Puzzle challenges!

[Samonella]

Spoiler:

I'm not surprised, I was thinking about how 4 questions have 16 possible answer sets, so I suspected that it was possible to do better.

Judging by your hint, this isn't the "easiest" way either, but this just uses 3 questions:

"Are you human? Are you human and vampire? Are you vampire?"

Sane human: yes, no, no
Insane human: no, yes, yes
Sane vampire: yes, yes, no
Insane vampire: no, no, yes
Insane faerie: no, no, no
Sane alien: either yes, no, yes or no, yes, no

[Velensk]

Very nice, you even got the bonus version of the question which was which set of three questions would work for all cases.

[Samonella]

Yay!

I can't think of any more really hard ones, but this is the hardest one I made up for my RPG campaign. It's not much compared to the others on this thread, but if you try doing it without pencil and paper it should be a fun challenge.

Witness 1 says 'If 2 is telling the truth, then 3 or 4 also is (or all three of them).'
Witness 2 says '1 is telling the truth and so is 3 or 4 (or all three of them).'
Witness 3 says 'If 4 is telling the truth, then 2 is not.'
Witness 4 says 'Either I am telling the truth, or both 1 and 2 are (or all three of us).'

Which one(s) are telling the truth?

Inky's winning solution:

Witness 3 is the only lier.
(I'm still pretty sure that's the only solution.)

[Inky]

Wow, really nice short and clear solution by Samonella!

As for the above puzzle, I don't think the solution is unique?

Spoiler:

For example, if both 1 and 2 are telling the truth, then 4 is also telling the truth and 3 must be lying.
If both 1 and 2 are lying, it could be that 3 and 4 are telling the truth, or that 1, 2 and 4 are lying and 3 could be either telling the truth or lying.
I think there are also a couple more valid solutions involving one of 1 or 2 being false and the other true.

Were your "if" statements meant to go in both directions? Like was statement 3 supposed to mean "4 is telling the truth if and only if 2 is not" (i.e. if 4 is lying then 2 is telling the truth)?

If you're looking for an interesting one, there's one I remember reading in a book

That sounds like a really fun book! Do you happen to remember what it was called?

[Samonella]

Here's the way I understand ifs, using this definition I believe there is only one solution:

spoiler, but not the answer:

If includes a hypothesis and a conclusion- if the hypothesis is true, then the statement has the same truthiness as the conclusion (example, if <true> then <true> is true, if <true> then <false> is false).
However, the statement is true whenever the hypothesis is false (example, if <false> then <false> is true). After all, the statement claims nothing unless the hypothesis is true.

So the only way for an if statement to be false is if the hypothesis is true but the conclusion is false.

So with that definition:

If both 1 and 2 are lying

doesn't really make sense because if 2 is lying then 1 isn't claiming anything at all, and therefore can't be lying.

[Inky]

Ohhh of course, I totally missed that!!

But isn't there still a second solution?

Spoiler:

2 is lying, so 1 is automatically telling the truth. If 4 is lying (the second half of the or statement will be false, and "I am telling the truth" is also false, so this would be consistent) then 3 is automatically telling the truth.

edit: oh wait never mind that doesn't work. I should think more before posting

[Samonella]

edited: ninja-ed by Inky's edit. So it sounds like you still know one solution, right?

[Ravana]

I found several solutions still

statements for truth table

Someone truths:
A&B => C|D
B => A & (C|D)
C&D => -B
D => D | (A&B) - always true

Someone lies:
-A&B => -(C|D)
-B => -A | -(C|D)
-C&D => B
-D => -D & -(A&B)

[Samonella]

Hm, I think I understand your notation (=> is if, & is and, | is or, - is not) but I don't know what each statement is supposed to mean. Here is the truth table I made when making up this problem:

Spoiler, including (one) correct answer::

There are two sides of the table. The left side is just guesses; basically, it says "suppose this combination of witnesses is truthing/lying." The right side then represents which statements are made true or false by that combination. So a combination is a valid solution if and only if the two sides match.
To save time, I just put "-" in slots that are irrelevant because an earlier column already proved that row to be inconsistent.

