A racehorse trainer has 25 horses and needs to find the fastest three horses in the string. He can only race five horses at any one time, because of space constraints. His additional problem is that he has no stopwatch, so cannot simply time the horses in their races.
What is the minimum number of races to determine the three fastest horses, and how do you achieve this?
This can be achieved in seven races, as follows:
Firstly, split the 25 horses into five groups of five, and then run each group of five in a race. Let us call these five races A, B, C, D, E and F, and the horses' positions in the races 1, 2, 3, 4 and 5. Thus the winner of race A is A1, third in race B is B3, etc.
The fastest horse must be one of A1, B1, C1, D1 and E1, and so the sixth race is between these five horses. The winner of this race is the fastest horse.
The second fastest horse is either the horse that came second in the sixth race or the horse that came second to the fastest horse in one of the first five races. So these two horse go into the seventh race.
The third fastest horse is either the horse that came third in the sixth race, the horse that came third behind the fastest horse in one of the first five races, or the horse that came second behind the second fastest horse in the sixth race in one of the first five races. So these three horses also go into the seventh race.
The seventh race will determine the second and third fastest horses overall.