Puzzles & Paradoxes

Started by AOR6 pages
Originally posted by Storm
Which method did you follow to derive the solution?

I drew it out....drawingouttion? shrug

Here is another one...


Three switches are in the "off" position outside a windowless room with each being connected to one of three light bulbs inside the room. How can you determine which switch is connected to which bulb if you may enter the room only once?

Here is another...


It's night and the electricity is gone in your room. You need a pair of identical socks from your drawer. You have 20 red, 30 green, 50 blue pairs of socks and every sock is identical except its color. Since it is dark, you can't see the colors of the socks. So you pick randomly some socks. At least how many socks should you pick so that you are sure that you picked at least one identical pair (identical pair means a pair of socks with the same color).

The majority of people can't answer this question correctly.

Originally posted by Hydrono
Here is another one...

Switch one light on; turn it off and turn another on and leave it on. Go into the room and feel the off-bulbs. The warm one is connected to the first switch, the on-bulb is connected to the second switch and the third heatless bulb is connected to the third unused switch.

Originally posted by AOR
Switch one light on; turn it off and turn another on and leave it on. Go into the room and feel the off-bulbs. The warm one is connected to the first switch, the on-bulb is connected to the second switch and the third heatless bulb is connected to the third unused switch.

Correct!

Originally posted by Hydrono
Here is another...

The majority of people can't answer this question correctly.


Four. I find it hard to believe most people can't answer it correctly.

The Hardest Logic Puzzle Ever

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.

Clarifications:[list][*]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.[/list]

Originally posted by Storm
[b]The Hardest Logic Puzzle Ever

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.

Clarifications:[list][*]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.[/list] [/B]

😑 Wow

How do they react to answers they can't know, for example, how would the liar and the truthteller answer "Would God A say he always tells the truth if I ask him" if that was the God that randomly chose?

Originally posted by Storm
[b]The Hardest Logic Puzzle Ever

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.

Clarifications:[list][*]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.[/list] [/B]

This question isn't even possible to find an answer to. 12 possibilities and only 3 bits of information....wow.

Spoiler:

Your puzzle can be solved by asking self-referential questions after one with a known answer.

The second question would be “Was your previous answer correct?

Then you have a lot of information.

The truth teller will give identical answers.

The liars would alternate.

The other’s are unpredictable.

If you get two sets of identical responses you have identified the liar, because his alternated.

If you get two alternating responses, you have identified the truth teller and know which response means true.

If the one with the unpredictable responses happens to answer truthfully three times, he will be indistinguishable from the truth teller. Similarly, if he lies three times his answers will be identical to those of the liar. So, his answers are useless, unless they show a pattern incompatible with those that the other two can present, for example TTT and FTF, to simple questions about previous answers. Are there any restrictions on the one with the random answers that prevent him from mimicking the answers of one of the other two players? If not, I give up.

(posting for a friend)

ja and da are not the only possible answers...if you ask the truth god "Are you going to answer this question with the word that means no in your language?" then he cannot answer truthfully and so he cannot answer

Originally posted by jaden101
ja and da are not the only possible answers...if you ask the truth god "Are you going to answer this question with the word that means no in your language?" then he cannot answer truthfully and so he cannot answer
That would be additional information we need before solving.

Originally posted by Bardock42
That would be additional information we need before solving.

its actually part of one of the solution...to which to my knowlege there is 2

http://www.uweb.ucsb.edu/~rabern/SSHardPuzzle.pdf

Originally posted by jaden101
its actually part of one of the solution...to which to my knowlege there is 2

http://www.uweb.ucsb.edu/~rabern/SSHardPuzzle.pdf

It's only a solution if that is what happens if ask the truth god "Are you going to answer this question with the word that means no in your language?", if in that case the truth God would answer randomly you would have no information. So, that needs to be included in the question.

I hate questions that refer to other questions because all they are is a way of escaping the spirit of the three question formula (and I don't mean because it creates a fourth question, because that is only semi-true, but really because it escapes the point of the issue. It's the sort of answer that just makes the originator change the puzzle).

Originally posted by Ushgarak
I hate questions that refer to other questions because all they are is a way of escaping the spirit of the three question formula (and I don't mean because it creates a fourth question, because that is only semi-true, but really because it escapes the point of the issue. It's the sort of answer that just makes the originator change the puzzle).
What do you mean?

I'm referring to the given solutions provided above, which involve asking a question that refers to another question (that you know the answer to) which sidesteps the point of the issue.

Originally posted by Ushgarak
I'm referring to the given solutions provided above, which involve asking a question that refers to another question (that you know the answer to) which sidesteps the point of the issue.
Is there a way to solve it without either knowing the answer or asking something paradoxical?

By the parameters of the puzzle, yes.

This is because, as mentioned, if you ask any god

Spoiler:
"If I asked you [insert question here] would you say 'ja'?" automatically gets you a truthful answer (assuming the Gods know the answer, that is). This is because the true god would answer the question about the queastion truthfully, saying he would say 'ja' or 'da', therefore meaning if you asked him the actual question he would say 'ja' or'da' respectively. If the question is asked of the false God, he would switch his response around (saying 'ja' where the true god say 'da' and vice versa), but then he is lying about what his lie would be, so if you asked him the question above his response is still actually the truthful answer. And as the random God impersonates either true or false, whatever he says to that question would give you the correct answer to the subsidiary question as well, so long as you add a "in your current mental state" rider onto your question.

Not only are they giving the truthful answers, but without even knowing which of 'ja' or 'da' means 'yes' and 'no', we can even discern the truth of the answer by asking such a self-referential question (this is why you specifically ask 'would you say 'ja'?' instead of 'would you say 'yes'?'.). No matter which God you ask, if the God replied 'ja' the answer to the subsidiary question is yes, and if he says 'da' the answer is no, even though we still don't know what ja and da mean.

So, to summarise, ask any God "In your current mental state, if I asked you [insert question here] would you say 'ja'?" gets you the correct answer to the [insert question here], so long as the God can answer it. Now you have a truthful answer it's only a short hop to unravelling the whole puzzle.

It is this 'bouncing a question off of a question' technique that basically shortcuts the entire riddle, because it turns all three Gods into True Gods, which I doubt was intended.

So now you can force a truthful yes/no answer out of any God it's easy. You just ask, say, the first God if he is random (phrasing the question as above). if he says 'ja' then he is, if he says 'da' he is not. And so on; you;ll easily solve it in three questions.

Some of the above may look complex but the logic involved is actually extremely straightforward and those who specialise in this sort of area would solve it in a minute or so. It really was not intended and destroys the idea of it being the 'hardest puzzle'. You are MEANT to ask a series of questions that tive you meaningful information even with all the ignorance inherent to the scenario, not abuse the asking of questions to force all three Gods to tell you the truth.

---

So to answer your question... yes, it is possible, easily, it's just abusive.

Is it possible to answer it without being abusive? if, say, we put in a rule saying you are not allowed to ask them questions about questions? Yes... but it's very fiddly and frankly not much fun unless you are into logic and maths and so on.

I prefer something like the Monty Hall paradox.