Mimi - Ch. 11 - Two Guards Riddle.
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This could be read as guy 2 crying because he's happy and guy 1 is a liar or guy 1 tells the truth and guy 2 is devastated
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I pray that my subconscious mind recalls this tactic the next time I encounter the 2 guard problem in D&D
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If anyone is interested about this scenario, it is solvable with discrete maths (propositional logic). The correct answer is to ask "what would the other guard say is the right door?" and then pick the opposite door. The reason for this is that one will lie about the truth whereas the other will truthfully tell a lie.
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The whole class of logic puzzles are sometimes known as "Knights and Knaves", and was originally made up by a mathematician, and thus traditional "correct" answers delve into abstract/Boolean logic, matrices, and enough double negatives that any non-mathematician guard would likely be confused by the "correct" answer.
But I am an engineer; I don't care that it's apparently heretical to ask physical or practical questions. You know, things that could solve the simple form of the puzzle unambiguously, (even if limited to yes/no questions) such as, "Is the sky blue?", "Am I holding up three fingers?", or "Am I a tree frog?".
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well making questions that determine which guard is the lying one is trivial, but then you have used up your question and can't ask about which door is the correct one
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The most familiar format allows you to ask each guard one question; it doesn't necessarily have to be the same question. If it does, then honestly, you've picked your route poorly.
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but then it's not a riddle or puzzle at allThe most familiar format allows you to ask each guard one question; it doesn't necessarily have to be the same question. If it does, then honestly, you've picked your route poorly.
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can you just ask one guard "am i alive" and if they say yes theyre telling the truth and if they say no theyre lying?
No, the most familiar format only lets you ask one single question to both guards. Precisely because if you can ask two questions, then there’s no challenge, as is obvious to anyone with an IQ above room temperature.The most familiar format allows you to ask each guard one question; it doesn't necessarily have to be the same question. If it does, then honestly, you've picked your route poorly.
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Honestly based, get that bag so you don't have to sell the feet pics from the last chapter
Identity theft not doxxing
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I feel like this premise doesn't work when the guards have to explain the premise to the person solving it.
If the guard who always tells the truth is explaining the whole premise, then you already know which guard tells the truth because they explained the puzzle. If the guard who always lies is explaining the whole premise, then the premise is itself is a lie, and therefore, this is not at all the premise of what you're supposed to be solving for and that defeats the point of explaining the premise, which means the guard who is explaining the premise has to be the one telling the truth, or the logic puzzle doesn't work because the explanation is a lie.
In the case of the comic here, it doesn't work with one guard saying "one of us, only tell lies" and the other guard saying "the other only tell truth" because it subverts its own logic; both those can't be true statements because one of the guards has to tell only lies, meaning you have to decipher which of those statements—"one of us only tells the lies" and "the other one always tells the truth"—is the lie. Except this creates a paradox or a breakdown of the premise, because if "one of us only tells lies" is a lie, then that means either both or neither of them only tells lies—the "lies" portion itself can't be the lie, because that would mean one of them always tells the truth, which would still be a truth within the premise the speaker is trying to construct and therefore not a lie, and the "always" part can't be the lie because then that means one of them either "sometimes" or "never" tell lies, in which case the former renders the entire premise useless and the latter loops back around to it not longer being a lie because "never lies" is the same as "always tells the truth"; in the case of both of them only tell lies, "the other only tells the truth" itself is a lie when taken in conjunction with "one of us only tells lies" because it keys off the first guard breaking them up into a dichotomy, and you can't have an "other" without the dichotomy—unless you're going for a really pedantic "one of us always tells lies, and the other [also] always tells lies" kind of setup, and if "always" is the part of the sentence that is a lie, then the other guard either "sometimes" tells the truth or "never" tells the truth, and we loop back around to "sometimes" being useless as part of a logic puzzle and "never tells the truth" looping back to "only lies"; if the lie is that neither guard lies, then it immediately contradicts itself because for the statement "one of us only lies" to be a truth, one of the guards has to lie, and if both guards aren't liars, then that makes the statement "one of us only lies" is itself a lie.
Basically:
Essentially, this logic puzzle only works if its explained by a trustworthy external source and not by the guards themselves.
If the guard who always tells the truth is explaining the whole premise, then you already know which guard tells the truth because they explained the puzzle. If the guard who always lies is explaining the whole premise, then the premise is itself is a lie, and therefore, this is not at all the premise of what you're supposed to be solving for and that defeats the point of explaining the premise, which means the guard who is explaining the premise has to be the one telling the truth, or the logic puzzle doesn't work because the explanation is a lie.
