How logical are you? A legendary experiment
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- čas přidán 16. 08. 2023
- How logical are you? This simple riddle is challenging for most people, and even mathematicians as a whole struggle to solve it.
Wason Selection Task
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Honestly I think the "90% fail this test" sentence is already a big hint that caused us to think twice about our answers, made us more careful, and raised our probability of answering correctly.
It also is a huge red flag that the problem is deliberately deceptively worded.
@@johnbreitmeier3268 ...or... That 90% of people either do not understand written text, or are not very good at logical thinking...
@@MichalMracka Yes, that would be the other "logical' conclusion, but the evidence does NOT support that one. More than half of the well trained, logical math staff and 70% of math students missed it, too. So did I who have considerable training in math and logic and ordinarily score in the high 90s on such tests. I score in the 99,9 percentile on reading comprehension. If I miss it, it IS badly written, It is a badly worded question and probably meant to be a trick question. When the same concept was tested with some practical context, the "beer question", the results were very different.
@johnbreitmeier3268 the flaw is your assertion that mathematical thinkers are inherently logical thinkers.
The rules at play are modus ponens and modus tollens. I mention them for you to investigate and verify if you disbelieve me. All "logical thinkers" immediately picked D7.
D must be checked for modus ponens conformity
7 must be checked for modus tollens conformity
The other cards are irrelevant.
This is not a poorly worded question.
For clarity, modus ponens and modus tollens are elementary rules of deductive logic. They are Day 1 of a 101 level logic course
I like these short problems! They’re not insanely complicated, and virtually anybody can complete them. It’s a brain teaser for all ages and skill levels.
Jesus loves you ❤️ please turn to him and repent before it's too late. The end times described in the Bible are already happening in the world.
at 0:47 I'm convinced the answer is every D card has to be checked. If the answer is some mathematical formula I'm going to feel some type of way.
Found out the answer and I'm glad it was not a mathematical formula. Guess I took the title a little bit too seriously.
@@L17_8 I think you might be a robot, but in case you're a human, please don't reply to a comment if you're not actually responding to the comment. My comment has nothing to to with my religion, so I'd appreciate if you'd just make your own comment instead of replying to me.
I live in a town where most people can't visually distinguish baked/roasted chicken from fried chicken, so the statistics in this video must be fake. 🤣🤣🤣
@@L17_8
yeah go back to sleep
The way to make this simple and avoid confusion is to confirm that the statement “every card has a letter on one side and a number on the other” is 100% factual. This stops people from wondering if the K card has a D on the other side
I was just about to write the two options, one assuming that -rule- statement was true and another that didn't make that assumption.
I also note it was the third most common answer among math students and math staff.
Although, the "just the D" people in those groups are still depressing. Maybe... (insert sex joke about "just the D" here.)
Edit: For the record, I did not notice the first time around that one was a flat statement and then the second statement was identified as a rule.
I still think it's not a great way to write a puzzle, but I recognize that it's... _technically_ fine.
I went back to the beginning of the video and checked that. If you follow the introduction it's 100% clear that each card has a letter on one side and a number on the other side. I wonder how the problem is usually presented in the studies. Should not be too difficult to figure out the correct answer as long as it is clear how the problem is constructed.
@@johanneschristopherstahle3395 No, it is not 100% clear.
Two rules are presented, and you're immediately told that one of them is suspect, while not being told the other one is not suspect.
Edit: Read the edit on my first comment.
@@Mythraen - I disagree with the premise of the "just the D" people.
I have seen all the varying interpretations of this, and all become valid based on assumptions.
However, in the case of the "just the D" group, this is cold, machine-level logic. If you strip all mental gymnastics and assumptions you only have "If D then 3".
Only the D card fits this explicit, cold, absolute ruling. K, 3 and 7 instantly fail the machine-logic "If D".
@@iv3nomousi That doesn't make any sense.
Your idea of cold logic ignores a logical conclusion.
So, if "cold logic" means "wrong," then... cool, I guess?
Also, that wasn't a premise.
People answer this question trying to follow the rule, instead you are trying to determine if the rule has been followed. Using logic! I like it!!
You nailed it - perfect.
The first answer was my initial answer but then I figured you need to check the K card too because if rules can be broken then it may have the letter D on the other side too. 😂
You are correct tho 🙄
No you are not correct.
Already given in the question that opposite side of alphabet is number.
You are right, it should be D, K and 7... those saying you dont check K, might as well not check D or 7 if you are just going to accept that the rules were followed. Any that works in auditing would also check K.
@@CopyCat...and it's given that D on one side requires 3 on the other. My initial answer is D7, but if the second rule can be violated why not the first? Therefore the only one you DON'T need to check is the 3, because it can have any letter or number without violating the rule. So I accept DK7 as an answer too. DK37 is just overkill.
@@Gideon_Judges6 given statement and rule are two different things.
Statement is correct always.
Rules can be violated only.
In my view the most critical skill needed for these sort of puzzles is the ability to correctly understand the task that was given to you to solve plus to be mindful not to take any additional (often hidden) assumptions that don't come straight from the task's description (e.g. those that come from common sense, education, intuition etc.). The latter is sometimes tricky as people may tend to interpret the text they read and create their own extra rules that were not included. Example: if one side of card is 3 then I need to check whether the other is indeed D (while in fact it doesn't matter what letter is there) and the hidden assumption might be that the same number will always have exact same letter on the other side.
that was a ton of words to say nothing. you said literally nothing.
@@sharpnova2But he met the point I also wanted to raise. If we wrote the initial task as "Every card D must have a 3 on the other side" I would almost immediately pick the right answer. But given it as "every D has a 3" I also tended to understand D 3 instead of D -> 3.
You're right. And the reason people make these assumptions is that everyday language is nothing like as rigorously literal as the questioners assume. That is, we often in everyday speech refer to biconditionals as simple conditionals, and words like or can be either exclusive or inclusive - such ambiguities usually being resolved in the real world by context and convention. Hence, a significant part of getting the questions right is knowing the context of these types of questions and to be just literal enough to get the gist of the question but not so pedantically literal that one sees the question makes no sense. For example, if there really is a rule that all D cards have 3 on the other side then there's no need to check any because there's a rule and a rule that isn't followed simply isn't a rule (or is it?).
That was indeed the mistake I made.
@@TheMofRider2 Why would you interpret "every D has a 3" as "every card with a 3 must have a D on the other side"?
If A then B has many different meanings in everyday speech. It sometimes means A iff B. It depends on the context. I guess this is the reason why people get confused when logical language is used in an unfamiliar situation. In a familiar situation, people seem to find correct interpretations.
