INTENSITY²
Start here => Games => Topic started by: Calavera on August 25, 2011, 06:30:31 PM
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Please do not answer this problem if you already know from before.
Here's a nice brainteaser for you all. I'm writing in my own words, so feel free to ask for any clarifications if needed.
There are 5 autistic men trained to act in certain ways.
Four of them are socially trained to be Togglers while the fifth is trained to be the one and only Truthteller.
The Truthteller always tells you the truth. He never lies to you.
The Toggler alternates between saying the truth and lying. One statement coming out of his mouth may be either a lie or not, but the next statement is always the opposite, and the next statement after that is like the first, and so on.
Your objective in this brainteaser is to figure out which one is the Truthteller by asking two questions to only one of them.
What questions would you ask?
A hint: Your second question does not have to be defined before you start asking the random person your first question. It may depend on what the person answers for your first question.
Free karma to the first person who solves it properly.
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Sorry, Mcalavera; messing it up already.
To man number one:
Are you the truth teller?
Who is the truth teller?
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You need to ask two questions to one of them to figure out who the Truthteller is.
You can't find out by just that one question.
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Fixed.
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Sorry, Mcalavera; messing it up already.
To man number one:
Are you the truth teller?
Who is the truth teller?
What if it was an initially honest Toggler who you ended up asking?
He will honestly answer "no" to the first and lie to the second question. And you won't know who the Truthteller is.
Not saying that you're completely wrong. But keep in mind you need to list all necessary variations of the second question (since the second question has to depend on the varying answer to the first question).
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First ask who are all the 4 togglers point to them in your answer, then ask who is the truthteller and point to them. This is presuming that the togglers must know all information that's required and must strictly follow the truth/lie or lie/truth oscillation and can alternate within the same question by distinct sentences, without invoking a contraction within one or two statements adjoining and thereby violate the rules (like they can't say two lies in two statements in a row or have a half-truth answer, must be truth or lie) and can be allowed to answer by pointing instead of talking (but even with talking it's still possible too).
I've invoked a contradiction of rules if he tries to start with a lie/truth with a four statement method; because the toggler will be forced to tell the truth two statements in a row (as there's only one truthteller, and I'm asking for four inputs). Even if they try to break the statements into three statements, it must strictly be truth-lie-truth to not invoke a contradiction, and the second answer is virtually unnecessary. No matter how he does it he cannot do it without invoking a truthful statement at some point and cannot proceed with that method of purely lying.
The only way they can avoid this contradiction other than what I corrected before is to cite all the names as one or two statements, and be forced to be truthful with one of them about it. However trying to play it as two statements will look awkward and why would you single out a person from a explicit list? He can only say, "Those three. Oh him as well" basically. So depending on whenever or not it's one, two or three statements:
* If he says, "Oh it's him, him, him, him" as one statement (bear in mind this can only be truthful), then the second answer will show a contradiction by citing the same name twice and the one never mentioned is the truth teller. But you don't even really need the second answer anyway because he's forced to confess he's one too using this method. The second question is merely insurance.
* If he says, "Oh it's him, him, him. Also him too" as two statements, the singled out person is the truthteller and the second answer isn't really necessary but to confirm the person I'm talking too isn't the truthteller, but then the phrasing of statements alone shows him obeying the toggler rule anyway.
* If he says, "Oh it's him, him. Also him. Also him" as three statements, and he attempts to say he's the truthteller why did he need to split up those names? So it's obvious he's lying and thus the truth teller is the middle statement as the first and last statements must be truths, the other way around results in a contradiction of rule. The same applies if he says any other name because of the way he phrased those statements, and it must follow the truth-lie-truth sequence to not contradict the rules.
By statements, I presume you mean they must be like sentences, and thereby noticeably separate or that's just cheating.
However, in the Truthteller's case, he'll tell me who the others togglers are as one unbroken statement and himself is the truthteller without trouble or invoking a contradiction.
I think I broke/solved the brainteaser by accident by trying to be a smartass. :zoinks:
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Who are the togglers? Very smart, professor.
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Was also thinking the first question could be something the asker knows, like what does 1+1 equal. Then who are the togglers.
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Was also thinking the first question could be something the asker knows, like what does 1+1 equal. Then who are the togglers.
Now thinking that might only identify if the person questioned is lying or telling the truth, but not really identifying the truth teller if it's not the one questioned.
