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@arthur-godart when modern mathematicians say "category", they usually refer to the mathematical object studied by category theory. BCT is the only big result that use the word in its normal sense. (Category theory didn't exist back then)
At 3:40 the texts are backwards, as the person who is answering the phone is the same as the person who they are responding to, unless they each randomly decided to name you as themselves in their contacts.
Nothing is more devastating than when you're watching a (g+)+ video, at some point you think "Wait, but isn't that...", and immediately get hit with the *HELLLL NAWW TO THE NAW NAW NAW.*
Just wanted to say this is extremely well made, in particular the hints and pushes to solve the problem for yourself and spend time thinking about it - looking at easier analogous problems and showing how someone solving the problem might come across a solution all make this a really well made video!
there's a far easier solution, just ask: "hey there" * 10,000 + "what is your job?" this way, they will have sobered up by the time you get to the actual question and will just answer normally...
@@SheafificationOfG LOL :D since they need to be perfectly logical to respond to any question we ask them, they will be able to work out that your suspiciously specific phrasing is indicative of you not knowing their names as well! the only real solution is to get them even drunker so they slip up...
Interesting bonus puzzle, I've never heard that variation before! Naively I'd assume that 5 is the best possible since there are 24 permutations of alice, bob, charlie, and dan being the mathematician, physicist, and philosopher. However, there are two complications that I see: 1. If we're concerned about the truth values of the statements, the set of logical operators needed to formulate those questions to extract useful information may not admit an injective function to the set of possible questions one can phrase under the established rules. Thus we might need strictly more than 5 questions. 2. If we consider just the case where there is no obsfucation with foos and bars and such, it might be possible to extract more than 1 bit of information out of each question since excluded middle is no longer excluded. It might make more sense to consider "tribits"(ternary bits) in which case, 3 tribits would be enough. However, while I find it hard to believe that 3 is actually possible, but I'm not convinced that 4 is impossible. The combination of both will make this a fun way to spend an evening or two when I have time!
The reason I don't think 3 is possible is the following example: There are 4 people. The mathematician answers "Yes" or "No" truthfully. The physicist answers "Yes" or "No" untruthfully. The engineer randomly answers "Yes" or "No". (But not idk) The philosopher answers "idk". In this case, if we ask Alice a question and we get the answer "idk", then the problem is reduced to the intermediate one with no additional information, and so we need at least another 3 questions, for a total of 4. If we allow the engineer to answer "idk" as well, then because they can answer adversarially, then they can simply choose to never answer "idk" and reduce the problem to the one described above. Thus, with no obfuscation of the responses, then we need at least 4 questions, and adding the obfuscation cannot reduce the amount of questions we would need, since we could simply apply discard the meaning of the responses "yes", "no", and "idk" and apply the strategy for the obfuscated answers. Thus I believe this proves at least 4 questions are needed. (Technically there are gaps but I think the argument is sound and just needs fleshing out)
@@spinachstealer If the word used by the philosopher is known, then we only need 6 questions (unfortunately, we’re a bit short of needing only 5). For example, if we know that U = Baz, then we first ask Alice: Would you answer “Foo” to “Is Bob or Charlie an engineer?” * If Alice answers “Foo”, then one of A, B, or C is an engineer, and Alice is not a philosopher. We can then ask Dan: Would you answer “Foo” to “Is Bob a philosopher?” This identifies either B, C, or D as the philosopher. We can then ask Dan whether Alice is an engineer and whether he is a mathematician. The only exception is when Dan is the philosopher, in which case we don’t have anyone known to be neither an engineer nor a philosopher. In that case, we actually need to ask 5 questions. * If Alice answers “Bar”, then either A or D is an engineer, and Alice is not a philosopher. We can then ask Bob: Would you answer “Foo” to “Is Dan a philosopher?” If Bob answers Foo, then Dan is the philosopher and Alice is the engineer, and we can ask one more question to identify B and C. Otherwise, we have identified either B or C as the philosopher and can ask the other person to identify the other people. * If Alice answers “Baz”, then she is either the engineer or the philosopher. Ask Bob: Would you answer “Foo” to “Is Charlie or Dan an engineer?” If Bob answers Foo, then either B, C, or D is an engineer and Bob is not a philosopher, and we can continue in a similar manner as if Alice had answered Foo initially. If Bob answers Bar, then either A or B is an engineer and B is not a philosopher, and we can continue in a similar manner as if Alice had answered Bar initially. If Bob answers Baz, then he is either the engineer or the philosopher. In that case, we can ask either C or D two questions to determine which of A and B is the engineer and which of C and D is the mathematician.
I haven't watched the video yet, trying to work through the puzzle myself. And I think I've found a problem. Suppose I ask A "If I were to ask B , would they answer foo?" If A would be the random person, they would respond with foo or bar. If B would be the random person, then A couldn't respond with foo or bar, because doing so would imply that A can predict the randomness of B.
You are definitely right that there is ambiguity in what should happen in this case! Per the implementation, if you asked the mathematician what the engineer would say, the mathematician will make their best guess (e.g. the mathematician's response will be based on a random choice of response from the engineer).
I'm moderately suspicious that a highly drunk mathematician, physicist, and engineer would all be able to keep their own foo/bar mappings straight, or be able to remember that one of the other two is using the opposite mapping.
Due to the Pauli exclusion principle, the states of the mathematician and physicist are forced into entanglement - they're forced to be opposites. The engineer, by definition, has a brain with so few neurons as to only be capable of producing uniformly distributed random answers
simple, ask what is the value of pi. If they say 3, they are engineerings. If they say 3.14... to 14 decimal places then is a physicist because "the result will work for the radius of the universe". If they write an infinite series, they are mathematicians
6:51 I think I found a way to get the correct answer by asking two questions Question 1: Determines is he a Knight or a Knave? The question which I will ask is something which is a universal fact and everybody agrees upon. Just for the sake of argument let the question be "Is water a universal solvent?" The Knight will say Yes while the Knave will say No. Now, that we know who we are dealing with could be a Knight or a Knave we can Easily determine which gate leads to which. My thinking was to ask a question on which both of them don't agree on!