In the case of the comic here, it doesn't work with one guard saying "one of us, only tell lies" and the other guard saying "the other only tell truth" because it subverts its own logic; both those can't be true statements because one of the guards has to tell only lies, meaning you have to decipher which of those statements—"one of us only tells the lies" and "the other one always tells the truth"—is the lie. Except this creates a paradox or a breakdown of the premise, because if "one of us only tells lies" is a lie, then that means either both or neither of them only tells lies—the "lies" portion itself can't be the lie, because that would mean one of them always tells the truth, which would still be a truth within the premise the speaker is trying to construct and therefore not a lie, and the "always" part can't be the lie because then that means one of them either "sometimes" or "never" tell lies, in which case the former renders the entire premise useless and the latter loops back around to it not longer being a lie because "never lies" is the same as "always tells the truth"; in the case of both of them only tell lies, "the other only tells the truth" itself is a lie when taken in conjunction with "one of us only tells lies" because it keys off the first guard breaking them up into a dichotomy, and you can't have an "other" without the dichotomy—unless you're going for a really pedantic "one of us always tells lies, and the other [also] always tells lies" kind of setup, and if "always" is the part of the sentence that is a lie, then the other guard either "sometimes" tells the truth or "never" tells the truth, and we loop back around to "sometimes" being useless as part of a logic puzzle and "never tells the truth" looping back to "only lies"; if the lie is that neither guard lies, then it immediately contradicts itself because for the statement "one of us only lies" to be a truth, one of the guards has to lie, and if both guards aren't liars, then that makes the statement "one of us only lies" is itself a lie.
Basically:
Guard A says "One of us only tells lies".
Guard B says "The other only tells the truth".
Guard A's statement can either be true, or be a lie, and in the case of the latter, there's three places where it can be a lie: "one", "only" and "lies". The truth behind "one" can be "both" or "neither", the truth behind "only" can be "sometimes" or "never", and the truth behind "lies" is "the truth".
In the case of "Both of us only tells lies" being the truth behind Guard A's lie, you're creating a situation where A&B both have to lie. However, for that to work, then "The other only tells the truth" has to contain a lie, which has to once again either be at "other", "only" or "truth". For "other" to be a lie, that would mean "the same guard only tells the truth", which is paradoxical because a guard who always lies can't also always tell the truth"; for "only" in Guard Be's statement to be the lie, it has to mean "sometimes" or "never", and we can reject "sometimes" because it turns the logic fuzzy, and "the other never tells the truth" creates a linguistic problem because Guard A's truth behind the lie already created a set that includes both guards already not telling the truth, so who is this "other" guard who isn't included in the set of both guards who also doesn't tell the truth?
In the case of "neither of us only tells lies" to be the truth behind Guard A's lie, you fall into the trap of meaning either "both of us sometimes tells lies", which creates a fuzzy answer problem, or "both of us only tells truths", which is self-contradictory with statement "one of us only lies", because the same person can't be both always lying and always telling the truth at the same time.
For "only" to be Guard A's lie, that has to become either "sometimes" or "never", and "one of us sometimes tells lies" wrecks the entire premise of the puzzle by making whether the answer to a question is a lie or the truth fuzzy (and we should just rule out the use of "sometimes" as the lie replacing "only" in any statements because it makes the entire logic puzzle fuzzy)
, while "one of us never tells lies" is essentially, "one of us only tells the truth", which, when taken in conjunction with "the other only tells the truth", creates a situation where both tells the truth, which then contradicts Guard A's lie of "one of use only tells lies" being the truth, because it can't be both a lie and the truth at the same time.
In the case of "one of us never tells lies" being the truth behind Guard A's lie, that's paradoxical because it'd have to be a true statement when taken in conjunction with Guard B's "the other only tells truths" create a set where both guards only tell teh truth, except Guard A would be paradoxically lying about lying. Likewise, in the case of "one of us only tells the truth" being the lie behind Guard A's statement, it creates a paradox with Guard B's statement where they assert the "other" guards also tells the truth, which means, if Guard A is the liar, then Guard B's statement becomes a lie because it asserts that both guards ("one" and "the other") are both telling the truth.
In the cases of "both of us only tells the truth" and "neither of us only tells the truth" being the truth behind the lie, it becomes a paradoxical statement because the former is self-contradictory, and the latter is contradicted by Guard B's true statement of "the other only tells the truth".
If Guard A is telling the truth and Guard B is lying, then some or all of "the other always tells the truth" has to be a lie, and the only places where the lie in the sentence can be is "other", "only" or "truth". We can immediately rule out "other" as the lie, because the only thing that leads to is "same", and then it becomes paradoxical with the truths being Guard A's being "one of us only lies" and Guard B's being "the same only tells the truth".
If we substitute "never" for "only", then we get Guard A's truth of "One of us only lies" and Guard B's truth of "the other never tells the truth", which creates a set where both guards are lying, but that would contradiction Guard A telling the truth. Likewise, if we substitute "lies" for "the truth", then we get "One of us only tells lies" and "the other only tells lies", which again leads us to a situation where a set of two liars is created, which contradicts Guard A telling the truth.
Essentially, the only way this logic puzzle can work if the guards are explaining the premise is if the truth within is "one guard only lies, the other sometimes tells the truth" or "one guard sometimes lies, and the other always tells the truth", but then you've got a logic puzzle that can't be solved with just one question.