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Was also thinking the first question could be something the asker knows, like what does 1+1 equal. Then who are the togglers.
Now thinking that might only identify if the person questioned is lying or telling the truth, but not really identifying the truth teller if it's not the one questioned.
The real problem then is whenever or not multiple statements can be used to answer one question. Hence why my answer is complicated. But I proved that just knowing the rules empowers your judgement to read between the lines of how they answer that first question. 8)
Only drawback is that it makes the assumption that half-truths are not allowed. But MCalavera never explicitly stated they can tell both a truth and a lie, embellish or show ambiguity leaning either way within the same statement.
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Am assuming it's cut and dry; alternating full truth and lie from the togglers.
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You need to ask two questions to one of them to figure out who the Truthteller is.
You can't find out by just that one question.
I beg to differ with my question. Read my answer lol. :zoinks:
Am assuming it's cut and dry; alternating full truth and lie from the togglers.
I presume so because here's what MCalavera said:
The Toggler alternates between saying the truth and lying. One statement coming out of his mouth may be either a lie or not, but the next statement is always the opposite, and the next statement after that is like the first, and so on.
This mean they may start off either lying or telling the truth, but every subsequent statement must be opposite in nature to it's previous one.
So basically, start of with a lie, then it's truth, lie, truth, lie, and so on.
He didn't mention anything about the same statement being capable of harboring both, otherwise why bother specifying such switching rules? It would render the switching rule useless if wasn't so cut and dry.
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Your who are togglers question is the key. First ask, are you a toggler? If the answer is no, then it's either the truth teller or a lying toggler. Either way, the next answer will be true, so if the answer is no then the second question should be, who is the truth teller? If the answer to the first question is yes, then it has to be a toggler telling the truth, because the truth teller would answer no. Since the second answer will be a lie, the second question should be, who else is a toggler?
Oh, and don't be messing with my karma. :P
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Woah, give me some time to process your post, Professor. :autism:
5 minutes.
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Woah, give me some time to process your post, Professor. :autism:
5 minutes.
Sorry, and may I warn you, it's an utter mess. I just hope I at least got the principle explained enough. To sum it up, it's about asking that first question and reading between the lines of how the person answers. Due to their rules, togglers will give themselves away by obeying their rules.
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I'm unable to fully understand your points, Professor. But I appreciate the effort you made in coming up with your own answer.
Your answer could be correct for all I know, but my simple mind is just unable to figure out if it's so. Sorry, mate.
But that was pure ownage nevertheless. :autism:
Let's see Jack's answer next.
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Aso had trouble with the professor's answer but after thinking about it, believe it would certainly work. The first question is, who are the four togglers? The truth teller will answer, everyone but themself. A lying toggler will also answer everyone but them self. Either way, the second quesiton of, who is the truth teller, will be true. If the answer to the first question includes their self as a toggler, then one knows they're telling the truth, and no second quesiton is needed.
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Your who are togglers question is the key. First ask, are you a toggler? If the answer is no, then it's either the truth teller or a lying toggler. Either way, the next answer will be true, so if the answer is no then the second question should be, who is the truth teller? If the answer to the first question is yes, then it has to be a toggler telling the truth, because the truth teller would answer no. Since the second answer will be a lie, the second question should be, who else is a toggler?
Oh, and don't be messing with my karma. :P
Correct, Jack. Well done. You've thought it through carefully.
Here's some kar ... actually, nevermind. I'll just give it to Professor for you. :P
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Here's some kar ... actually, nevermind. I'll just give it to Professor for you. :P
Professor got it right first. :)
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Aso had trouble with the professor's answer but after thinking about it, believe it would certainly work. The first question is, who are the four togglers? The truth teller will answer, everyone but themself. A lying toggler will also answer everyone but them self. Either way, the second quesiton of, who is the truth teller, will be true. If a toggler includes their self as a toggler, then one knows they're telling the truth, and no second quesiton is needed.
If that's what Professor said, then that does seem to be correct.
Ok, then. Professor got it correct first. Congrats, mate.
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Question 1 could be: Are you a liar?
The truthteller will always answer 'no' to this, as they never lie. The togglers will answer either yes or no, depending if they are lying/telling the truth. Either answer could still provoke a second question, as you can't confirm the liars/truthtellers from just the one question.
