Math Riddles

 
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Question: You have a bag with 'N' strings in it. You randomly grab two ends and tie them together until there are no more loose ends.

In the end, what is the expected number of loops (strings tied to their own end)?

Answer: 1 + 1/3 + 1/5 ... + 1/(2N-1).

Each time you tie two together the number of string ends available decreases by 2. The chance of grabbing a string and its end is 1/(2N-1).

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By srnejad

Question: If 1+9+8=1, what is 2+8+9?

Answer: 10, take the first letter of each spelled out number:

One+Nine+Eight= ONE
Two+Eight+Nine= TEN

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Rat maze (medium)

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Question: A rat is placed at the beginning of a maze and must make it to the end. There are four paths at the start that he has an equal chance of taking: path A takes 5 minutes and leads to the end, path B takes 8 minutes and leads to the start, path C takes 3 minutes and leads to the end, and path D takes 2 minutes and leads to the start.

What is the expected amount of time it will take for the rat to finish the maze?

Answer: 9 minutes.

Each path has an equal chance of occurring and if B or D are chosen they will just add 8 or 2 minutes to the time because the rat must restart the maze: time = (1/4)*5 + (1/4)*(8 + time) + (1/4)*(3) + (1/4)*(2 + time). Time = 9 minutes.

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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.

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Question: How can you make the following true by adding a single line: .9 = 1.

Note: ≠ is not the answer.

Answer: .9 = 1.

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