this problem lies.
There are five runners who are in contention for the second and the third best positions. These five runners are the following: The runners who finished second and third in the sixth sprint (the sprint of the best runners, runners B and C in the figure), the runners who finished second and third in the preliminary sprint in which the fastest runner finished best (runners F and H in the figure), and the runner who finished second in the preliminary sprint in which the runner (runner G in the figure), which came second in the sixth sprint, finished first.
These final five runners run the seventh sprint which will decide the second and the third best runners.
7
We need the first 5 sprints to ensure that each of the 25 runners complete a sprint once.
We are going to call these five sprints as preliminary sprints. From these 5 preliminary sprints, we get 5 winners.
The sixth sprint will be a sprint among these runners, who are the winners of the preliminary sprints. The winner of the sixth sprint is clearly the fastest runner. This way we have identified the fastest runner (runner A in the figure).
We need to identify the second and the third best runners. This is where the real trick in this problem lies.
There are five runners who are in contention for the second and the third best positions. These five runners are the following: The runners who finished second and third in the sixth sprint (the sprint of the best runners, runners B and C in the figure), the runners who finished second and third in the preliminary sprint in which the fastest runner finished best (runners F and H in the figure), and the runner who finished second in the preliminary sprint in which the runner (runner G in the figure), which came second in the sixth sprint, finished first.
These final five runners run the seventh sprint which will decide the second and the third best runners.