Guard B says "The other only tells the truth".
Guard A's statement can either be true, or be a lie, and in the case of the latter, there's three places where it can be a lie: "one", "only" and "lies". The truth behind "one" can be "both" or "neither", the truth behind "only" can be "sometimes" or "never", and the truth behind "lies" is "the truth".
In the case of "Both of us only tells lies" being the truth behind Guard A's lie, you're creating a situation where A&B both have to lie. However, for that to work, then "The other only tells the truth" has to contain a lie, which has to once again either be at "other", "only" or "truth". For "other" to be a lie, that would mean "the same guard only tells the truth", which is paradoxical because a guard who always lies can't also always tell the truth"; for "only" in Guard Be's statement to be the lie, it has to mean "sometimes" or "never", and we can reject "sometimes" because it turns the logic fuzzy, and "the other never tells the truth" creates a linguistic problem because Guard A's truth behind the lie already created a set that includes both guards already not telling the truth, so who is this "other" guard who isn't included in the set of both guards who also doesn't tell the truth?
In the case of "neither of us only tells lies" to be the truth behind Guard A's lie, you fall into the trap of meaning either "both of us sometimes tells lies", which creates a fuzzy answer problem, or "both of us only tells truths", which is self-contradictory with statement "one of us only lies", because the same person can't be both always lying and always telling the truth at the same time.
For "only" to be Guard A's lie, that has to become either "sometimes" or "never", and "one of us sometimes tells lies" wrecks the entire premise of the puzzle by making whether the answer to a question is a lie or the truth fuzzy (and we should just rule out the use of "sometimes" as the lie replacing "only" in any statements because it makes the entire logic puzzle fuzzy)
, while "one of us never tells lies" is essentially, "one of us only tells the truth", which, when taken in conjunction with "the other only tells the truth", creates a situation where both tells the truth, which then contradicts Guard A's lie of "one of use only tells lies" being the truth, because it can't be both a lie and the truth at the same time.
In the case of "one of us never tells lies" being the truth behind Guard A's lie, that's paradoxical because it'd have to be a true statement when taken in conjunction with Guard B's "the other only tells truths" create a set where both guards only tell teh truth, except Guard A would be paradoxically lying about lying. Likewise, in the case of "one of us only tells the truth" being the lie behind Guard A's statement, it creates a paradox with Guard B's statement where they assert the "other" guards also tells the truth, which means, if Guard A is the liar, then Guard B's statement becomes a lie because it asserts that both guards ("one" and "the other") are both telling the truth.
In the cases of "both of us only tells the truth" and "neither of us only tells the truth" being the truth behind the lie, it becomes a paradoxical statement because the former is self-contradictory, and the latter is contradicted by Guard B's true statement of "the other only tells the truth".
If Guard A is telling the truth and Guard B is lying, then some or all of "the other always tells the truth" has to be a lie, and the only places where the lie in the sentence can be is "other", "only" or "truth". We can immediately rule out "other" as the lie, because the only thing that leads to is "same", and then it becomes paradoxical with the truths being Guard A's being "one of us only lies" and Guard B's being "the same only tells the truth".
If we substitute "never" for "only", then we get Guard A's truth of "One of us only lies" and Guard B's truth of "the other never tells the truth", which creates a set where both guards are lying, but that would contradiction Guard A telling the truth. Likewise, if we substitute "lies" for "the truth", then we get "One of us only tells lies" and "the other only tells lies", which again leads us to a situation where a set of two liars is created, which contradicts Guard A telling the truth.
Essentially, the only way this logic puzzle can work if the guards are explaining the premise is if the truth within is "one guard only lies, the other sometimes tells the truth" or "one guard sometimes lies, and the other always tells the truth", but then you've got a logic puzzle that can't be solved with just one question.
Essentially, this logic puzzle only works if its explained by a trustworthy external source and not by the guards themselves.
It's not usually framed like that. The rules are either just given to you, or they only apply to the question you ask them. Presumably the lying guard isn't only telling lies 24 hours a day 7 days a week.
Also you are usually only allowed to ask a question to one guard, not one to each be it the same question or a different one, but the manga slightly bends the rules for the comical effect.
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Usually, the rules are given to you by an outside, objective, truthful party. It doesn't work when the person telling you is one of the guards and they also tell you that one of the guards always lies.
As for the latter part, I've only really heard of the puzzle as "you may ask one question" with the implication that both guards will answer that one question, not that you can ask one guard one question and the other won't answer.
Well, the origin is a mathematical riddle, usually presented to children, and it's solvable by just asking a single guard. In fact both guards answering the question doesn't help you at all: for any good solutions both guards answer will have to be the same.
Also, probably the most famous movie that includes this puzzle is 1986's Labyrinth, where the guards do tell Sarah the rules, and she can only ask one of them, so there you have it. The clip (and the movie) is on Youtube.
