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).
Question: You come across a Native American tribe and the leader wants to kill. He tells you, you can say your final words. If you tell the truth you will be burned at the stake. If you lie he will shoot you. What do you say to ensure survival?
Answer: You will shoot me