Puzzle challenges!

[Deciton_Reven]

Wine is easy:

Spoiler:

Split the barrels up into 23 groups of 22 twice (sans six for the last group), using numbers for the first set and letters for the second, make sure none of the barrels have the same combination of letter and number, then every hour (EDIT: and 1 minute) have the first man drink from the each barrel of the current numbered set in order of lowest to highest and have the second man drink from each barrel of the second in alphabetical order. Then you can time when the first man dies to find the number and when the second man dies to find the letter, and the barrel with that combination is the poisoned barrel.

[Inky]

Yeah! That's exactly correct
This also easily generalizes to using more people:

Spoiler:

If you have T possible starting times and N people, then you can assign each barrel an N-tuple (t1, t2, ... tN) which lets you test TN barrels! (ti ranges from 0 to T-1 and indicates the time person i should drink from this barrel)

Of course, you don't want to kill too many people, or there might be riots

For the Four Witnesses thing, I think this is the issue with Ravana's truth table:

Spoiler:

I think converting statements such as

Witness 3 says 'If 4 is telling the truth, then 2 is not.'

to -C&D => B (If 3 is lying and 4 is telling the truth, then 2 is telling the truth) isn't quite accurate.

I think it would actually be a nested implication: -C => -(D => -B), in other words "If 3 is lying, then it is not the case that 4 telling the truth implies 2 is lying."

[Ephraim]

Here goes other puzzle:

The impossible math riddle:

2316=1
6786=4
7671=X
2759=1
9750=2

Which is the value of X?
(Note)=This puzzle can be solved without calculator.

Solution and Winner:

skeptical_troll solved it:

I think I got it, X=1 isn't it?
It's the number of circles in the four digits, right?

[Samonella]

I've seen it before so I'm not answering, but I'll give a hint:

Spoiler:

It's not actually a math riddle.

[Inky]

I've also seen this one before. Maybe we could have a rule that when no one posts for a certain amount of time (a week or something?) then anyone can post a new one, to keep things going. I'd hate to see this thread die since it's been really fun!

[skeptical_troll]

I think I got it, X=1 isn't it?

reason:

it's the number of circles in the four digits, right?

If the solution is correct, I propose another one:

in a garden, there are 100 tigers and a sheep. Everyone can eat grass, but tigers are only half happy in doing so. The closest tiger to the sheep has the opportunity to eat it, which would make it entirely happy, but there's a problem: if a tiger eats a sheep, it will be transformed itself into a sheep. The tigers are aware of it and are perfectly trained in logic. What will happen? Will the tiger eat the sheep or not?

[Ephraim]

Yeah, it's correct! Is the number of circles.

About the tigers...

Spoiler:

There can happen two things:

The tiger won't eat the sheep, because is scared to been eaten by another tiger, because if he eats the sheep, why the next one won't do the same?

The tiger will eat the sheep, then the next one will eat the new sheep, then... and finally, the last tiger will be a sheep, and he will be entirely happy, because no one will eat him because is the last one, and he will eat grass.

[Samonella]

Here's an idea: for this puzzle, everyone just make your final answer without explaining it, then in a couple days skeptical_troll tells us who's right?

I definitely could be wrong, but I think I have found a good reason that they will not eat the sheep.

[Elder2]

Spoiler:

Tigers are not concerned about their own happiness but rather about the survival of their species and genes, it makes more sense considering the theory of evolution. Therefore they won't eat sheep XD

[Inky]

Tigers:

Spoiler:

I also think that the tigers will see the health benefits of a vegan diet, and refrain from eating the sheep

[skeptical_troll]

Inky and Samonella are right, the tigers will not eat the sheep. I'll let them explain how they come to that conclusion, if they want

[Samonella]

Wooh! I figured that since the tigers are all perfectly logical, they must come to the same conclusion as each other, so if one eats the sheep it's guaranteed that the next one will too. Since that would be a bad outcome for the tiger, it must decide to not eat the sheep, regardless of how it solves the chicken-or-the-egg logic.

[Inky]

Hmm, this was my reasoning, though I don't know whether it's right

Spoiler:

If we have 1 tiger (and 1 sheep), the tiger will just eat the sheep.
If there are 2 tigers, they will not eat the sheep, because if one does, then the other tiger would eat him immediately.
If there are 3 tigers, the nearest tiger will eat the sheep, because it knows that with 2 tigers left neither tiger will eat him.

Continuing the pattern, if there's an odd number of tigers the nearest tiger will eat the sheep, and if there's an even number they won't.

Since Samonella said he's out of ideas, I'll go ahead and post another one, a classic logic problem:

Two Paths

You come to a fork in the road, where one path leads to something awesome like 1000 gold and the other leads somewhere really unpleasant, like a corpse infested swamp.
There are two people standing at the fork who know which path leads where, but one always tells the truth and one always lies and you can't tell them apart.
You can only ask one question to one person. How do you determine which way to go?

Answer by GunChleoc:

Ask what the other person would say, then choose the opposite. The truth-teller would tell you the lie that the lier would produce, and the lier would lie about that the truth-teller would say.

(If the above was too easy, here is a more difficult bonus question:
Now in addition to the truth teller and liar, there is a third person who answers questions randomly, telling the truth 50% of the time and lying 50% of the time.
Using a total of two Yes/No questions (each addressed to one person, though not necessarily the same one) how do you determine the correct path?)
Edit: I forgot to mention, each person knows the truthtelling/lying habits of the other(s).

Answer to extra question:

Second question: If you know you're asking the truthteller or liar, you can just ask the same question in the 2 person case ("If I were to ask whether this is the correct path, would you say yes?")

First question: For convenience label the 3 people A, B and C. Ask person A "Is person B more likely to tell the truth than person C?" If yes, choose C for asking the second question, if no, choose B.

Cases (if A answered yes):
-If A is random, either B or C works
-If A is truthful, then B is the random person and so you want to ask C (the liar)
-If A is lying, then B is the random person and you want to ask C (the truthteller)

[Samonella]

Tigers: Ooh, I think Inky's reasoning was right, not mine.

Two Paths: Very nice wesnothy version. I've heard the main question before but will have to puzzle on the bonus. To be clear, the third person is truly random, not alternating between truths and lies?

[Inky]

Two Paths: Yeah, I meant truly random. EDIT: Oops I phrased it wrong, I meant the third person tells the truth 50% of the time and lies 50% of the time at random. (Though the original wording of randomly choosing between yes/no probably works too. I don't remember the exact wording of this problem, the only important point is: the third person sometimes lies and sometimes tells the truth.)

Edit2: Another important thing I forgot to mention is that each person knows the truthtelling/lying habits of the others.

Glad you like the "wesnoth version" (The only thing is, if it's a necromancer or something I think they'd also love the corpse infested swamp )