I love how accurate is the convention. As engineer studant, it's hilarious how each field has their own notation on things that really would make everyone's life easier if it was just consistent. Is 0 a natural number? Please, let's just agree to say yes and just define N* as naturals without zero. Imaginary unit? Tough one, just make clear what is the imaginary unit in the beginning and roll with it.
I would love to see an information theory video or article on the tiktok challenge thingy with the 5 colored balls and you guess the color of each ball and then they tell you how many correct you have. (PLEASE)
Are you talking about the game Mastermind? That is also a guessing game of balls of different colors, and the code-maker (or computer) responds to your guess with a black peg for each correct color in correct place, and a white peg for each correct color in incorrect place. (This video made me think of that game too!)
Something a little interesting. You said your solution to the challenge uses 7 questions and fully determines the system. There are 4!*3! = 144 possible configurations of the fields and responses, and 7 bits would have 2^7 = 128 possibilities. So your 7 question solution actually gets a little more than 1 bit worth of information per question. Which can make sense given that there are up to 3 possible responses per question.
I feel so happy with myself that I was able to solve the knight and knaves question. I ended up solving it with a truth table, but had a really convoluted question that is ultimately equivalent to the question given in the video (parenthesized for readability): not (are you guarding the castle xor (are you a knight or a knave))?. The second part is just a convenient way of expressing something that is always true. (maybe my logic class is rubbing off on me with silly logic speak).
10:30 why would asking politely change the result? Holding a Red Flag up and asking the Knave "would you say this is red?" should never result in a "Yes" (feels like the words receive some extra portion of logic operators) isn't the usual way to "solve" this to ask: "would the other guy say Left leads to the Castle?" -> if Left leads to the Castle, asking the Knight would result in "No" (as the Knave asked directly would lie to you) -> if Left leads to the Castle, asking the Knave would result in "No" (as the Knight would tell you Yes, but the Knave lies about that result) -> Right Castle, asking Knight results in "Yes" (as the Knave asked directly would tell you "yes, left leads to the castle" which is a lie) -> Right Castle, asking Knave results in "Yes" (as the Knight would tell you No, but the Knave lies about that result ) So, Yes -> Right Castle, No -> Left Castle this way you use the negation in the behavior to streamline the results and not interpret a politely asked question differently than a normally asked one. Edit after writing the comment below this one, the key is not the "Would you" the key is to map the "true/false" result into the question: So instead of "would *you* say Left leads to the Castle?" we have to ask "would you answer 'Left leads to the Castle' with True". this makes the asked person evaluate "left leads to the castle" first and then compare that to "True" -> Left Castle, asked Knave -> LLTTC would be answered with False, False==True? -> Result: True (as he lies about it) -> Left Castle, asked Knight -> LLTTC would be answered with True, True==True? -> Result: True -> Right Castle, asked Knave -> LLTTC would be answered with True, True==True? -> Result: False (as he lies about it) -> Right Castle, asked Knight -> LLTTC would be answered with False, False==True? -> Result: False
For some reason, I had a lot of trouble understanding this video. I felt like the concepts made sense and were also stupidly simple, but it was damn near impossible to manipulate them in my head or check whether your manipulations made sense. I paused for so long staring at the screen and I just felt like a helpless large language model who could never learn and apply novel systems without training on them properly. I just woke up after having a really runny nose and didn't eat much so maybe that's why Yeah I just tried playing a game and I completely lost my edge, so that pretty much confirms I can't think properly. Since I won't remember the solution though, I'll try and figure it out for myself later after I have some decent food
Another way to think about xor is identity, like if a implies b and b implies a, they might as well be the same thing, meaning we could ask "is the knight guarding the castle" Knight/castle: yes Knave/castle: yes Knight/dungeon: no Knave/dungeon: no And, likewise, "is the mathematician a Foo Truther?" Math/Foo: Foo Math/Bar: Foo Phys/Foo: Bar Phys/Bar: Bar
My question for the simple form was to ask Alice "Will Bob say Foo if I ask Bob whether Alice studies Mathematics", I think it works the same in that Foo/Bar become irrelevant
I think I figured out a simpler question for the easy mode. If you ask either of them the question "Would the Mathematician between you two say 'Foo' to mean 'Yes'?", then the Mathematician will always say Foo and the Physicist will always say Bar, allowing you to much more easily determine their fields. There are two cases: The Mathematician uses 'Foo' for 'Yes', thus The Mathematician wants to say 'Yes', so they say 'Foo' and The Physicist wants to say 'Yes', so they say 'Bar'. or The Mathematician uses 'Foo' for 'No', thus The Mathematician wants to say 'No', so they say 'Foo' and The Physicist wants to say 'No', so they say 'Bar'. Of course, this isn't as powerful as being able to completely negate Foo and Bar, like the nested question in the video, but it's still a neat solution to the simpler problem.
The timestamp is 8:55. Also, rewatching it, I realize you could also say “either … or …” instead of “… if and only if …” and it would sound completely normal.
My teacher sent me this video and told me to watch it as an introductory course to logical problems. Very good, really enjoyed the humor you put in to satisfy my ADHD brain! However, when I saw the challenge version I immediately thought his idea of an "introductory course" was asking me to solve the challenge version in a week and that *did* give me a slight panic attack. Great video though!
The equivalence of the knight-knave riddle to the simple question makes me wonder - can the original problem be rephrased in terms of three doors you must identify in three questions, with a knight, a knave, and a joker who answers randomly? It's pretty easy to identify a non-joker in one question via the method in the video ("If I were to ask you (guard A) if guard B is a joker, what would you say?") but that leaves two questions to nail down six possibilities, so that doesn't work.
