You have 25 horses. You need to find out which 3 are the fastest. Only 5 horses can race at a time. You are only given the order in which the horses finish the races, not their actual times. What is the fewest number of races you need to find the 3 fastest?
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ANSWER:
It can be done in 7 races.
Race 5 groups of 5 horses each. This eliminates the fourth and fifth horses in each race. Then race the first place finishers from each of your first five races. The top finisher here is the fastest horse. The horses that come in 4th and 5th can be eliminated and the rest of their horses in their initial 5 races can be eliminated.
For race 7: take the 2nd and 3rd place finishers in race 6, take the 2nd and 3rd place finishers from the initial race that had the fastest horse in it, and take the 2nd place finisher from the original race that had the 2nd fastest horse in it. The two fastest from this race and the fastest horse from race 6 are the fastest 3 horses.
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