Yup, the human brain automatically assumes a "just" in the sentence even if it's not there. As in "JUST the cards with a D on it have a 3 on the other"
Yes and similarly, folk use the word AND when they really mean OR. Example: "We accept payment by credit cards and cash". Two problems with that: "cards" should be singular and they probably mean or rather than and.
@@chrisengland5523Actually what they mean is they accept payment with credit cards and they accept payment with cash. They're just speaking efficiently rather than precisely, because that's how natural language usually works...
Is there actually an example of a case where "If A then B" unambiguously means "B iff A" (and it should not be "A iff B")? I suspect there's no such case, and it's just more imprecise thinking.
@@peter9477 It is in all binary cases. "The light is on if the switch is in the up position." heavily implies, if not mathematics-logically prooves that putting the switch in the down position will turn the light off...
From a QA perspective, you're also going to check the K and the 3, and then redo the test with each different possible order of turning over the cards, then put the cards away and get them out again, then leave the cards on the table overnight to check for any memory leaks.
Then the first real customer turns one of the cards sideways, and the whole deck explodes.
The only reason to check the K and 3 is to see that each letter has a number on the other side and vice versa. But if that is known to work...
Absolutely. Systematically, all cards need to be validated. We made these cards in a specific way for a specific reason and every possibility needs to be considered, even ones we find unintuitive.
just get the CI to check the cards while devs are sleeping 😴
The devs are all refusing to work with cards any more now that the dice 2.0 framework has been released. It's going to make everything a lot easier in the long run so they want to re-write the whole thing from scratch.
If only 10% of people are logical… How can society function at all?
I ask myself this all the time.
Is logic necessary to function in a well ordered society? No, obviously not. There are very few critical decisions that need to be made that also require an understanding of formal logic. And when these are necessary, one simply hires out or gets assistance. Or, of course, another option is that one just gets it wrong. The negative consequences and penalties of such errors are rarely so catastrophic that even one's neighbors or community are affected.
Perhaps the real danger to a society is the members who are so elite as to believe that only elite members deserve any care or respect - those who give up on their neighbors, ridicule and ostracize them. Now, that's a profoundly negative impact on culture.
@@rcb3921 Logics are very important in decision-making and data analyzing. The consequences of bad decisions or actions can be anywhere from very negligible to extremely catastrophic. Which means we need to have good logics to precisely analyze data and make the right decisions so we can prevent a terrible consequences and get better results.
I agree with your anti-elitism idea. It's a terrible idea to leave muscles of our society behind and go for the backbones and brains alone. Because we'll have much worse power to drive our civilization ahead or even maintaining it. Like a disabled genius, he can think a lot and make a powerful mind but incapable of taking any actions.
that is a very logical doubt.
@@rcb3921 yes to make proper orders.
It doesn't. Take a look around.
The interesting thing for me was the table of actual answers. I'd love to know the thought processes of the 9% of history students who thought that they didn't need to check D.
Maybe they were hungry and just randomly selected answers to get it over with. What was their incentive to try to get it right?
@@XJWill1 I suppose they should have had "I don't know" as an option
When people get confronted with an easy problem they get suspicious. They think they are missing the catch. So they rule out the obvious solution as a trap and resort to a more 'sophisticated' solution, even if it makes no sense. I myself was completely unsure about my solution because: Come on, this is MindYourDecisions! It can't be so trivial. I must be missing something.
Excuse me that isNOT CORRECT YOU DO NEED TO CHECK THE 3 CARD!! Because it mayy have a D or not..it doesn't say clearly whether 3 or KY appears with D or not
@leif1075 if it has the letter F, then it's ok cuz other letters can have 3, too. Rule never disallowed that.
I got this one pretty quickly, but I'm sure it helped that I was expecting it to be tricky and was looking at it extra carefully. I don't usually get your channel's puzzles so I feel good about this one 🥰
I think the 75% is very telling that we struggle with abstract logic but can handle concrete logic more. Thinking about drinking ages is a common real-world problem while arbitrary cards are not. I'm surprised that the Math Staff struggled with this, though I wonder how the Computer Science staff would do (Boolean and Truth Tables being even more prominent in that field). Either way, I'm using this for my middle school classes!
This feels related to the phenomenon of people,being generally terrible at probability, until money becomes involved in the question.
I don't think this shows a problem of logic.
It's a reading comprehension problem, or a problem of inserting own bias/assumptions.
The context of the question is important too. I didn't really think much about I first though of turning everything but then change my mind and decide than D and 3 were enough because we don't actually have any info in K and 7 and then I realized that all 3 don't have to have a D behind them so I discard the 3 and I came to the conclusion to turn over D alone . All of this in less than a minute and then I proceeded to watch the rest of the vide to see the answer. I was wrong, never considered 7 what so ever. My logic was flawed. But if it was an actual test you make seriously instead of a silly video you only think about for a minute. say... someone give you 10 minutes to think about it, you have a pen and paper and you only have to give out an answer at the end of the 10 minutes. You are not distracted by anything. In that context you may have considered possibilities you didn't consider before because you have time to do so and nothing else to do. You may still not find the right answer but more time to think of the problem may lead to better result.
One of the strongest points of humans, that distinguishes them from most other animals is the ability to think abstractly. Which basically means that 90% of people are no different from, let's say, pigeons.
I would be very scared if 10% of Computer Science fails this, but I am afraid that is also the truth.
I think a lot of these "logic problems" that lots of people get wrong aren't actually problems with logic as much as _comprehension problems._ The people simply misunderstand the stated rule(s), or misunderstand what is being asked of them.
This is not people failing at _logic,_ it is simply people who are not used to _the wording of logic problems._ This is why the second example, which works with more familiar real-world conditions, is much more successful. Most people actually can solve the _problem_ just fine, _if it is communicated in a way that they understand in the first place._
PS: At 6:23 *this video itself invokes a logical fallacy.* Just because only 10% of people get _this one particular logic problem_ correct does *not* mean that "only 10% of people are logical". It is entirely possible to be a logical person and still get one logic problem wrong (it's even possible to be an illogical person and get one logic puzzle right, for that matter). The one does not logically follow from the other at all.
Your final paragraph just states the point made by the final section of the video. You're explaining to Presh something that he clearly understands because, in the video you're commenting on, he explains it himself.
If you were right that "This is not people failing at logic, it is simply people who are not used to the wording of logic problems." then people would have the same difficulty on two versions of the problem with the same wording (but different subject matter). So the worse performance on the original Wason problem is a refutation of that.
@@MartinPoulter You've clearly missed the point I was actually trying to make, because Presh does not actually address it at all, in fact, what you claim is his addressing it is actually just doubling-down by essentially then just making the same logical mistake in the opposite direction, too.