You can! The goal isnt to identify the full permutation of 6 in that case, but just to locate the single safe path. In that case, after finding a non-joker you ask them "Is A safe?" and "Is B safe?" Then you know which path is safe without fully determining the system.
@@spinachstealer That does work, but I'm wondering if there's a way to identify all three doors. If there is, the answer to the first question would have to have some door-related info, although I'm not sure how that could be captured with non-joker-related info as well.
That indicates we need at least 5 questions if we assume every question gives at most 1 bit worth of information regarding who has what job, but it doesn't prove it is actually doable with 5 questions.
I think I can prove it at least confidently say that 6 is the lower bound for the challenge (i do not have an example for it). That is because by knowing who the philosopher is we will (most likely) know what is the word for idk, therefore we already need to be able to tell 72 cases apart instead of 24. Moreover we can divide by 3 only once bc in one assumption we know what means idk and then only yes/no answers are meaningful, and in the other assumption we know what doesn't mean idk and then even learning what idk means would bring uncertainty about answers from 4 to 2. Sadly i can't do it rigourously
20:10 I am just left wondering how you knew it was a knave, as your solution to the Knights and Knaves problem didn't require you to distinguish between them
1:11 is that notation a physics thing?? I've been seeing it in placed and getting very confused about the intended meaning. The picture here seems to suggest it's alternate notation for measures? I'd appreciate a thorough explanation (note that I'm not well-versed in measure theory, I've only heard about it a little).
is the knave/knight solving question really the solution though? if i asked the knave that, and he *was* giarding the castle, would he not just lie and say no? i thought the solution involves asking one of the guards about the other guards.
The point is to get them to answer two questions in one. truth + truth = truth, while lie + lie = truth, so you get the truth either way. It's a double negative
Hello, this video could actually be legit, solving every logical problems if you make another video about "The Hardest Logic Puzzle Ever" by the American philosopher and mathematician George Boolos.
Haven’t given this much thought but for the “Knight and Knave” problem wouldn’t asking about any factual statement in addition to whether they are guarding the castle give the correct answer? Say “2+2=4” which the knight says yes to and the knave no. Then if the knight is guarding the castle he says yes, if not no The Knave if guarding the castle would say yes because of inverting the logic So the one that says yes is guarding the castle. I suppose it makes the puzzle much more interesting if you limit questions to be about the guards, but in principle any “P” works for the if and only if statement Very well could be wrong in my logic here, in which case please humble me.
@@pokemonrampagemake You: is 2+2=4 and are you guarding the castle? Knight, Castle: (yes and yes) => yes Knight, Dungeon (yes and no) => no Knave, Castle: !(yes and yes) => no Knave, Dungeon: !(yes and no) => yes So you get the same problem as when trying to ask a question naively. I think the problem in this case is that an answer to (A and B) doesn't bring you as much information as two separate answers to (A) and (B)
@@pmmeurcatpics Yes and no would give no for the Knave, Yes and Yes would give yes or am I missing something here. Actually maybe if the trigger for inverting the logic is the "Would you" part then you're right, but then you couldn't use the logician's "if and only if" method
@@pokemonrampagemake you're right - yes and yes gives yes, and yes and no gives no. But the knave then proceeds to say the opposite of that, so you get e.g !(yes and yes) = !yes = no
Seems fun! might try to submit something for hard mode once I'm available Edit: There's already 5 questions solution submitted :( Would still do it myself tho!
GPT o1: To Alice: "Is 'foo' one of your words for 'yes' or 'no'?" To Bob: "Is 'foo' one of your words for 'yes' or 'no'?" To Charlie: "Is 'foo' one of your words for 'yes' or 'no'?" To Dan: "Is 'foo' one of your words for 'yes' or 'no'?" Identify the philosopher as the person who responds with the third word. To Alice: "If I asked you 'Are you the engineer?', would you say 'bar'?" To Charlie: "If I asked you 'Are you the engineer?', would you say 'foo'?" Determine the engineer based on inconsistent or random answers. To the suspected mathematician/physicist (e.g., Alice): "Is 'foo' your word for 'yes'?" Identify the mathematician and physicist based on their response. done in 7?
The premise is flawed. If they're so drunk they only answer yes or no questions, they're too drunk to comprehent the complicated nested questions used in the solution
wait if you have 2 possible responses from 3 people, and your extended vesion has 3 possible responses with 4 people, can this be generalized to n possible responses with n+1 people?
Okay, here's my solution after pausing at the start 1) Ask person A: Is the answer to the question "Is person B the engineer" the same as the answer to the question "Do you mean Yes when you say Foo"? If the person does match Foo with Yes, then they would say Foo (yes) whenn person B is the engineer (since both are true). But if they match Foo with No, then they would still say Foo (no) whenn person B is the engineer (since now they are opposites). Now, if person A says Foo, you know C is not the engineer, but if they say Bar, you know B is not the engineer. This is because if A answered genuinely, you know this from the above logic. But if they were the engineer, you know both of the others are not. 2) Ask the person you now know not to be the engineer: Is the answer to the question "Is person A the engineer" the same as the answer to the question "Do you mean Yes when you say Foo"? Similar to the above, this XOR operation ensures that Foo will always count as a Yes to the first clause. And since we know this person now is not an engineer, we get a genuine answer - and now we know exactly who the engineer is. Since we knew it wasn't them, and now there were just 2 options for who it was left, we now reduce this to 1 option. 3) Ask the person you now know not to be the engineer: Is the answer to the question "Are you the mathematician" the same as the answer to the question "Do you mean Yes when you say Foo"? Now, we can use this same trick to get a genuine answer on whether they are the mathematician. With simple deduction, we now know all three identities.