The second question therefore is a tricky one, and as you still have all 5 participants in play, it means it has to be a question that will nail the case shut. Unfortunately, I haven't the foggiest of what to ask for that one.
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Question 1 could be: Are you a liar?
The truthteller will always answer 'no' to this, as they never lie. The togglers will answer either yes or no, depending if they are lying/telling the truth. Either answer could still provoke a second question, as you can't confirm the liars/truthtellers from just the one question.
The second question therefore is a tricky one, and as you still have all 5 participants in play, it means it has to be a question that will nail the case shut. Unfortunately, I haven't the foggiest of what to ask for that one.
Well, if you or anyone else can come up with another correct answer, it'd be good to post. Who knows how many correct answers this problem has.
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Aso had trouble with the professor's answer but after thinking about it, believe it would certainly work. The first question is, who are the four togglers? The truth teller will answer, everyone but themself. A lying toggler will also answer everyone but them self. Either way, the second quesiton of, who is the truth teller, will be true. If a toggler includes their self as a toggler, then one knows they're telling the truth, and no second quesiton is needed.
If that's what Professor said, then that does seem to be correct.
Ok, then. Professor got it correct first. Congrats, mate.
Thanks. Although I think I misinterpreted statement as meaning sentences within the same answer. So my answer to this was more elaborate than needed.
My method is more about exploiting the rules and forcing them to answer in a way that makes it piss easy to know the solution without the need of a second question, even if they try to get smart and invoke multiple statements in one answer.
But here's the thing, a lying toggler actually cannot say everyone but himself, because it's an half-truth as one statement/answer and that contradicts the rules and also renders the rules meaningless if allowed. So he's forced to tell the truth and include himself on the list. The second question is then never needed, but in case you're unsure, might as well use it. :orly:
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lol, I'll just keep it simple for my own sanity.
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lol, I'll just keep it simple for my own sanity.
Heh, and I'll keep it complicated for my own insanity. :toporly:
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If that's what Professor said, then that does seem to be correct.
Ok, then. Professor got it correct first. Congrats, mate.
Wasn't entirely sure that's what he said, but agree the question of who are the four togglers works perfectly.
Question 1 could be: Are you a liar?
The truthteller will always answer 'no' to this, as they never lie. The togglers will answer either yes or no, depending if they are lying/telling the truth. Either answer could still provoke a second question, as you can't confirm the liars/truthtellers from just the one question.
The second question therefore is a tricky one, and as you still have all 5 participants in play, it means it has to be a question that will nail the case shut. Unfortunately, I haven't the foggiest of what to ask for that one.
Are you a liar is the same as asking are you a toggler, so an answer of no would prompt the quesion of who is the truth teller. An answer of yes would prompt the question of who else is a liar.
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Asking only one person makes it a bit more difficult to get a conclusive answer, as you are never goi8ng to know which one is which straight up. Using my theory:
Q1 - Are you a liar?
#1: No
#2: No
#3: No
#4: No
#5: No
One of those statements is definitively the truth, as the truthteller can never lie. So the togglers would be lying if they said no as the the formula goes lie/truth/lie; or if it went truth/lie/truth, then they too would be telling the truth. Assuming the first formula is correct, the next question will be:
Q2: Is your answer to Q1 correct?
You will get a yes from the truthteller, but you may still not know exactly who they are, as each haven't answered their questions. But, for example, let's say it's person 1:
#1: Yes - truth
#2: Yes - lie
#3: Yes - lie
#4: Yes - lie
#5: Yes - lie
The problem with this scenario is that an assumption has to be made who is the truthteller, and all 5 participants still have to be asked.
Very tricky problem indeed.
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But here's the thing, a lying toggler actually cannot say everyone but himself, because it's an half-truth
Yes he can say everyone but himself and it still be a complete lie. The question is who are the four togglers, not who among you are togglers.
That makes me think of another one. The first quesion is, who among you are togglers. The truth teller will name everyone but himself, a truth telling toggler will have to include himself, and a lying toggler will only be able to name the truth teller. Either way, no second quesion is needed.
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That's right.
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But here's the thing, a lying toggler actually cannot say everyone but himself, because it's an half-truth
Yes he can say everyone but himself and it still be a complete lie. The question is who are the four togglers, not who among you are togglers.