He implies that because they can't solve the first version, they are "not logical people", but then he "addresses" that by presenting a different version which people do get more readily, and then implies that this means that they actually _are_ "logical people", but *both of these conclusions are equally wrong.* The point is that being a "logical person" and "being able to solve any particular logical puzzles" are related in some case, but _are not actually dependent on each other_ and therefore even attempting to suggest one based on the other is just _always wrong._ Whether they can solve the second form or not is actually _equally irrelevant_ to the question of whether they are "logical people" or not, so it doesn't actually "address" anything at all.
As for your second point, it is fundamentally impossible to have the same wording but different subject matter. (If it is a word problem, and the wording is exactly the same, then by definition all of the elements of the problem, including the subject matter, must be exactly the same. The only way to change the subject matter would be by changing some of the words.) Therefore your argument on that point is basically nonsense.
More specifically, in this case, the second version actually _does_ have dramatically different wording (in addition to changing the subject matter) which changes the problem to more closely resemble scenarios that most people are already used to thinking about from their daily lives, and therefore already understand intuitively. Therefore they do not need to use the wording of the problem as their sole reference for understanding the task, and will rely on the knowledge of the problem space they already know instead, which is why they are more successful (because unlike the first version, _they don't have to_ understand the words precisely to still understand the problem correctly). This actually _supports_ my point, rather than refuting it.
the question was worded very clearly, with a bunch of a cards and numbers. people get it wrong not because of a comprehension problem but because of a "can't think enough" problem. which is why they do better in the second example because the thought that a minor shouldn't be drinking comes easily, but not the thought that if the card with 7 has a D on the other side, it would break the rule.
people also fail at other similar questions like: "if 3 cats take 3 minutes to kill 3 rats, how much time will 300 cats take to kill 300 rats? people try not to think and skip a step and that's where they make a mistake. i guess the biggest logical fallacy that most people make is not thinking enough and coming to conclusions.
You are both correct. The phrasing from the first problem to the second drastically changed the wording, and there is often a "skip to the end, I've hear it before" mentality that causes mistakes.
Comprehension is a part of logical thinking. Let's start by defining what it means to be "logical." We're talking about a precise and methodical analysis of something, starting with comprehending the original state of the information we're working with and the assumptions we're given, then comprehending the task we're being asked to perform, then following those things out to the logical conclusions. Think of a computer executing a piece of code: it does so with absolute precision, doing only what you asked of it how you asked of it with a clear and repeatable result. Even if you as the programmer were intending a different result, the computer will only perform _exactly_ the task as written. That is "logical." Contrast that to how humans more commonly process information, which is with many shortcuts, relying on intuition, taking hints from preexisting assumptions and information outside of the problem. That's all well and good for what it's well and good for, but it's not representative of "logical thinking." In this case, the premise was worded precisely enough; the people who failed to comprehend it, interpreting it in a different way than precisely what was written, failed in applying logical thinking.
I think the confusing part isn't the problem and solution you describe, but that you take for granted the rule that every card has a letter on one side and a number on the other. If someone making the cards may have broken the rule D => 3, then why can't they break the rule Letter Number. The K could have a D behind it and the 7 a 2, if rules are broken, and thus all cards need to be checked. Obviously not all who got it wrong thought like this, but I'm sure it contributed to a few faulty answers.
Yeah I didn't realise the k couldn't have a d behind
I thought the same thing. To avoid this ambiguity, the problem statement needs to say categorically that the manufacturer can be trusted to have consistently made cards with a number on one side and a letter on the other.
You are absolutely correct. With the specific information provided, each card needs to be checked to make sure there is no D behind it.
Agree! This was my answer, the K needs to be turned over as well. There colors suggest that all cards have a letter on the green side and a number on the blue side, if so that needs to be stated as part of the problem.
My exact thought process. DK7. Either they can be trusted to manufacture the cards following the rules or they cannot. If the K has a D on the other side this is breaking a rule. If we're purely checking to make sure D=3 then we have to check anything that isn't 3 to confirm. Rewording the problem with the beer and coffee changes what we're looking for from the question.
I don't know, I feel that its almost like younger and normal people lack familiarity with mathematical language that causes them to fail more just because they couldn't properly wrap their head around the problem. For me the second and first problems were the same, since I just assumed that "every card has a letter on one side and a number on the other" was the premises for the problem the same way an average person assumes the premises of the problem from understanding the context of alcohol and ages.
8:10 Your right it is a skill, it allows you to abstract logic from one context to any abstract context - that's what you get if you study mathematics (or in my case, computer science). This sort of puzzle is exactly how you start to learn intuition for these sorts of concepts! I had to get this stuff from books lmao. Try to approach learning logic from a very grounded perspective - its really extremely intuitive once you get a hold of the fundamentals and the language used for mathematical abstractions.
Yeah, the existence of a letter on one side and a number on the other side of the card is meant to be a universal law within the problem, just as a rounded value of pi or assuming that air resistance doesn't exist can be.
One of the things that gets me about these sort of problems, is that the reason so many people get them wrong is that they're so divorced from the real world. In the real world, you'd check K as well. For one, if we're assuming that one rule is potentially not being followed, then it's extremely risky to assume that the other is being followed 100% faithfully. Secondly, even if the rule were being followed, there could be a misprint or any manner of other issues that could have lead to a D being printed on the back of a K card- unless you were familiar enough with the manufacturing process to rule it out as an impossibility, which we aren't.
The only reason we don't NEED to check K in this circumstance is because we're in a hypothetical question where it's impossible for K to have a D on the back. But in any real circumstance where there's a chance of error, K would also need to be checked.
I agree with adamperdue3178, if you are checking that the manufacturing is following the D->3 rule, its also logical that you are checking them to following the Letter on one side, Number on the other side rule. I would have checked the K card.
Not necessarily, because you're also making assumptions there. You could, for instance, postulate they are printed on a machine that prints both sides of the card at the same time, where the top printer only has numbers, the bottom only has letters, or one where the cards have to physically flip over with the between a printer that does letters and one that does numbers. In either case, it would be impossible to have two letters on opposite sides of the same card. Not hypothetical, by the by, as some printing processes do exactly this.
@@keith6706The thing is, if the manufacturing process makes it impossible to create errors, then we don't need to check any cards in the first place. If we assume errors are possible, we have to assume that errors are possible- unless we have concrete knowledge that one type of error is impossible while another type of error is possible, which is information that we don't have.
Also sometimes it's best practices to check for errors even if you believe a process to be impossible to cause errors. There could always be some way that it could go wrong that you didn't envision.
I also use the "if then" logic. Therefore, there are exactly two cards that are needed to be checked:
Conditional: "If the card contains D, then it has 3 on the other side". Therefore, I have to check D.