About the simplified question: I never heard the solution only involving one of the guards, always both. So the solution would be "What would the other guard say if I asked him what's behind this door" and since you now have both guards (truth+lie) there is one inversion of the answer guaranteed and you just pick the other one to get to the door you asked for. Can someone please explain how the "Canadian solution" works because I can't see it working testing it myself as the liar would just... y'know lie
I can't believe there was no solution at the end of the video. Spent 1mth on this. ehh. Well here we go. Q1 gives no information (we don't know identity or meaning) Q2 gives 2 information (same as before / different from before) Q3 gives 2 information if you were unlucky and got duplicate answer from Q2, 3 otherwise but we care about worse case scenario Q4: gives 3 information as even if you got a duplicate before, asking questions in specific way circumvnts that Q5: gives 3 information Q6: gives 3 infromation 2*2*3*3*3 = 108 > 72 (4! * 3 (what philosopher says = required to find him)) 5 questions are impossible. :-( Managed to do this in 6 questions from a SAT solver, Questions are 9-10 elements long listing a lot of possible sitations that are not easily interpretable by language as a decision tree (Would you say 'baz' if #1 person is engineer and #3 person is not philosopher or #1 person is ...). I doubt there is a concise representation that allows to achieve that. There is however a solution I found that can beat the game in 5 questions but I use technique called cheating. You can ask #1: Would you say 'baz' if "#2 would say 'baz' "'if they were asked if they are an engineer'" ". If #2 is an engineer than physicist or mathematician would be unable to answer this question (they would need to say they don't know because they don't know how would engineer answer'). If they don't respond you just got extra bit of information. Chaining it to binsearch the engineer costs 2 questions this way. (+1 if you asked the engineer first or philospher first) Finding philospher takes 1 question once identity of enginer is know And finally 1 question to distinguish math vs physicist. Cheers.
You should check out the solutions submitted to the github link (or maybe even submit your own)! There are human-readable solutions that solve the puzzle in 6 questions, and less readable solutions that can solve the puzzle in 5 (without "cheating", but using SAT solvers). Also, your "cheating" technique is addressed in the README: if the mathematician is asked about the response of the engineer, then the mathematician may respond randomly (i.e. make an educated guess about what the engineer would say).
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i accidentally got the if-and-only-if solution to the simple problem by asking "would a mathematician say foo is yes" lol oops
This was explained so much better than the TedEd video and I can say I no longer have a grudge against information theory.
Thanks! All I needed was 4x the number of minutes
Legends say the drinks at the bar contained fizz and caused buzz
That snapped me backwards in time so fast
the “category (in the sense of Baire)” joke is too good to only use once
@arthur-godart when modern mathematicians say "category", they usually refer to the mathematical object studied by category theory. BCT is the only big result that use the word in its normal sense. (Category theory didn't exist back then)
At 3:40 the texts are backwards, as the person who is answering the phone is the same as the person who they are responding to, unless they each randomly decided to name you as themselves in their contacts.
Crap.... now people are going to figure out that nobody texts me (thanks for pointing that out)
@@SheafificationOfG Hope you gain friends in hyperspecific unusual ways that will cause you to never make other friends from other methods
@@trinity5893 that sounds oddly menacing
Clocking this problem as the TedEd three alien gods riddle was a strange experience
Nothing is more devastating than when you're watching a (g+)+ video, at some point you think "Wait, but isn't that...", and immediately get hit with the *HELLLL NAWW TO THE NAW NAW NAW.*
The conormal sheaf at 8:55 is the kind of deep cut meme that gives your videos that special spice.
In reality you can only guess Charlie because communication between Alice and Bob is always encrypted.
it's Shor's algorithm time
hah
Unless your name happens to be Eve
God I fucking love the word canonical
its cromulence is hard to understate
It's mathematicians' canon event
I was thinking about the riddle and came up with the idea to ask, "... xor foo means yes. "
👉 Proceeded to get roasted over logician speak.
😂 I thought the same thing. "either ... or ..." sounds ordinary enough to me, so that's an option!
Just wanted to say this is extremely well made, in particular the hints and pushes to solve the problem for yourself and spend time thinking about it - looking at easier analogous problems and showing how someone solving the problem might come across a solution all make this a really well made video!
Thank you so much! I'm glad it all came together for you.
there's a far easier solution, just ask:
"hey there" * 10,000 + "what is your job?"
this way, they will have sobered up by the time you get to the actual question and will just answer normally...
But then they'll remember that you asked, and realise you didn't know to begin with!
@@SheafificationOfG LOL :D since they need to be perfectly logical to respond to any question we ask them, they will be able to work out that your suspiciously specific phrasing is indicative of you not knowing their names as well!
the only real solution is to get them even drunker so they slip up...
@@WoolyCow they're able to work out but they won't remember.
not only the video is educational but also the comment section. You've got an amazing community ngl❤️
Interesting bonus puzzle, I've never heard that variation before! Naively I'd assume that 5 is the best possible since there are 24 permutations of alice, bob, charlie, and dan being the mathematician, physicist, and philosopher. However, there are two complications that I see:
1. If we're concerned about the truth values of the statements, the set of logical operators needed to formulate those questions to extract useful information may not admit an injective function to the set of possible questions one can phrase under the established rules. Thus we might need strictly more than 5 questions.
2. If we consider just the case where there is no obsfucation with foos and bars and such, it might be possible to extract more than 1 bit of information out of each question since excluded middle is no longer excluded. It might make more sense to consider "tribits"(ternary bits) in which case, 3 tribits would be enough. However, while I find it hard to believe that 3 is actually possible, but I'm not convinced that 4 is impossible.
The combination of both will make this a fun way to spend an evening or two when I have time!
Well, the combinatorial lower bound for the number of questiones is log_3(4!) = 3 since whe have 3 possible answers.
My gut tells me 5 is possible, and perhaps optimal.