That makes me think of another one. The first quesion is, who among you are togglers. The truth teller will name everyone but himself, a truth telling toggler will have to include himself, and a lying toggler will only be able to name the truth teller. Either way, no second quesion is needed.
That's assuming you get the correct person on the first attempt. As I said, the truthteller can't actually be revealed until Q2 has been answered, as no-one will know for sure who is who (except those being asked) and the questioner has to do the finding out.
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Yes he can say everyone but himself and it still be a complete lie. The question is who are the four togglers, not who among you are togglers.
That makes me think of another one. The first quesion is, who among you are togglers. The truth teller will name everyone but himself, a truth telling toggler will have to include himself, and a lying toggler will only be able to name the truth teller. Either way, no second quesion is needed.
That's true.
Hence why I mentioned the idea of making them point to all four of them, because it prevents the whole "everyone but themselves" style vague answers and forces them to name names.
But I suppose like you said asking, "Who specifically are the four togglers among you?" would circumvent vague deceptive answers like that.
But it's important to specify the number of togglers too as leaving anything to open interpretation in your question, allows them to be more deceptive in answering.
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But here's the thing, a lying toggler actually cannot say everyone but himself, because it's an half-truth
Yes he can say everyone but himself and it still be a complete lie. The question is who are the four togglers, not who among you are togglers.
That makes me think of another one. The first quesion is, who among you are togglers. The truth teller will name everyone but himself, a truth telling toggler will have to include himself, and a lying toggler will only be able to name the truth teller. Either way, no second quesion is needed.
That's assuming you get the correct person on the first attempt. As I said, the truthteller can't actually be revealed until Q2 has been answered, as no-one will know for sure who is who (except those being asked) and the questioner has to do the finding out.
No. My logic is sound. It doesn't matter who's asked. No second question is needed.
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Yes he can say everyone but himself and it still be a complete lie. The question is who are the four togglers, not who among you are togglers.
That makes me think of another one. The first quesion is, who among you are togglers. The truth teller will name everyone but himself, a truth telling toggler will have to include himself, and a lying toggler will only be able to name the truth teller. Either way, no second quesion is needed.
That's true.
Hence why I mentioned the idea of making them point to all four of them, because it prevents the whole "everyone but themselves" style vague answers and forces them to name names.
But I suppose like you said asking, "Who specifically are the four togglers among you?" would circumvent vague deceptive answers like that.
But it's important to specify the number of togglers too as leaving anything to open interpretation in your question, allows them to be more deceptive in answering.
Good point on the deceptive truthful answer of not naming them all; naming only two or three. Though now convinced this shouldn't need two questions and will think on better wording which neither includes specific numbers nor leaves room for trick answers. Who are the togglers is key.
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Question 1 could be: Are you a liar?
The truthteller will always answer 'no' to this, as they never lie. The togglers will answer either yes or no, depending if they are lying/telling the truth. Either answer could still provoke a second question, as you can't confirm the liars/truthtellers from just the one question.
The second question therefore is a tricky one, and as you still have all 5 participants in play, it means it has to be a question that will nail the case shut. Unfortunately, I haven't the foggiest of what to ask for that one.
Well, if you or anyone else can come up with another correct answer, it'd be good to post. Who knows how many correct answers this problem has.
Kill them all, God will know his own. :angel:
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Question 1 could be: Are you a liar?
The truthteller will always answer 'no' to this, as they never lie. The togglers will answer either yes or no, depending if they are lying/telling the truth. Either answer could still provoke a second question, as you can't confirm the liars/truthtellers from just the one question.
The second question therefore is a tricky one, and as you still have all 5 participants in play, it means it has to be a question that will nail the case shut. Unfortunately, I haven't the foggiest of what to ask for that one.
Well, if you or anyone else can come up with another correct answer, it'd be good to post. Who knows how many correct answers this problem has.
Kill them all, God will know his own. :angel:
Stuff what we want to know, eh? :P
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What do you think of the professor's point, Mcalavara?
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It's not my brainteaser, so I can't really know whether a half-truth is considered a lie.
But, personally, I prefer the answer you gave, which avoids such conundrum and still ends up being correct.
My approach is: the simpler, the better.
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Maybe just who are the togglers is a better choice of words than who among you are togglers.
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But that question is never going to reveal the truthteller, unless you already know the answer.
And as the questioner, you are supposed to work out who is who without any background information.