The equivalent statement with conditional is contrapositive:
Contrapositive: "If the card does not contain 3 on the other side, then it does not have D". Therefore, I have to check 7.
This felt like one of the easier problems you posted.
I still got it wrong by assumption that 3=D as well. Which makes me one of the 9/10 people who got it wrong.
Jesus loves you ❤️ please turn to him and repent before it's too late. The end times described in the Bible are already happening in the world.
@@Questerer
That wasn't an incorrect assumption.
This isn't a logic problem.
It's changing the common usage of words.
In the real world if you made this test and flipped over the 3 card and it had a D on it, would you say the rule wasn't followed?
@@hederahelix622You don't need to check 3. If the other side has D, it wouldn't disprove the rule. If the other side has any other letter, it doesn't disprove the rule.
The rule is that whenever D -> 3. That doesn't mean that whenever 3 -> D.
Cards with the same letter can have different numbers. Same goes the other way around.
@@vez3834 My point is, this is a play on words rather than a logic puzzle.
If the problem was formulated like this, would anyone make a mistake?
"The rule is that whenever D -> 3. That doesn't mean that whenever 3 -> D."
No, right?
Therefore this puzzle isn't about logic at all, its taking the normal way we use language and pretending we don't use it the normal way to confuse people.
It's not a logic puzzle at all
The reason that many more people can solve the "beer" problem is that that problem has a practical "real world" application that people can relate to. I am a 67 YO retired engineer and have taught math and math science at all levels. I have met many students that suddenly could do geometry, algebra and logic once they saw it had a purpose - estimating materials, laying out a staircase, etc. It also helps to understand the boundary conditions. There is no real reason why D should always mean 3 so we easily assume D=3 is the rule. We do grasp why a a 16 YO might not be served a beer'
If a problem is being missed by 90% of the people including this logical engineer and half of the math department, a truly logical person would conclude that it was probably very badly and deceptively worded (and perhaps deliberately so) , rather than that 90% of the people are illogical.
Totally agree. This is very common with "brain twisters" and other puzzles.
@@dermick Yep. It is totally fair game as a riddle where entertainment is the object. It is NOT a test of logic ability. For what it is worth If you rewatch the opening of the video you see the question was developed by a psychologist NOT a logician or a math guy, so it was probably intended to deceive.
I think the reason the second version is so much easier is a clearer understanding of the significance of items within the rule. Its word problem and solving them requires recognizing significant (or germane) information to develop the logic/equation.
The question here really isn't how logical you are - it is how well you pay attention to instructions. When I first heard the instruction, I incorrectly interpreted it to be a two-way relationship (3 behind the D AND D behind the 3), but that was not what the instruction actually said so I got the answer wrong.
Same
I thought about writing code efficiently (with a variable number of cards). Because it isn't code, I didn't bother checking if it was technically correct (which would be wasting time in this case).
That's called the Fallacy of the Inverse. A lot of people make that mistake.
Your incorrect interpretation to the rule is what is called being illogical. It is a logic test. It isn’t expected that every person understands the rule. Understanding the rule is part of the logic test.
Love how you just redefined what illogical means when you failed the test. Being "logical" isn't just about forming a logical conclusion, but also about properly identifying and processing premises. Your inabiltiy to do the later is a textbook example of being illogical. When you have "IF A then B", you don't get to say "well, I thought NOT B because you didn't explain A very well." Recognizing A is part of the task in forming a logical conclusion.
When you said only 10% of people correctly answer, I was a bit floored. But then I wonder if backgrounds in programming can be handy for this, as it uses Boolean style logic. I think the easiest way to approach it is to find the most sensible wording of the problem or method in your head. Such as “CAN this card fail the rule? If so, then it must be checked. If not, then move on to the next.”
See, the real problem is: is this rule an inclusive rule or an exclusive rule? As long as that is not stated at least two solutions can be reached. I would say, the people solving that riddle in the way it is explained just prove to *interpret* the phrasing exactly as the teacher wanted, nothing more.
I'm not sure what you mean by this. "Behind every D there is a 3" is perfectly unambiguous as far as I can tell. What is this supposed go be inclusive or exclusive with respect to?
@@Nuclearburrit0 but how do you know that there's always a letter on one side and a number on the other? Theoretically I could flip the K and there's a portrait of Dua Lipa printed on it. how do i know there's just blue numbers and green letters? That's your interpretation of the task no one told you.
@francojosemuertes4273 that's a different rule besides the one I said was unambiguous that was stated separately
@@francojosemuertes4273 Although I like your creativity, this puzzle has three parts:
1. An axiom about the card attributes, which are not part of the rule, there is no mention of „rule“ in that phase.
2. The rule.
3. A question about the rule.
To solve the puzzle, you are asked to answer the question regarding the rule.
I worked for years at a job where I often wrote suites of tests for rules like this that have implication operators in them (validating computerised tax forms and other financial reporting). It still took me a minute or so to work this out; I got the D straight away but had a nagging feeling that symmetry meant there was another I had to check, so I went through them all and realised the need for turning over 7, which made me say "Oh!".
I facepalmed when it was revealed I need to check the 7. It was a "DOH!" moment for me.
Awesome
same man
I find this kind of test extremely trivial with one exception. If it's certain that the first rule has been followed then you must turn all Ds and all numbers that are non-3s. However, if you specifically want to test this rule and the first rule being followed is not certain then you must turn all but three. However, if the first rule might not have been followed then you must turn all of them because that would need to be checked as well. Tests like this are vulnerable to wording and interpretation. If you don't state the precondition as a certainty then it leaves people uncertain. You know flipping all will work. You also then consider that if rule 2 might be broken why not rule 1? If you look in the results, you might see a lot of maths people choosing DK7 when historians don't and then thinking huh, what's that about?
As a software engineer I always see " IF A THEN B" or "A IMPLIES B" as the equivalent boolean expression "B OR NOT(A)" from which it is easy to see what to test
Wait is it actually equivalent??
A,,, B,,, If A then B
T,,, T,,, T
T,,, F,,, F
F,,, T,,, T
F,,, F,,, T
A,,, B,,, B or not(A)
T,,, T,,, T
T,,, F,,, F
F,,, T,,, T
F,,, F,,, T
Damn, it IS really equivalent.
@@xXJ4FARGAMERXx wait, what does ,,, stand for?
@@ravivdesai those just serve as spaces between the F/T symbols in the two (identical) truth tables.
Indeed A->B is equivalent to "(not A) or B".
Howdy hi hi,
On this one I got the D card, but missed following through on the logic for the 7 card to ensure it didn't have a D. Well done Presh! You got me on this one! Well done indeed. In my defense, while it took me a few seconds once I heard the answer. I did deduce the reasoning behind it prior to your explaining why those two cards in particular needed to be checked.