But what do I know, I'm no logician ¯\_(ツ)_/¯
The reason I don't think 3 is possible is the following example:
There are 4 people.
The mathematician answers "Yes" or "No" truthfully.
The physicist answers "Yes" or "No" untruthfully.
The engineer randomly answers "Yes" or "No". (But not idk)
The philosopher answers "idk".
In this case, if we ask Alice a question and we get the answer "idk", then the problem is reduced to the intermediate one with no additional information, and so we need at least another 3 questions, for a total of 4.
If we allow the engineer to answer "idk" as well, then because they can answer adversarially, then they can simply choose to never answer "idk" and reduce the problem to the one described above. Thus, with no obfuscation of the responses, then we need at least 4 questions, and adding the obfuscation cannot reduce the amount of questions we would need, since we could simply apply discard the meaning of the responses "yes", "no", and "idk" and apply the strategy for the obfuscated answers. Thus I believe this proves at least 4 questions are needed. (Technically there are gaps but I think the argument is sound and just needs fleshing out)
@@spinachstealer If the word used by the philosopher is known, then we only need 6 questions (unfortunately, we’re a bit short of needing only 5). For example, if we know that U = Baz, then we first ask Alice: Would you answer “Foo” to “Is Bob or Charlie an engineer?”
* If Alice answers “Foo”, then one of A, B, or C is an engineer, and Alice is not a philosopher. We can then ask Dan: Would you answer “Foo” to “Is Bob a philosopher?” This identifies either B, C, or D as the philosopher. We can then ask Dan whether Alice is an engineer and whether he is a mathematician. The only exception is when Dan is the philosopher, in which case we don’t have anyone known to be neither an engineer nor a philosopher. In that case, we actually need to ask 5 questions.
* If Alice answers “Bar”, then either A or D is an engineer, and Alice is not a philosopher. We can then ask Bob: Would you answer “Foo” to “Is Dan a philosopher?” If Bob answers Foo, then Dan is the philosopher and Alice is the engineer, and we can ask one more question to identify B and C. Otherwise, we have identified either B or C as the philosopher and can ask the other person to identify the other people.
* If Alice answers “Baz”, then she is either the engineer or the philosopher. Ask Bob: Would you answer “Foo” to “Is Charlie or Dan an engineer?” If Bob answers Foo, then either B, C, or D is an engineer and Bob is not a philosopher, and we can continue in a similar manner as if Alice had answered Foo initially. If Bob answers Bar, then either A or B is an engineer and B is not a philosopher, and we can continue in a similar manner as if Alice had answered Bar initially. If Bob answers Baz, then he is either the engineer or the philosopher. In that case, we can ask either C or D two questions to determine which of A and B is the engineer and which of C and D is the mathematician.
@flirora ive been able to construct a solution in 5 if the philosophers word is known, but its harder when we cant identify them so easily.
I haven't watched the video yet, trying to work through the puzzle myself. And I think I've found a problem. Suppose I ask A "If I were to ask B , would they answer foo?" If A would be the random person, they would respond with foo or bar. If B would be the random person, then A couldn't respond with foo or bar, because doing so would imply that A can predict the randomness of B.
You are definitely right that there is ambiguity in what should happen in this case! Per the implementation, if you asked the mathematician what the engineer would say, the mathematician will make their best guess (e.g. the mathematician's response will be based on a random choice of response from the engineer).
so it simulates it a step by step?@@SheafificationOfG
Omg my favorite channel on TH-cam :D
I'm moderately suspicious that a highly drunk mathematician, physicist, and engineer would all be able to keep their own foo/bar mappings straight, or be able to remember that one of the other two is using the opposite mapping.
You'd be surprised what mathematicians and physicists will remember while drunk!
Due to the Pauli exclusion principle, the states of the mathematician and physicist are forced into entanglement - they're forced to be opposites.
The engineer, by definition, has a brain with so few neurons as to only be capable of producing uniformly distributed random answers
So tightly written and edited, and pithy! that it’s basically standup comedy. Superb!
simple, ask what is the value of pi. If they say 3, they are engineerings. If they say 3.14... to 14 decimal places then is a physicist because "the result will work for the radius of the universe". If they write an infinite series, they are mathematicians
14:03 This image is just too funny. But seriously, what is a QUADRUPLE integral doing there?
10:50 That made me laugh waaay more than I would like to admit... great job, love these videos!
6:51 I think I found a way to get the correct answer by asking two questions
Question 1: Determines is he a Knight or a Knave?
The question which I will ask is something which is a universal fact and everybody agrees upon.
Just for the sake of argument let the question be
"Is water a universal solvent?"
The Knight will say Yes while the Knave will say No.
Now, that we know who we are dealing with could be a Knight or a Knave we can Easily determine which gate leads to which.
My thinking was to ask a question on which both of them don't agree on!
That works for determining the desired gate with two questions. The challenge for the Knight/Knave problem however is to do it with a single question.
This reminds me of the puzzle in Boolos's book Logic, Logic, and Logic
You know the sauce!!
most useful rust program
Lmao
Violates code of conduct
the only application of rust: crappy toy projects
hi dad thanks for bringing back the milk 🙏🙏
. _ _ _
(_) | |
_ __ ___ _| | | __
| '_ ` _ \| | | |/ /
| | | | | | | | <
|_| |_| |_|_|_|_|\_\
XNOR in the wild I'm pogging
I love how accurate is the convention. As engineer studant, it's hilarious how each field has their own notation on things that really would make everyone's life easier if it was just consistent.
Is 0 a natural number? Please, let's just agree to say yes and just define N* as naturals without zero.
Imaginary unit? Tough one, just make clear what is the imaginary unit in the beginning and roll with it.
I would love to see an information theory video or article on the tiktok challenge thingy with the 5 colored balls and you guess the color of each ball and then they tell you how many correct you have. (PLEASE)
Are you talking about the game Mastermind? That is also a guessing game of balls of different colors, and the code-maker (or computer) responds to your guess with a black peg for each correct color in correct place, and a white peg for each correct color in incorrect place.
