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By lemontart

Question: A very famous chemist was found murdered in his kitchen today. The police have narrowed it down to six suspects. They know it was a two man job. Their names: Felice, Maxwell, Archibald, Nicolas, Jordan, and Xavier.

A note was also found with the body: '26-3-58/28-27-57-16'.

Who are the killers?

Answer: Felice and Nicholas are the murderers. The numbers correspond to atomic numbers on the periodic table of elements: 'Fe-Li-Ce/Ni-Co-La-S'.

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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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Question: Three gods A, B, and C are called, in no particular order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer all questions in their own language, in which the words for yes and no are da and ja, in some order. You do not know which word means which.

What three questions can you ask?

Answer: A possible solution is:

Q1: Ask god B, "If I asked you 'Is A Random?', would you say ja?". If B answers ja, either B is Random (and is answering randomly), or B is not Random and the answer indicates that A is indeed Random. Either way, C is not Random. If B answers da, either B is Random (and is answering randomly), or B is not Random and the answer indicates that A is not Random. Either way, you know the identity of a god who is not Random.

Q2: Go to the god who was identified as not being Random by the previous question (either A or C), and ask him: "If I asked you 'Are you False?', would you say ja?". Since he is not Random, an answer of da indicates that he is True and an answer of ja indicates that he is False.

Q3: Ask the same god the question: "If I asked you 'Is B Random?', would you say ja?". If the answer is ja, B is Random; if the answer is da, the god you have not yet spoken to is Random. The remaining god can be identified by elimination.

For more information about the answer visit the following Wikipedia page.

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Question: There is a party of 100 high-powered politicians. All of them are either honest or liars. You walk in knowing two things:

- At least one of them is honest.
- If you take any two politicians, at least one of them is a liar.

From this information, can you know how many are liars and how many are honest?

Answer: Yes, from the information you know 1 is honest and 99 are liars.

One of them is honest satisfying the first piece of information. Then if you take the honest man and any other politician, the other politician must be a liar to satisfy the second piece of information, 'If you take any two politicians, at least one of them is a liar.' So 99 are liars.

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Question: There are 1600 people sitting around a circular table. The first person (person 1) has a sword and kills the second person then hands it to the next alive person (in this case person 3). Person 3 stabs person 4 and gives the sword to person 5. This goes on until person 1499 kills person 1500. Then person 1 kills person 3 and so on. This is repeated until there is only a single person remaining.

Who remains in the end?

Answer: Person 1153.

If you have any number of people equal to a power of 2 (2, 4, 8, etc.) then the first person will be the last remaining. The closest power of 2 to 1600 is 1024 (210). So the first person to go of the 1600 when there is 1024 people left will be the last person remaining. 1600 - 1024 = 576. 576 * 2 = 1152. Person 1152 will be the 576th person killed and person 1153 will be the first person to go of the remaining 1024 people.

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