The reason that most people fail this is because it doesn't occur to them that "If D then 3" is not equivalent to "If 3 then D". That aspect of the puzzle is taken out in the second version, and you see the expected boost in solvability.
I'm a former community college math teacher, and this is why we teach students how to do regular math before we teach abstract math (abstract algebra, etc.) One of the hardest topics to teach in algebra was cancelling in generic formulas (e.g. if a*b = a*c, then b = c.) No matter how many examples with actual numbers you show (2b = 2c, 3b = 3c, 4b = 4c, etc.), students struggle with the concept you can cancel "a" like you can cancel "2." It turns out that IME at least, most people need to be able "link" the math they're being taught with something they know from the real world to be able to do it well; the average person just isn't a good abstract thinker.
I believe this problem has an unstated assumption that a 0. If a = 0, then b might not equal c, yet a*b = a*c = 0.
@@sidkemp4672 ZERO BREAKS ALL THE RULES
You should stop using the word "cancel" because it's a very broad term, so it makes it hard for students to actually identify what it means.
Does it mean "removing the x in x+y = x+z"? Does it mean "removing the x in x/y = x/z"? What about "removing the x in (x+2)/y = (x+1)/z)"? It's not clear.
Instead, use "subtract from both sides" and "divide both sides". It's clearer what is happening.
Was it Richard Feynman who developed the habit of running actual numbers through formulas being discussed just to check that they still made sense? I seem to recall him catching an error that would have suggested that the entire Observable Universe is about a foot wide 🤣
@@user-jc2lz6jb2e I like the way you raised the issue of use of the word "cancel." It is an interesting and relevant case of the failure of a precise technical term in a specialty (in this case, algebra) due to an unfortunate, vague, and threatening shift in natural language. "Cancel," until recently, was a harmless term in natural language, as in "please cancel this order." And that allowed it to be part of the precise jargon (using "jargon" as a neutral term) of algebra. For students learning algebra in the larger context of "cancel culture," hearing hte word might well be a barrier to learning. That's unfortunate, and the alternative you suggest of "...from both sides" is, as you say, clearer.
At the same time, I found a barrier in reading your otherwise fine suggestion. Your opening words, "You should stop using the word" are an example of authoritarian language used by participants in the cancel culture you are writing about. I would encourage, instead, the cooperative, respectful language of supportive experts. Perhaps "We may benefit from stopping our use of the word cancel ...". Personally, I find the phrase "You ahould stop using the word ..." to be an iconic example of the cancel culture at the root of the problem you are encouraging us to solve. The phrase strikes me as an authoritarian, insensitive, disrespectful usage. So I encourage us all to be clear in our language and respectful of others in our choice of words.
Your second example opened my eyes a little bit. I figured most mathematicians would be able to quickly and easily solve this problem, and the outliers would be people who did it too quickly. It makes sense that correctly deriving the logical statement D implies 3 from what was written is a place where a mistake could be made. However, I think the reason that it was made by so many math faculty was because there does tend to be a lot of non-native English speakers among that group. I would wager the native English speakers among the math faculty all got it correct. That said, I'm not sure if it was a familiarity with the problem after the first example or the real life connection, but I admit that I was able to answer the second question much more quickly even though I am a native English speaker and a PhD mathematician.
Context plays a major role in making a person at ease with a puzzle. Great video!
Well done including the second example to clarify the point -- I recognized when you explained why I mis-interpret the rule as a '3' needing to also have a 'D' (not the rule as described)... Though the second example made it much more obvious (as you intended).
Interesting. I'd suggest using a Tru/False table to "prove" the contrapositive. It makes it very clear and rigorus imho. Images/diagrams are somewhat more open to interpretation perhaps.
I would like to point out that this example is also mentioned in the appendix of our class 9th maths book in India, the appendix covers logical reasoning and topics like necessity of axioms in mathematics
And personally I saw this puzzle first time in a TedED video when I was a kid
Another thing about this puzzle is that while it might seem like a logical puzzle, it's more of an efficiency puzzle. Yes, you get the answer with logic, but now imagine you give this not as a puzzle but as a job to someone. They will stand beside a conveyor belt and need to check the cards to ensure they are printed correctly. You might start trying to check every card, but as you get the rhythm of your job down, you'll start to find ways to take shortcuts. Eventually, even if your logic skills are low, you'll get to the right answer just from going through it so often. It might take someone a while to reach the correct shortcut of only checking D cards and non-3 cards, but most people if they stay in the job long enough will eventually get there.
And sure enough, you show that most people understand the booze thing. It's little surprise that the one that actually IS a job people do, more people are able to reach the correct answer faster.
Really glad half the video wasn't about the problem itself and explored the natural concern one might have about so many people being bad at it. It brings light to both perspectives. Context is a huge help that allows the average person to be decent enough so that "society can function" so those of who find this natural and easy can be more understanding and hopeful in them, but the riddle also helps show the value for those "most people" in realizing logic better, because in cases where we don't or can't grasp enough context, we can be terribly wrong, and get validated by an unstoppable and confident majority.
This was a fresh new idea. Loved the video. Logical puzzles in mathematics helps the brain overcome difficulties in life!
That was easy, but also fun! Great video!
I only checked the D, but as soon as the right answer was given, I immediately knew why. This is brilliant. This video randomly showed up on my home page, but I'm subscribed now!
In the second half of the video, you explain, why we don't *need* those "logical problem solving skills".
- Statement A) Most people don't find it (too) difficult to solve everyday-situations, aka context related problems, such as the beer drinking age check.
- Statement B) Most people on the other hand fail to solve logical puzzles or riddles efficiently.
Let me add three more statements to show what I mean:
- Statement C) Solving everyday-situations is crucial for everyday life (within a society or as a hermit doesn't matter).
- Statement D) Solving puzzles is a fun activity, because of the challenge.
- Statement E) Solving puzzles as easily as everyday-situations (like when to cross the street, which key to use to unlock my door or whether or not to go over the speed limit) makes these puzzles boring and defeats their purpose.
Also the mathematicians in that statistic seem to indicate that logical training can get you only so far, while context related problems provide a tiny but essential reward for solving them. So does solving puzzles, but only as long as the puzzles provide a challenge (and thus a *desire* for a reward).
I agree that everyone should solve some riddles and your videos provide a good opportunity to do so, but I don't think *training* is the right motivation.
I thought you only had to flip D, but once you showed that 7 need to be flipped too, I was like "oh yeah duh, need to check there isn't a D on the 7 card"
I did at least get that K and 3 didn't matter what they had on the other side as only D needed 3.