(This video made me think of that game too!)
@@ilikehandsprings Yes it's quite similar, however the location of the correct/wrong colors are not mentioned just the amount
The non canonical illustration is gold!
1:12 dx usually naturally conventionally stands for Lebesgue measure so there's nothing wrong about the second expression.
Im so immensely confused but im all here for it
The inherent problem of the setup is it expects drunk people to be able to accurately answer non trivial logical questions
this was amazing! i want more high-level math like this always. keep up the amazing quality, i know i will be seeing the next one!
> if your still here you must have liked the video and youtube has conventions for showing this
death threats in comments?
Nobody's thrown a cinder block through my window yet smh
I think a cum tribute is what he had in mind. For all we know, he is an engineer after all.
19:20 "tricking a rock to give you segfaults" lmao
Something a little interesting. You said your solution to the challenge uses 7 questions and fully determines the system.
There are 4!*3! = 144 possible configurations of the fields and responses, and 7 bits would have 2^7 = 128 possibilities.
So your 7 question solution actually gets a little more than 1 bit worth of information per question.
Which can make sense given that there are up to 3 possible responses per question.
Nice observation! One of my final questions indeed splits into 3 cases.
Great video, loved the explanation!
I feel so happy with myself that I was able to solve the knight and knaves question. I ended up solving it with a truth table, but had a really convoluted question that is ultimately equivalent to the question given in the video (parenthesized for readability): not (are you guarding the castle xor (are you a knight or a knave))?. The second part is just a convenient way of expressing something that is always true.
(maybe my logic class is rubbing off on me with silly logic speak).
Thank you ❤for the video. You are awesome teacher
Thank you!!
Sheeeeesh! This problem ALWAYS eluded me, no more!!!
10:30 why would asking politely change the result? Holding a Red Flag up and asking the Knave "would you say this is red?" should never result in a "Yes" (feels like the words receive some extra portion of logic operators)
isn't the usual way to "solve" this to ask: "would the other guy say Left leads to the Castle?"
-> if Left leads to the Castle, asking the Knight would result in "No" (as the Knave asked directly would lie to you)
-> if Left leads to the Castle, asking the Knave would result in "No" (as the Knight would tell you Yes, but the Knave lies about that result)
-> Right Castle, asking Knight results in "Yes" (as the Knave asked directly would tell you "yes, left leads to the castle" which is a lie)
-> Right Castle, asking Knave results in "Yes" (as the Knight would tell you No, but the Knave lies about that result )
So, Yes -> Right Castle, No -> Left Castle
this way you use the negation in the behavior to streamline the results and not interpret a politely asked question differently than a normally asked one.
Edit after writing the comment below this one, the key is not the "Would you" the key is to map the "true/false" result into the question:
So instead of "would *you* say Left leads to the Castle?" we have to ask "would you answer 'Left leads to the Castle' with True".
this makes the asked person evaluate "left leads to the castle" first and then compare that to "True"
-> Left Castle, asked Knave -> LLTTC would be answered with False, False==True? -> Result: True (as he lies about it)
-> Left Castle, asked Knight -> LLTTC would be answered with True, True==True? -> Result: True
-> Right Castle, asked Knave -> LLTTC would be answered with True, True==True? -> Result: False (as he lies about it)
-> Right Castle, asked Knight -> LLTTC would be answered with False, False==True? -> Result: False
The phrasing is not about being polite, it's a hypothetical
Holy shit, a video by you I actually understood!
thanks for yelling, i was cutting my cuticles instead of paying full attention to the screen, im sorry, it will happen again
For some reason, I had a lot of trouble understanding this video. I felt like the concepts made sense and were also stupidly simple, but it was damn near impossible to manipulate them in my head or check whether your manipulations made sense. I paused for so long staring at the screen and I just felt like a helpless large language model who could never learn and apply novel systems without training on them properly. I just woke up after having a really runny nose and didn't eat much so maybe that's why
Yeah I just tried playing a game and I completely lost my edge, so that pretty much confirms I can't think properly. Since I won't remember the solution though, I'll try and figure it out for myself later after I have some decent food
I felt the same way watching this, it was weird. All the words made sense individually and I got the overall picture but I still felt lost.
16:45 We live in a society.
Another way to think about xor is identity, like if a implies b and b implies a, they might as well be the same thing, meaning we could ask "is the knight guarding the castle"
Knight/castle: yes
Knave/castle: yes
Knight/dungeon: no
Knave/dungeon: no
And, likewise, "is the mathematician a Foo Truther?"
Math/Foo: Foo
Math/Bar: Foo
Phys/Foo: Bar
Phys/Bar: Bar
Took me at least 5 minutes of staring at the examples but I think I understand now
the easter eggs were crazy
These videos are so good! More puzzles please:)
My question for the simple form was to ask Alice "Will Bob say Foo if I ask Bob whether Alice studies Mathematics", I think it works the same in that Foo/Bar become irrelevant
"... and this is Dave, who stabs people who ask tricky questions"
For the challenge 3 should be possible. I’ll take another look at it tomorrow :)
I think I figured out a simpler question for the easy mode.
If you ask either of them the question "Would the Mathematician between you two say 'Foo' to mean 'Yes'?", then the Mathematician will always say Foo and the Physicist will always say Bar, allowing you to much more easily determine their fields.
There are two cases:
The Mathematician uses 'Foo' for 'Yes', thus
The Mathematician wants to say 'Yes', so they say 'Foo' and
The Physicist wants to say 'Yes', so they say 'Bar'.
or
The Mathematician uses 'Foo' for 'No', thus
The Mathematician wants to say 'No', so they say 'Foo' and
The Physicist wants to say 'No', so they say 'Bar'.
