Question: The London Racetrack needs to submit its 3 fastest horses to the Kentucky Derby out of 25 horses. However, all of their information was lost and they don't know any of the horse's times. Similarly, they all look identical so they can't remember who's fastest.
They can only race 5 horses at once, so what is the fewest number of races they can conduct to find the 3 fastest horses?
Answer: 7 races are required.
First you divide the 25 horses into 5 groups of 5. You conduct the 5 races and take all of the fastest horses in those races and have a race with them, giving you the fastest horse. Then you take the remaining 24 horses (excluding the fastest) and remove the 4th and 5th horses in the first set of 5 races (since they definitely have 3 horses faster than them), leaving you with 14 horses. Next you can remove all of the horses that were beat in the preliminary race by the horses that got 4th and 5th in the championship race, leaving you with 8 horses. Finally, you can remove the horses that remain that lost to the 3rd place horse in the final race in the preliminary race and the horse that got 3rd in the preliminary to the horse that got 2nd in the championship race, leaving you with 5 horses.
You can then run a final race where the 1st and 2nd place horses are the 2nd and 3rd fastest. Then you know the 3 fastest horses.
Question: A man is found dead on a Sunday morning. His wife calls the police immediately. The police question the wife and staff. The wife said she was asleep, the cook said he was cooking breakfast, the gardener said she was picking vegetables, the butler said he was cleaning the closet, and the maid said she was getting the post. The police immediately arrested the murderer.Who was the murderer?
Answer: The maid because there's no post on Sundays.