This is a version of the very famous Wason Card Selection Test. We seem to have a bias to confirm things rather than try to prove ourselves wrong
So the mathematicians read the problem: «if D is on one side => then 3 is on the other side», but historians instead: «D 3 must be together on both sides». Historians do not understand what's the difference between statement and its converce, and most people don't understand what is a contraposition.
Pretty trivial, although just have to catch the person in the right frame of mind to solve it
This question isn't really hard because of the logic, as you show in the second case. It's a challenge of phrasing and the messiness of English. So I'd be curious to see how well technical writers and grammarians perform on this test, since they might be more likely to understand that the abstract version is identical to the drinking age version. I write tabletop game rules, so I have to deal with challenges like this every day. :)
As someone who absolutely hate ambiguous board game rules I applaud you.
Wow, a sighting of Cheapass Games in the wild!
I am a technical writer. I was tired when I listened, but I took the "only 10% get it right" as a challenge and as a warning that the obvious answer might be wrong. It took some thinking and checking, but I got it right.
The second example shows exactly why it ISN'T a phrasing problem.
It's exactly the same wording, just with the subjects swappd out.
It also shows that people aren't actually as smart as they think they are, since they're just pulling the answer out of experience, not by actually deducing it.
I've asked this very question to many people, and blaming the phrasing is a common excuse for when they get the answer wrong.
Most people say "most people are stupld", but they cannot cope with the fact that they themselves are part of that "most", so they create excuses like this. If that statement is true, then you can't all be smart. At least half of you have to accept at some point that you're part of the bottom 50%.
I believe we would have the exact same problem with this at least in Russian too. Implication operation is implicit in our languages.
As a history student I’m proud to be in the 8%
In what part of history might that 8% reside?
gotta love the 9% that did not check the d-card.
*9%
jk lol
The problem with this test is that the rules AS STATED require you to test all cards because it was worded ambiguously. What if on the other side of the K card there is a D? The question has too many alternate states and that sneaky (s) you added to the video text that wasn't in the spoken or thumbnail instructions doesn't change that. To fix this you would need to specify which face of the card needs to be checked, the one currently up or the one currently down. Currently the rule can apply to both faces of the card.
The rules state that every card has a letter on one side and a number on the other. That rule is kind of fundamental to understanding the problem
You're waaaaay overthinking the problem.
@@lostsoulman wrong. even if we assumed that it was possible for the K card to have a D on the opposite side, there is no reason to check the 3 card because the rules do not stipulate that a 3 must have a D on the opposite side, just that D must have a 3.
0:04 - every card has a letter on one side and a number on the other side
there is no ambiguity here, you just need to pay more attention.
The task was not ambiguous. The question is based on a card game where every card has a letter on one side and a number on the other side as stated clearly in the very beginning of the video.
It is also clear based on the thumbnail, text and spoken instructions that it can be one or several cards.
Ahh! Very clever. Great experiment. No trick questions, just in-depth logic.
Most of the explanation here (venn diagrams, contrapostives, etc.) is undertandable only by people who would already have gotten the answer correct, I think.
Here's what I would say to someone who doesn't get the answer: "We obviously need to check the D card, and make sure there's a 3 on the other side. But we also need to check the 7 card. There better not be a D on the other side as that would also violate the rule. The other two cards cannot violate the rule no matter what's on their other side. You might think that the 3 should have a D on the other side, but the rule doesn't say that other letters can't have a 3."
Its not the rule. Its the statement. You can't just assume things on your own.
I thought I was so smart by not falling for the 3 card trap. But I must admit that I missed the 7 card. DAMN!
I looked at the thumbnail and I thought I figured it out which made me too confident to pay attention when he said all of the cards have a letter on one side and a number on the other.
Having taken symbolic logic (as a philosophy student) these questions are easy. But I can only answer them well because I suffered through an entire term of this mind-melting stuff. Bring back so many stressful memories lmao.
Where did you do your degree? I did a Philo MA & PhD at Bristol, and taught logic to undergrads there for several years.
I think it's natural for humans to equate implication and equivalence. I'm sure a lot of the math students and staff were just not respecting the problem enough to think it through :)
Yes exactly, my mind went straight to “if and only if” equivalence D3.
But the rule is just one-way implication D=>3
This is exceptionally simple. The main problem is of course the way the question is asked and people being patient and following the rule.
You'll reach the point WHERE even mathematicians ARE envious of your skills.
This video is so logical. I love it! 😊🎉
This is one of the tests I generally put in front of programmer during my hiring process. Efficient programming requires shortest path to solution.
@@JonaasK it is more to do with efficiency testing. Someone who can arrive at a solution effectively can always become better programmers.
Excellent video, thank you for putting these fascinating topics out there.
I'm less surprised at the first one. But the second one, how do 25% of people mess that up?
The majority of people are not very bright. During the whole Covid thing, we were told that crowds were bad, so they shortened the hours that the supermarkets were open, forcing more people to shop in fewer hours, instead of spreading the crowds across MORE hours - and everyone just accepted that. Then they told us to 'Stay Home' because it wasn't safe outside as the air could be 'full' of germs, but they simultaneously advised us to open a window in every room, in case the air in the house was - you guessed it - 'full' of germs.
In the first version, i know the question didn't outright say that a D must be on the other side of a 3, but by not outright specifying it, i made the assumption that a D must be on the other side of a 3, so i needed to check all of them.
I know that was my mistaken assumption, but the point i'm coming to is that for the 2nd version of the puzzle, it is a real-world scenario - one that is already well-defined in our heads, and as a result there is a lot less room for false assumptions. I reckon that's why the 2nd version of the puzzle has such a higher success rate.
The answer is actually every card for the opening problem though :) There is one small issue missed here. These are specified to be 'cards'. By posit, they are 2 sided and physical objects. The rule states that a d card must have a 3 on the other side. By rule of them being a card, the opposite is required due to object permanence. Yes this problem has a nice answer assuming a logic puzzle, but sadly, they can't be called cards for it to be solved as intended!
Edit: Ah, ok. He stated that the cards were manufactured to the rule. That was where my above issue stemmed from. Yeah, there is more ambiguity needed. Like it could have been fine if it were just a card game, and there was an ambiguous rule created to play the game. But since the cards were said to be manufactured to the rule, my above thoughts do hold true.
I was confused by this answer until I really went back and studied the wording. I thought you had to turn over the 3 as well because all cards with a D and 3 should have to be proven to have each other on the back. But it does indeed specify that all D cards must have a 3 on the back, and not the reverse. I bet a lot of people get it wrong because of the tricky way it's phrased!
It's not necessarily confusing.
D implies 3, but 3 doesn't necessarily imply D. The equivalence only works in one direction.
That's why you don't need to turn over the 3 card. Our only objective is to the test the rule given for D, but we have zero information on all the possibilities that 3 is allowed.