Code: Select all

1 | 2 | 3 | 4 |   2=>3|4   |   1&(3|4)   |   4=>-2   |   4|(1&2)

0 | 0 | 0 | 0 |      1     |      -      |     -     |     - 
0 | 0 | 0 | 1 |      1     |      -      |     -     |     - 
0 | 0 | 1 | 0 |      1     |      -      |     -     |     - 
0 | 0 | 1 | 1 |      1     |      -      |     -     |     - 
0 | 1 | 0 | 0 |      0     |      0      |     -     |     - 
0 | 1 | 0 | 1 |      1     |      -      |     -     |     - 
0 | 1 | 1 | 0 |      1     |      -      |     -     |     - 
0 | 1 | 1 | 1 |      1     |      -      |     -     |     - 
1 | 0 | 0 | 0 |      1     |      0      |     1     |     - 
1 | 0 | 0 | 1 |      1     |      1      |     -     |     - 
1 | 0 | 1 | 0 |      1     |      1      |     -     |     - 
1 | 0 | 1 | 1 |      1     |      1      |     -     |     - 
1 | 1 | 0 | 0 |      0     |      -      |     -     |     - 
1 | 1 | 0 | 1 |      1     |      1      |     0     |     1 
1 | 1 | 1 | 0 |      1     |      1      |     1     |     1 
1 | 1 | 1 | 1 |      1     |      1      |     0     |     - 

I won't rule out the possibility that I made a mistake, but by this table only one row matches all the way across.

[Velensk]

Ravana: You know, I actually don't remember the name of that specific book however I do remember the name of the original book in that set. The name of the original book is "What is the Name of this Book" and it has sequels. If you find it and can hunt down everything else by that author you'll probably find it.

[Inky]

Thanks Velensk! (that was actually me who asked)

So I guess we're done with the previous one? Here is a new one, hopefully I remembered everything right.

The poisoned wine
The king has 500 barrels of wine, exactly one of which is poisoned. The only way to detect the poison is drinking it, which will result in death between 23-24 hours later. He needs to use the wine for a feast taking place in two days (48 hours). He has a couple... expendable... subjects on which he can test the wine. How can he identify the poisoned barrel in 48 hours using only 2 testers?

[Ravana]

my truth table with 5/16 true

I made that script 2 years ago.

[Ephraim]

About the poisoned wine...

Spoiler:

Hehe... I got the answer! Just, simplify it:
500 barrels/2 testers = 250 barrels/tester
Both testers should drink 250 barrels (obviusly only some wine, no all the wine in the barrel) in 48 hours, but only 24 of these are useful to drink and all the 48 hours are useful for let see if the tester gets poisoned.
What should they do? Just drink the wine on intervals of some time, and they will get poisoned one day after drinking it. If he gets poisoned in the first interval, then the first barrel is poisoned, if he gets poisoned during the second interval of time, then the second barrel is poisoned.

There is a mathematical solution to calculate the time that should take every interval, but I'ts too late here for think about numbers...

Wait! We got the poisoned barrel. What can we do? Just sell it for outlaw assassins throwing knifes, and go to seek the aid of a white mage for heal the tester. But don't worry about it, in the world of Wesnoth, soldiers can't die from poison ! (Just a joke)

[Samonella]

Four witnesses:

Maybe your code interprets implications differently? It shows several correct solutions that include both 1 and 2 lying, but like I said, I don't think that makes sense because 1 can only be lying if 2 isn't. Otherwise he makes no claim at all. Similarly, I don't think 3 and 4 can both be lying, which would eliminate all your solutions but one.

Poisoned wine: Way to go, Inky! Now I'm not the only one posting morbid puzzles!

About Ephraim's solution:

I think it's a little off, because they can only drink wine at intervals of 1 hour, or else the time periods for which they should die will overlap (they die in 23-24 hours). That would mean you couldn't tell which taste killed them. So they can only take so many tastes each--not enough to taste every barrel before the feast. A feast at which the guests are apparently going to consume a staggering amount of wine.

[Inky]

Four witnesses: I think maybe there's some self-referential stuff going on? I'll have to think about it a bit more.

Poison: As Samonella said, the poison takes effect anywhere from 23 to 24 hours later - the exact time it takes is different every time, so if you drink a poisoned and normal barrel in the same hour interval you won't be able to tell which of the two killed you later.

And congratulations to Samonella for already solving it! He didn't post the answer here to give other people time to think about it.