# Puzzles and riddles



## Nightriser (Nov 8, 2008)

Some puzzles for you all: 










I'm still working on that problem. 

While I'm working on that, I'll give you an easier one. 
1.) Say that the black hat's score is n. How many different combinations of mathematicians and physicists could he have sniped? (Note, I used "combinations," not "permutations," so order does not matter.) 
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(From Wikipedia)
2.) Three gods A, B, and C are called, in some 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. 
Some clarifications are offered:

It could be that some god gets asked more than one question (and hence that some god is not asked any question at all). 
What the second question is, and to which god it is put, may depend on the answer to the first question. (And of course similarly for the third question.) 
Whether Random speaks truly or not should be thought of as depending on the flip of a coin hidden in his brain: if the coin comes down heads, he speaks truly; if tails, falsely. 
Random will answer 'da' or 'ja' when asked any yes-no question.
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3.) Now I wish to extend the puzzle and make it even harder! Then I'll demonstrate how to solve it.

* Suppose there are 2N+1 gods. Each is one of the following three types:
o A truth teller: they always answer questions truthfully
o A liar: they always answer questions falsely
o A randomer: the answer they give to any question is entirely arbitrary
* You don't know how many of each type there are, except that there are no more than N randomers.
* Each god speaks one of the two languages in L, but they might not all share the same language. 


* There is a fork in the road. One path leads to the castle. Your task is to find the way to the castle in 2N questions.

(The "castle" question is arbitrary. It's just a question you don't originally know the answer to.) 
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3.) Given are X and Y, two integers, greater than 1, are not equal, and their sum is less than 100. S and P are two mathematicians; S is given the sum X+Y, and P is given the product X*Y of these numbers.

* P says "I cannot find these numbers."
* S says "I was sure that you could not find them."
* P says "Then, I found these numbers."
* S says "If you could find them, then I also found them."

What are these numbers?
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4.) A man comes across a hungry cannibal tribe. They give him a deal. If what he says is true, they will boil him in water. If what he says is false, they will cook him in oil. What can he say to get out of the situation?
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5.) Finally, here's another that looks interesting. It's a self-referential puzzle. 
Drunk Men Work Here

These are not necessarily related, they are just puzzles I like.


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## de l'eau salée (Nov 10, 2008)

LMAO that comic was hilarious.

My brain exploded reading the rest of it, but I'll attempt number 4. 
4.) Answer: The man could run away. Yes yes?


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## Nightriser (Nov 8, 2008)

He could, but I forgot to mention that he was tied up. Also, the question is "What can he say to get out of the situation?"


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## de l'eau salée (Nov 10, 2008)

Oh, oops!
Hmmm, he could say "I'm actually an alien in disguise." Eh?


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## Nightriser (Nov 8, 2008)

Hehe, not quite what I'm looking for. Who knows, it might work on them, but they are pretty hungry.


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## de l'eau salée (Nov 10, 2008)

Aw  Okay..hmmm....

"Inside of me is a heat-activated bomb. If my body reaches a certain temperature, the bomb will detonate, obliterating everything within a half-mile of me. The choice is yours."


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## Nightriser (Nov 8, 2008)

Then they can cut him open to verify the situation. If he does have the bomb in him, the statement is true, so he'll be boiled in water. If he doesn't, then the statement is false and he'll be fried in oil.


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## EaRMo (Nov 10, 2008)

For riddle four, I assume that saying nothing isn't an option... It seems that the man's only option is to say something that is neither true nor false, or something otherwise unverifiable. Something about the existence of God, perhaps? Or he could say something ungrammatical, something that asserts nothing. "Sentence fragment." Or the man could ask a question. "Is the sky green?" In doing so, the man would indeed "say" something, but not assert a truth nor a falsehood. But given the complex nature of your other puzzles/riddles, these answers seem far too simplistic to be correct.

Of course, the man could say anything--true, false, or of indeterminate veracity--and he would indeed be "out of the situation"--likely boiled or cooked, but "out of the situation" nonetheless. I doubt that that's what you were going for, however.

How advanced is this tribe of cannibals? When I think of a "tribe of cannibals", a sophisticated information-gathering network isn't my first association. That would be pretty low on my list, actually. Are they still hung up on inductive reasoning? What's their verification process? How reliable is it? What is their definition of "truth"? How do these cannibals feel about "reasonable doubt"? I'd like to know more about these cannibals and their ways. They seem like fascinating folk.


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## εmptε (Nov 20, 2008)

*Couldn't he just say a word? The riddle never implied that he needed to ask a question but the word also needs to be neither true nor false. I'd personally say "Nothing".*


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## εmptε (Nov 20, 2008)

*Oh shit! What if he actually doesn't say anything?*


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## Nightriser (Nov 8, 2008)

Sigh. Have none of you heard of "coercive logic?" Basically, coercive logic means that you are in a situation like #4, but you say something so that, if the one presenting the problem abides by his word, he has no choice but to let one go. Hm, that wasn't very clear. 

Say something that will present a paradox for that specific situation. In other words, find a statement that if it is true, then it is false, and vice versa. I would give you an example, but that would obviously give it away even worse than this hint I've given you.


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## εmptε (Nov 20, 2008)

*or ... I'm correct and then he should just say nothing. They made the deal that if he gives them a statement that is true they would kill him, and if they gave a statement that is false they would kill him. They never said anything about him not giving a statement.

However, by your logic it should be something like "I'm not going to say anything." He said something but then he doesn't say anything. 
*


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## Nightriser (Nov 8, 2008)

Haha, EaRMo, you sound like another INFP I know. Still, your responses are plausible. I should have specified that the statement should be an assertion with a truth value. I'll give you bonus points. 

Lykos, if I were a hungry cannibal, I would give the traveler a deadline by which to reply; otherwise, I'll cook him however I want him to be cooked. Still, your solution is a possibility. 

It's just that neither of you have given the answer I was looking for (and that's partly my fault).


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## Nightriser (Nov 8, 2008)

"However, by your logic it should be something like "I'm not going to say anything." He said something but then he doesn't say anything."

Saying "I'm not going to say anything" is a false statement. So he gets cooked in oil. Perhaps that's another clue....I'm surprised.


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## Nightriser (Nov 8, 2008)

You know, there are actually potentially an infinite number of statements that could get the man out of the situation. I think pretty much any paradoxical statement would do.


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## εmptε (Nov 20, 2008)

*What if he asked them "What if I say something true that's false?"*


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## Nightriser (Nov 8, 2008)

That falls under the category of an expression (I think that's what it's called in Boolean logic). It has no truth value, it is simply a question, like what EaRMo suggested, as opposed to a statement, which has a truth value. 

Try saying something paradoxical. In the form of a statement, not an expression (or question).


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## εmptε (Nov 20, 2008)

*"I will be cooked in water."*


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## Nightriser (Nov 8, 2008)

Oh! So close!


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## εmptε (Nov 20, 2008)

*=_= "I will be fried in oil" "I will be boiled in oil" "I will be fried in water" " I will not die today"*


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## Nightriser (Nov 8, 2008)

So I've noticed. You seem fairly balanced.


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## εmptε (Nov 20, 2008)

*This blog has been awarded ...









*


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## Nightriser (Nov 8, 2008)

Well, thanks, Wolf. 

Also note, it's the first blog to reach three pages of comments. Beat that. :tongue:


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