Your solution would have been correct, if D and 3 had a relationship of equivalence (ie D implies 3 and 3 implies D).
@@Slade_the_dragon_slayer This is why I went into performing arts, I was never great at figuring this type of stuff out lol. Thanks for explaining though!
@@Slade_the_dragon_slayer But 3 does imply D. Idk why you think the rule doesn't imply that D and 3 don't have equivalence, the way its worded clearly implies equivalence to me.
@@MrBalor89 nope. If it did, it'll be explicitly stated. Équivalence always has to be unambiguously stated.
A implying B doesn't mean B implies A.
Implication != Équivalence.
The real problem with the wording is that we are not informed whether the cards are all facing the "correct side". It only says "one side" and "other side", but from the explanation it becomes clear that the sides matter, too. It wasn't explicitly explained.
my initial answer was D37
D - check if the rule is followed 🧐
3 - the same (I decided every letter should have a specific number)😅
7 - check if the rule is violated 🧐
but just when you started your explanation with D I figured out that 3 shouldn't be checked as it doesn't matter what is on the other side 😅
I'm not a genius 🤦🏻♀️🤭
It seems clear to me that the reason most people get it wrong is that the question/scenario is inadequately specified in the first place.
As a programmer I'm very accustomed to thinking logically about boolean expressions and if statements/rules, so getting this correct was not hard. Maybe if they had asked programmers instead of mathematicians the rate of correct answers had gone up?
I was wondering about this too
Experienced programmer here and I still included the 3 card in the set to check. So it's easy enough to make those simple errors even with years of coding. In fact -- while my programming experiences helps me with the logic side, due to the fast cycle time of programming, unit tests, etc, I've trained myself _not_ to be totally exhaustive with my first guess. Educated/considered guess, run, check, try again is so integral to programming.
So it wasn't a rule at all. It was a statement. That's all that accounts for the given anwer.
I wonder if they polled students that had recently finished a course of Logic 101 how they'd fare. :D
If you find a mathematician that gets this wrong, then they're not a mathematician, they're just some dude that does calculus
After watching this video, I find this purely logical. At first, I thought that the only correct was card "D". But after watching this video, I was missing one important part of this riddle: every card has a number on one side, and a letter on the other side. So we need to check also "7" card because there's a letter on the other side, and we need to make sure is not "D" to check if the rule is being followed. Got it, makes sense!💯
Either way, checking only "D" would be the wrong answer. If there could be two numbers or two letters on one card, you would need to check the "K" and the "7" as well, not just the "D", because these could have a "D" on the other side, which would invalidate the rule.
@@multiwebinc Its not a rule but a statement. Don't overcomplicate things
While I’m glad to see people can find the logical solution when it’s presented in terms they can associate with,
it’s quite shocking that 1 in 4 still fail to find the logical solution.
QA Manager: You need to check all cards.Bugs show up in places you least expect.
After answering D and 3 for the first 'problem,' and observing the logic used to find the correct answer, I was able to think of applications which would use that logic, and I came up with quality control in manufacturing - like making sure that a car with a red exterior doesn't go out the door with a green interior.
The second problem tells us, or at least lets us safely assume, what the objective is going to be, as far as what to scrutinize and what to ignore, so the correct selections more readily stand out as being such.
proud to say I got it correct. but it's definitely largely due to training. I learned about proving IFF and considering the converse. I learned about the completely encapsulated Venn diagrams. Without learning though, I may have made the mistake of picking D and 3. In fact that was my immediately guess, but a few seconds later, I corrected myself and chose D and 7. If I only had 1 second to answer this, I'd have gotten it wrong, even with my training. I think the question may have been unfairly asked. Looking at the distribution of answers chosen, a significant portion of the math guys chose DK7, and very few chose D3, in contrast to those without training. I think they were tricked, and it wasn't made COMPLETELY CLEAR to them that one side must have a number and one the other side must have a letter. I'm calling deceptive questioning. I also have observed the disparity between real world examples and abstract examples. I was trying to tutor a college student in dimensional analysis and converting units, which is universally difficult among students besides the math/science guys, and he sucked at it. But when I changed the units to dollars and fruits, using the same exact values, he IMMEDIATELY figured out the correct method to solve the problem!!! Mind-blowing!!!
And they say we are safe for now because AI is not able to generalize... :)
man, all this writing about training and thought-process, and i just figured it out because it seemed obvious to me
@@TarnishedProductions consider it a gift bro
To those people who don't understand how or why people got it wrong, I will explain why I did.
When I was told each letter has a number on the back, I (and others like me) erroneously assume that they are unique numbers. They read all D = 3 must also mean that all 3 = D. Given this incorrect assumption, it becomes necessary to also check the 3 to make sure it has a D on the back.
When we switch to the drinks and ages, then it is obvious that the ages are not unique. The puzzle is phrased in such a way to eliminate that assumption, making it an easy solution for at that point.
demonstrates that people tend to interpret “if” as “if and only if”
Hard to believe only 10% of people get this right! It felt so incredibly easy to me that I started second-guessing my immediate answer for a few seconds. But no, it was as obvious as I thought.
Nice goin! You also think the answer is "K" and "Beer", right?
Did you also conclude that the test is wrong because it is flawed?
@@Moowe291 👎
I got this one rather easily. However for most people math and logic are often too abstract for real world situations. So, a real world problem having the equivalent logic is much easier to solve because people can relate to it a lot more.
Me too. But then I studied and researched maths at university, and logic is pretty basic to maths.
The interesting thing is, transforming an abstract problem to an equivalent one that you'd likely come across in the real word is a good problem solving technique.
I used that technique to solve a logic puzzle on Mind Your Decisions not all that long ago., though I didn't have to do that here. The analogy of the drinking age problem is clever.
Finally I got one completely right. Normally I can get some of the answer, but then my lack of math past grade 11 comes back to bite me. Thanks for making the World a better place, one math question at a time.
I may struggle with some math problems, but I solved this in under a minute!
I'm glad that this time you show actual studies and papers that verify the often vague "almost everyone gets this wrong" claims in your other vids. Still amazing to me that people have trouble with this.
I'm in that 10%.
then you are wrong. Congrats. DK7 is correct based on set of rules given
The four cards can prove that the rule was not followed, but they can't prove that the entire deck follows the rule. The beverage test shows that a lot of otherwise logical people struggle to think abstractly.
I am at 1:18 - I got the answer right. Reasoning: The claim is D -> 3. We need to check the first to confirm it is actually 3. The second is irrelevant to the claim, it can be any number. The fourth is relevant because if it's a D, it means D -> 3 is false, so we need to check it. The third one doesn't have to be checked because if it's a D, we just have 1 more anecdotal evidence. If it's NOT D, it's fine because any letter can have 3 anyway.