Asking 'who are the togglers?' is only going to get one truthful response at first. The second question is needed for clarification.
Maybe a better question would be "Are any of you Jesus Christ?" You would know neither of them aren't, but you still don't know the truthful response.
Anyway, I think the definite correct answer to this is needed.
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I gave a definite correct answer. You're not reading what I wrote.
Q:Who are the togglers?
The truth teller can only answer, everyone but himself. This identifies him as the truth teller.
The truth telling toggler must include himself in the answer. This identifies the truth teller.
They lying toggler can only name the truth teller as a toggler. This identifies the truth teller.
Only one question is needed.
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It's not my brainteaser, so I can't really know whether a half-truth is considered a lie.
But, personally, I prefer the answer you gave, which avoids such conundrum and still ends up being correct.
My approach is: the simpler, the better.
My approach is to cover all bases by ruthlessly analyzing and construct as flawless solutions as possible, with contingencies in mind as insurance against failure. My paranoia disorder tends to make me think like that. :zoinks:
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I gave a definite correct answer. You're not reading what I wrote.
Q:Who are the togglers?
The truth teller can only answer, everyone but himself. This identifies him as the truth teller.
The truth telling toggler must include himself in the answer. This identifies the truth teller.
They lying toggler can only name the truth teller as a toggler. This identifies the truth teller.
Only one question is needed.
But there are no truthtelling togglers. They run on a pattern of lie/truth/lie, or vice-versa. So if their first answer is a lie, there is only one truth, and that comes from the truthteller. AAll the rest thus have to be winnowed out with a second question.
Say I asked you, are you a toggler? Your answer would be no, but the others are. If you are the truthteller, that still doesn't give me the information I need, because you could be a toggler lying. If you are a toggler lying, then you are hardly going to say the truthteller is the truthteller because you will admit you are lying. So a toggler will never say yes to that question, because they will be causght out. Problem ther is that if you only have one shot at asking the question, then finding the truthteller first go is like looking for a needle in a haystack. You have to assume they are all telling the truth, and then ask for clarification. Can't be done any other way, I'm afraid.
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Yeah. Thinking you're trolling me again. It's in plain black and white. Toggler, whether telling the truth, or telling a lie, identifies the truth teller. It's simple. The question isn't are you a toggler, but who is a toggler/ who are the togglers.
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Yeah. Thinking you're trolling me again. It's in plain black and white. Toggler, whether telling the truth, or telling a lie, identifies the truth teller. It's simple. The question isn't are you a toggler, but who is a toggler/ who are the togglers.
No, you said the question is 'are you a toggler?'
Even the question 'who is/are the toggler(s)?' won't give you the answer you want on the fiirst question.
Why do you accuse trolling when someone disagrees with you?
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Yeah. Thinking you're trolling me again. It's in plain black and white. Toggler, whether telling the truth, or telling a lie, identifies the truth teller. It's simple. The question isn't are you a toggler, but who is a toggler/ who are the togglers.
Even the question 'who is/are the toggler(s)?' won't give you the answer you want on the fiirst question.
It depends on how a lying toggler answers. If he's going to be completely lying, then yes, one question only is needed. If he's going to mention himself as a toggler along with the Truthteller, then yes it becomes a problem.
Both of you are right.
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Yeah. Thinking you're trolling me again. It's in plain black and white. Toggler, whether telling the truth, or telling a lie, identifies the truth teller. It's simple. The question isn't are you a toggler, but who is a toggler/ who are the togglers.
No, you said the question is 'are you a toggler?'
Even the question 'who is/are the toggler(s)?' won't give you the answer you want on the fiirst question.
Why do you accuse trolling when someone disagrees with you?
Like I said, not reading my posts. My first correct solution was to ask, are you a toggler. This required two questions. I've since come up with a better quesiton which requires no second question, and that question is who are the togglers. On the assumption of full truth and lie. My answer is correct. Not thinking you disagree, but aren't reading.
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You know, I love this thread, nice thinking exercise. But I think it was fluke that I solved it because usually I'm supposed to suck at brainteasers lol. :laugh:
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Yeah. Thinking you're trolling me again. It's in plain black and white. Toggler, whether telling the truth, or telling a lie, identifies the truth teller. It's simple. The question isn't are you a toggler, but who is a toggler/ who are the togglers.