Of course, this isn't as powerful as being able to completely negate Foo and Bar, like the nested question in the video, but it's still a neat solution to the simpler problem.
God I fucking love this channel
I love these videos, keep it up. 😁
I knew you'd say "ordinary" with mathematical pain... 😅
The timestamp is 8:55. Also, rewatching it, I realize you could also say “either … or …” instead of “… if and only if …” and it would sound completely normal.
My teacher sent me this video and told me to watch it as an introductory course to logical problems. Very good, really enjoyed the humor you put in to satisfy my ADHD brain!
However, when I saw the challenge version I immediately thought his idea of an "introductory course" was asking me to solve the challenge version in a week and that *did* give me a slight panic attack. Great video though!
I spoke with your teacher, and he expects you in the top 5 of the current leaderboard by the end of the week, good luck!
This is such a good puzzle!
The answer of lower bound is 4. I have discovered a truly remarkable proof which this margin is too small to contain.
I hecking love the knave
Isn't it also important to specify that you can change your question depending on the answer from the last question?
Note: this is indeed mentioned in the readme on github
The equivalence of the knight-knave riddle to the simple question makes me wonder - can the original problem be rephrased in terms of three doors you must identify in three questions, with a knight, a knave, and a joker who answers randomly?
It's pretty easy to identify a non-joker in one question via the method in the video ("If I were to ask you (guard A) if guard B is a joker, what would you say?") but that leaves two questions to nail down six possibilities, so that doesn't work.
You can! The goal isnt to identify the full permutation of 6 in that case, but just to locate the single safe path. In that case, after finding a non-joker you ask them "Is A safe?" and "Is B safe?" Then you know which path is safe without fully determining the system.
@@spinachstealer That does work, but I'm wondering if there's a way to identify all three doors. If there is, the answer to the first question would have to have some door-related info, although I'm not sure how that could be captured with non-joker-related info as well.
i love you for including philosophy
I’m from the 5th category, “hey I’ve seen this ted ed”
That's the 4th category 😉
Heh, you plebeian. I watched a Ted-Ed Riddle 7 years ago that had this question, now before me mortal!
Nvm I forgot
@@stickpfp6347 xD
The question wasn't "how to solve"
It was how many questions you need
And I paid attention to the lecture
24
That indicates we need at least 5 questions if we assume every question gives at most 1 bit worth of information regarding who has what job, but it doesn't prove it is actually doable with 5 questions.
2hu detected, activating bestie cannon
Please can you make the bit at 16:35 ish a short/separate clip. There may come a time i need to send it to someone…
Seems someone is way ahead of us!
th-cam.com/users/clipUgkxZQjjRe8YXXaeQ5RR_Ph6LTgHow0yLU4a
I think I can prove it at least confidently say that 6 is the lower bound for the challenge (i do not have an example for it). That is because by knowing who the philosopher is we will (most likely) know what is the word for idk, therefore we already need to be able to tell 72 cases apart instead of 24. Moreover we can divide by 3 only once bc in one assumption we know what means idk and then only yes/no answers are meaningful, and in the other assumption we know what doesn't mean idk and then even learning what idk means would bring uncertainty about answers from 4 to 2.
Sadly i can't do it rigourously
A solution with 5 has already been found via computer search, though it's monstrous
@@viliml2763 oh wow, cool. I wonder where else you conserve information
20:10 I am just left wondering how you knew it was a knave, as your solution to the Knights and Knaves problem didn't require you to distinguish between them
really nice video.
If I asked you if you get this reference, would you answer “ozo”?
1:11 is that notation a physics thing?? I've been seeing it in placed and getting very confused about the intended meaning. The picture here seems to suggest it's alternate notation for measures? I'd appreciate a thorough explanation (note that I'm not well-versed in measure theory, I've only heard about it a little).
There's an issue with the PR update-scoreboard action btw!
This was inevitably going to happen. >_> I'll look into it, thanks!
is the knave/knight solving question really the solution though? if i asked the knave that, and he *was* giarding the castle, would he not just lie and say no? i thought the solution involves asking one of the guards about the other guards.
The point is to get them to answer two questions in one. truth + truth = truth, while lie + lie = truth, so you get the truth either way. It's a double negative
Hello, this video could actually be legit, solving every logical problems if you make another video about "The Hardest Logic Puzzle Ever" by the American philosopher and mathematician George Boolos.
cool vid!
it's obviously 5.5 questions for the final puzzle
can you make a web variant of this?
Haven’t given this much thought but for the “Knight and Knave” problem wouldn’t asking about any factual statement in addition to whether they are guarding the castle give the correct answer?
Say “2+2=4” which the knight says yes to and the knave no.
Then if the knight is guarding the castle he says yes, if not no
The Knave if guarding the castle would say yes because of inverting the logic
So the one that says yes is guarding the castle.
I suppose it makes the puzzle much more interesting if you limit questions to be about the guards, but in principle any “P” works for the if and only if statement
Very well could be wrong in my logic here, in which case please humble me.
That would make it two questions though, no?
@@pmmeurcatpics I mean you wouldn't ask "Is 2+2 = 4" rather you'd say '2+2 is 4 and...'
@@pokemonrampagemake
You: is 2+2=4 and are you guarding the castle?
Knight, Castle: (yes and yes) => yes
Knight, Dungeon (yes and no) => no
Knave, Castle: !(yes and yes) => no
Knave, Dungeon: !(yes and no) => yes
So you get the same problem as when trying to ask a question naively. I think the problem in this case is that an answer to (A and B) doesn't bring you as much information as two separate answers to (A) and (B)
@@pmmeurcatpics Yes and no would give no for the Knave, Yes and Yes would give yes or am I missing something here.