We cannot prove the rule correct, all we can do is to try to disprove it given what we have - these 4 cards.
You only have to check the 7 if the D card actually shows a 3. If the rule is already broken on the first card, no need to check a second card.
As a teacher I often found
that, for example, when
a student struggled with
a calculation involving decimals
that sticking a currency sign
at the beginning of the sum
made the students perform better.
The "magic" of the context
is a very powerful thing
Why is your comment written like a poem
@@antiprime4665
A mid twentieth century professor of mathematics
who lived in New York
wrote a series of books
introducing quite complex topics
to the average huMan in the Street
and I enjoyed them tremendously
and learnt a lot from them.
These texts were written in an unusual style
where every phrase or sense element was put on a separate line
and she felt that made it quicker and easier to read.
I liked the style and as on a smartphone
with its narrow screen
I like to see each idea on a line
so I try to emulate her style.
I failed it, but just because I asumed that not only D needs a 3 at the other side but also every 3 should had a D at the other side so my solution was all the cards, to stick to that rule. Missunderstood the problem damn.
90% of the people who failed probably assumed they are allowed only to turn over one card.
This puzzle is a rare example of puzzles posted on the channel that I could solve effortlessly within a couple of seconds. Usually I end up just scratching my head. Therefore, it puzzles me how something that someone like me can solve so easily, ends up baffling mathematicians. I don't understand my own brain. 😂
Arithmetic and Logic are interrelated but slightly different areas of Math
I think your last sentence applies to most of us😉🤯
For this scenario to make more sense, there needs to be the designation of a primary side. The card description is not compelety off, but a card, as described in this logic puzzle follows a simple set of rules, but ignores the simple attribute of a card. Two sides, while one is a letter and the other a number, the two sides hold their value regardless of which side is presented first. Both values exist at the same time. So one side needs to be designated as the primary or whatever that dictates the other side, for this to make sense to me.
The fact that this result has been replicated often basically just proves that human intuition is not really based on the logical rules, which is why logic does not come naturally to people and you have to teach it.
I suspect the 90% majority doesn’t lack the logical skill. Rather, they aren’t trained in parsing rules that have little meaning for them. My 2 cent contribution to the field of psychology.
I like how you edited the original problem to be more youtube-appropriate (For people unaware, the original version uses "AK47" as the cards. Not sure the reason, maybe the designer thought it'd be more memorable that way)
You're nearly right: the original version uses A, D, 4 and 7. There are lots of online materials about this. Maybe you remembered it as AK47 because of the firearm?
the ak47 problem
Well, the rule says that all D cards are 3 cards, but doesn't actually specify the reverse or that, so it's possible not all 3 cards are D cards. So the D has to have a 3 on the other side to follow the rule, and if the 7 has a D on the other side, that would be rule breaking. The K and the 3 could be any number or any letter respectively, on the other side, as far I know from the one rule given. You need to flip D and the 7.
Its' not a rule but a statement. Don' overcomplicate things.
@@mohitrawat5225 Was literally called a rule, in the video.
Question should be worded to include what’s the least amount of cards that need to be flipped in order to confirm the original hypothesis.
On the last example, don’t you have to check 25 too. Only someone who is 20 can drink beer according to the problem. He says you must be 20 years old. He did not say 20 years or older. So a 25 year old cannot drink beer.
I don't know if this problem is fully stated as per the original but you definitely need to check the K card too. There is nothing in the rule as stated that says that cards have to have a letter on one side and a number on the other. If the K card has a D on the other side then it breaks the rule.
I made the same mistake as you did, but go back to the beginning of the video, it clearly states that every card has a letter on one side and a number on the other.
0:03 - "every card has a letter on one side and a number on the other side". That's pretty clear I'd say!
@@onesquirrel2713 The very fact that we are having to check the rule means that it can be broken so it would seem perfectly possible that some cards do not have a letter on one side and a number on the other.
As someone who did get it correct, I had a bit of reservation beforehand, I assumed the test wanted me to say D and 7, but part of me wondered, if we're already questioning if the rule is followed, why am I trusting other rules, what if one of the cards has a number on the front and a number on the back, I was told every card had a number on one side, and a letter on the other, to make sure that rule is followed, I need to check them all.
Sadly the percentage of people who chose the correct cards is nearly as bad as if they'd just closed their eyes and randomly picked a random quantity of them.
this video really just shows how math is "create a problem to solve"
Sorry. But there are 2 rules. Every card has to have a letter on one side and number on the other. To check if the manufactures followed the "D" rule, you have to check both sides of every card unless it has a 3 on the first side. Every card could have a "D" on one side since error is possible by the manufacturer. The "K" card could have a "D" on the other side.
No.
The problem gets a LOT easier if you, like me, have already seen another video explaining this exact riddle 😀
"this is easy if you already know the answer" lol
Being a cynic I assumed I needed to check the 3 to see if the rule was really applied. They should have stated that the rule is followed absolutely.
If even mathematicians can't figure out the correct answer we are in a big trouble
As soon as you said the answer, I facepalmed because I realized my mistake.
K needs to be checked, because the entire premise is that the cards CAN have errors, which is WHY you are checking them to begin with.
Anyone that works in auditing would also check K.
Only the rule that all D cards have 3 on the other side was under question. Nothing said the initially established rule that there's a letter on one side and a number on the other was to be doubted.
@@DaSquyd If you dont flip K, you dont find that that specific K card has D on the other side.. it was a misprint from the manufacturer. Your manager is now looking at you, an auditor, sideways for making such a simple mistake.
the only card that is irrelevant is the 3 card... you cant assume the rules were followed cause if you assume one rule was followed, you might as well assume they were all followed.
@nephalm5357 Presh said..."Every card is manufactured according to a rule...." and then he said "...to check if THE rule has been followed".
Not sure which bit you don't understand. Presh was very clear.
@@ChrisLee-yr7tz He said they are manufactured based on 2 rules... he then asks you to check 1 rule, BUT a mistake in the other rule, can cause the 2nd rule to not be followed.
In the 2nd example, its irrelevant if on the other side of coffee theres a number or "Beer".. but in the first example, if there is a D, it breaks rule 1 and rule 2... just because you were asked to verify rule 2, doesnt mean rule 1 isnt at play.
I understand critical thinking is difficult, but thats what we have to do sometimes...
@@nephalm5357
Checking the K card is good due diligence, recognizing that it is possible that the letter-number requirement may not have been achieved. However, we are auditing the D-3 rule, not the letter-number requirement. Checking the letter-number requirement for all cards (including cases where it has no bearing on the D-3 rule) is outside of our scope of work, so I would not check the 3 card without a change order.
TLDR: I wholeheartedly agree with you.