So I saw this question and I figured I would take a shot at it...
"If you have 25 horses, each running at a consistent speed, what is the minimum number of races do you have to run in order to find the three fastest horses if you don't have a stop watch and can only race 5 horses at a time?"
I'll break this down with some visual aides to make the solution easier to see.
First group the horses into groups of 5 and race each group. I'll label these groups by letters. That is 5 races there to determine the fastest of each group.
Then race the fastest of each group in a race against each other. That is the 6th race.
(I the picture I arranged the groups slowest to fastest left to right and highlighted the 6th race group)
The winner of that race gives us the fastest horse but what if there is a faster horse in a the lettered groups than a winner of the other groups.
Just to make it easier in the describing things I'll just go with the assumption that the fastest horse of race 6 was in group A and it got slower each group. till group E.
I can eliminate all the horses in groups D and E as the fastest horses in those groups are slower than the 3 fastest horses in race 6.
Since I know that the winner from group A is the fastest overall I do not nee to re-race that one.
That leaves the 2nd and 3rd fastest in group A to try to find the 3 fastest horse. Then include the first and 2nd fastest in group B. And lastly include the fastest of group C. The first and second place of this race will be the second and third fastest horses in the herd of 25 horses.
So you need 7 races to find the 3 fastest.
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