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28march

Horse Race Problem Solution

Ok, so there are 25 horses and the race track only allows 5 horses to race at a given time. Given that there is no stop watch available your task is to determine the fastest 3 horses. Assume that each horses speed is constant in different races, what is the minimum number of races to determine the fastest 3?

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Solution:


Seven races.

1. Divide the horses into five groups

2. Do another race with the horses that stood first of each group. Obviously, the winner in this race is the fastest.

3. Do one more race of the horses which stood 2nd and 3rd of the group of the fastest horse, 2nd and 3rd of the race in step 2, and the horse that stood second from the group 2nd of the heat in step 2.

From step 2, we know the fastest horse, and from step 3 the second and third fastest horses.