Even the question 'who is/are the toggler(s)?' won't give you the answer you want on the fiirst question.
It depends on how a lying toggler answers. If he's going to be completely lying, then yes, one question only is needed. If he's going to mention himself as a toggler along with the Truthteller, then yes it becomes a problem.
Both of you are right.
Thanks.
It really is a tricky conundrum, one that can keep people going for ages.
Where did you find that one, MC?
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You know, I love this thread, nice thinking exercise. But I think it was fluke that I solved it because usually I'm supposed to suck at brainteasers lol. :laugh:
To be honest, I actually didn't expect such enthusiasm. But I'm pleasantly surprised.
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Yeah. Thinking you're trolling me again. It's in plain black and white. Toggler, whether telling the truth, or telling a lie, identifies the truth teller. It's simple. The question isn't are you a toggler, but who is a toggler/ who are the togglers.
Even the question 'who is/are the toggler(s)?' won't give you the answer you want on the fiirst question.
It depends on how a lying toggler answers. If he's going to be completely lying, then yes, one question only is needed. If he's going to mention himself as a toggler along with the Truthteller, then yes it becomes a problem.
Both of you are right.
Thanks.
It really is a tricky conundrum, one that can keep people going for ages.
Where did you find that one, MC?
Yeah, it's a brilliant exercise, isn't it? I got it from one of the brainteaser videos at Khan Academy. But even the guy speaking in the video seemed to have been confused by this problem.
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You know, I love this thread, nice thinking exercise. But I think it was fluke that I solved it because usually I'm supposed to suck at brainteasers lol. :laugh:
To be honest, I actually didn't expect such enthusiasm. But I'm pleasantly surprised.
If that were asked at WP, you'd get responses like 'what's a toggler?', 'autistics don't lie!', 'Autism Speaks will find a cure!' etc. I would say this is the thinking-persons' forum, alright.
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You know, I love this thread, nice thinking exercise. But I think it was fluke that I solved it because usually I'm supposed to suck at brainteasers lol. :laugh:
To be honest, I actually didn't expect such enthusiasm. But I'm pleasantly surprised.
It kind of pissed me off a little. :laugh:
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You know, I love this thread, nice thinking exercise. But I think it was fluke that I solved it because usually I'm supposed to suck at brainteasers lol. :laugh:
To be honest, I actually didn't expect such enthusiasm. But I'm pleasantly surprised.
It kind of pissed me off a little. :laugh:
That's what brainteasers for. ;)
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You know, I love this thread, nice thinking exercise. But I think it was fluke that I solved it because usually I'm supposed to suck at brainteasers lol. :laugh:
To be honest, I actually didn't expect such enthusiasm. But I'm pleasantly surprised.
It kind of pissed me off a little. :laugh:
Not me, I just posted a bonehead response and let the smart ones figure it out. :viking:
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Toggler. You knew the answer the whole time.
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Nah, I've never known PPK to lie, so he can't be a toggler.
Unless you're suggesting.....
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...We're all togglers?
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Well, think about it this way.
Only 5 have posted here in this thread. This matches the number of the 5 men in that riddle.
Therefore, four of us are Togglers and one of us is the Truthteller.
The question is ... who's who?
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This thread is Aspie gold :thumbup:
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...We're all togglers?
The truth hurts. :agreed:
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This thread is Aspie gold :thumbup:
Sure is.
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This thread gave me a headache.
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This reminds me of a similar brain teaser.
You die and you're standing between the gates of heaven and hell. The gates are identical and they are guarded by identical looking angels. One angel is a good angel who only tells the truth, the other is a bad angel who only tells lies.
In order to get to heaven, you're only allowed to ask one question to one angel. What question do you ask to guarantee that you make it into heaven??
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This reminds me of a similar brain teaser.
You die and you're standing between the gates of heaven and hell. The gates are identical and they are guarded by identical looking angels. One angel is a good angel who only tells the truth, the other is a bad angel who only tells lies.
In order to get to heaven, you're only allowed to ask one question to one angel. What question do you ask to guarantee that you make it into heaven??
Ask either angel, "What door would the other angel tell me was Heaven's door?" Then take the other door than the one indicated. If you ask the bad angel what door the good angel will point to, he will point to Hell's door. If you ask the good angel which door the bad angel would point to, he will point to Hell's door.