Actually maybe if the trigger for inverting the logic is the "Would you" part then you're right, but then you couldn't use the logician's "if and only if" method
@@pokemonrampagemake you're right - yes and yes gives yes, and yes and no gives no. But the knave then proceeds to say the opposite of that, so you get e.g !(yes and yes) = !yes = no
Seems fun! might try to submit something for hard mode once I'm available
Edit: There's already 5 questions solution submitted :( Would still do it myself tho!
GPT o1:
To Alice: "Is 'foo' one of your words for 'yes' or 'no'?"
To Bob: "Is 'foo' one of your words for 'yes' or 'no'?"
To Charlie: "Is 'foo' one of your words for 'yes' or 'no'?"
To Dan: "Is 'foo' one of your words for 'yes' or 'no'?"
Identify the philosopher as the person who responds with the third word.
To Alice: "If I asked you 'Are you the engineer?', would you say 'bar'?"
To Charlie: "If I asked you 'Are you the engineer?', would you say 'foo'?"
Determine the engineer based on inconsistent or random answers.
To the suspected mathematician/physicist (e.g., Alice): "Is 'foo' your word for 'yes'?"
Identify the mathematician and physicist based on their response.
done in 7?
6:56 deltarune
Here before this blows up
Nice video.
The premise is flawed. If they're so drunk they only answer yes or no questions, they're too drunk to comprehent the complicated nested questions used in the solution
You've clearly never hung out with drunk mathematicians and physicists before 😉
“is foo yes” also gets you the answer in the easy problem
How so? Both the mathematician and the physicist would say "foo" as a response to that question.
wait if you have 2 possible responses from 3 people, and your extended vesion has 3 possible responses with 4 people, can this be generalized to n possible responses with n+1 people?
what does it say about me that my first instinct is to generalize LMAO
the third category is satisfied
Okay, here's my solution after pausing at the start
1) Ask person A: Is the answer to the question "Is person B the engineer" the same as the answer to the question "Do you mean Yes when you say Foo"?
If the person does match Foo with Yes, then they would say Foo (yes) whenn person B is the engineer (since both are true).
But if they match Foo with No, then they would still say Foo (no) whenn person B is the engineer (since now they are opposites).
Now, if person A says Foo, you know C is not the engineer, but if they say Bar, you know B is not the engineer.
This is because if A answered genuinely, you know this from the above logic. But if they were the engineer, you know both of the others are not.
2) Ask the person you now know not to be the engineer: Is the answer to the question "Is person A the engineer" the same as the answer to the question "Do you mean Yes when you say Foo"?
Similar to the above, this XOR operation ensures that Foo will always count as a Yes to the first clause. And since we know this person now is not an engineer, we get a genuine answer - and now we know exactly who the engineer is. Since we knew it wasn't them, and now there were just 2 options for who it was left, we now reduce this to 1 option.
3) Ask the person you now know not to be the engineer: Is the answer to the question "Are you the mathematician" the same as the answer to the question "Do you mean Yes when you say Foo"?
Now, we can use this same trick to get a genuine answer on whether they are the mathematician. With simple deduction, we now know all three identities.
subbed for random french
Lol nicely made video
About the simplified question:
I never heard the solution only involving one of the guards, always both. So the solution would be "What would the other guard say if I asked him what's behind this door" and since you now have both guards (truth+lie) there is one inversion of the answer guaranteed and you just pick the other one to get to the door you asked for.
Can someone please explain how the "Canadian solution" works because I can't see it working testing it myself as the liar would just... y'know lie
The liar is lying about what the liar would say, so it gets negated twice.
Ozo.
Ulu.
this is truly one of the logic puzzles of all time 🗣️🗣️🗣️🔥🔥🔥
Aren't conjuctions a little bit more than one question?
Genie: You get three wishes. Me: ...
Not really, since you can't get the answers to the separate questions with a conjunction
I love you
though, the issue is that everyone is drunk, so I'm not sure that anyone's answer can be trusted, especially not if I ask complicated questions
I can't believe there was no solution at the end of the video. Spent 1mth on this. ehh.
Well here we go.
Q1 gives no information (we don't know identity or meaning)
Q2 gives 2 information (same as before / different from before)
Q3 gives 2 information if you were unlucky and got duplicate answer from Q2, 3 otherwise but we care about worse case scenario
Q4: gives 3 information as even if you got a duplicate before, asking questions in specific way circumvnts that
Q5: gives 3 information
Q6: gives 3 infromation
2*2*3*3*3 = 108 > 72 (4! * 3 (what philosopher says = required to find him))
5 questions are impossible. :-(
Managed to do this in 6 questions from a SAT solver, Questions are 9-10 elements long listing a lot of possible sitations that are not easily interpretable by language as a decision tree (Would you say 'baz' if #1 person is engineer and #3 person is not philosopher or #1 person is ...). I doubt there is a concise representation that allows to achieve that.
There is however a solution I found that can beat the game in 5 questions but I use technique called cheating.
You can ask #1: Would you say 'baz' if "#2 would say 'baz' "'if they were asked if they are an engineer'" ".
If #2 is an engineer than physicist or mathematician would be unable to answer this question (they would need to say they don't know because they don't know how would engineer answer'). If they don't respond you just got extra bit of information.
Chaining it to binsearch the engineer costs 2 questions this way. (+1 if you asked the engineer first or philospher first)
Finding philospher takes 1 question once identity of enginer is know
And finally 1 question to distinguish math vs physicist.
Cheers.
You should check out the solutions submitted to the github link (or maybe even submit your own)!
There are human-readable solutions that solve the puzzle in 6 questions, and less readable solutions that can solve the puzzle in 5 (without "cheating", but using SAT solvers).
Also, your "cheating" technique is addressed in the README: if the mathematician is asked about the response of the engineer, then the mathematician may respond randomly (i.e. make an educated guess about what the engineer would say).
I wish I could hit the subscribe button twice :(
anyways I'm going to try beat the hard mode high score!
(foo bar bar)th