Q3. There are 5 lanes on a race track. One needs to find out the 3 fastest horses among the total of 25. Determine the minimum number of races to be conducted in order to find the fastest three cars. | Eklavya Online

Q3. There are 5 lanes on a race track. One needs to find out the 3 fastest horses among the total of 25. Determine the minimum number of races to be conducted in order to find the fastest three cars.

Now, you can start solving the problem by considering the number of cars racing. Since there are 25 cars racing with 5 lanes, there would be initially 5 races conducted, with each group having 5 cars. Next, a sixth race will be conducted between the winners of the first 5 races to determine the 3 fastest cars(let us say X1, Y1, and Z1).

Now, suppose X1 is the fastest among the three, then that means A1 is the fastest car among the 25 cars racing. But the question is how to find the 2nd and the 3rd fastest? We cannot assume that Y1 and Z1 are 2nd and 3rd since it may happen that the rest cars from the group of X1s’ cars could be faster than Y1 and Z1. So, to determine this a 7th race is conducted between cars Y1, Z1, and the cars from X1’s group(X2, X3), and the second car from Y1’s group Y2.

So, the cars that finish the 1st and 2nd is the 7th race are actually the 2nd and the 3rd fastest cars among all cars.