How logical are you? A legendary experiment

[@badangolgi175]

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.

[@johnbreitmeier3268]

It also is a huge red flag that the problem is deliberately deceptively worded.

[@MichalMracka]

@@johnbreitmeier3268 ...or... That 90% of people either do not understand written text, or are not very good at logical thinking...

[@johnbreitmeier3268]

@@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.

[@kalan4787]

​@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.

[@kalan4787]

For clarity, modus ponens and modus tollens are elementary rules of deductive logic. They are Day 1 of a 101 level logic course

[@wilson0213]

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

[@Mythraen]

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.

[@johanneschristopherstahle3395]

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.

[@Mythraen]

@@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.

[@iv3nomousi]

@@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".

[@Mythraen]

@@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.

[@largestbrain]

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.

[@L17_8]

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.

[@mkovis8587]

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.

[@largestbrain]

@@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.

[@seanwilkinson7431]

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. 🤣🤣🤣

[@bearup1612]

@@L17_8 yeah go back to sleep

[@lenonkitchens7727]

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.

[@stupidaccountsoicanpost3395]

If the rule doesn't mean both "if 3 then D, AND if D then 3" then it really doesn't matter at all what is happening since attempting to verify is pointless without checking all cards. Logically it has to be true because if the D has a 3 then by inverse the 3 MUST have a D, since it's a card with two sides and the world is not flat.

[@lenonkitchens7727]

@@stupidaccountsoicanpost3395 Wow. Just...wow. Every card with a D on one side has a 3 on the other. Also, every card with a Z on one side has a 3 on the other. Tell me again why this is impossible and logically unsound?

[@gavindeane3670]

@@stupidaccountsoicanpost3395 Your "logic" is equivalent to arguing that because everyone who lives in California lives in the USA, then everyone who lives in the USA must live in California. The answer is clear. To verify "if D then 3" we do not need to check the K card or the 3 card. There is no number that can be on the back of the K card that would violate "if D then 3". And there is no letter that can be on the back of the 3 card that would violate "if D then 3". To understand why "if D then 3" is not the same as "if 3 then D" just imagine turning over the K card and seeing a 3. Such a card would violate "if 3 then D" but it would NOT violate "if D then 3". Or imagine turning over the 3 card and seeing an E. Again, that would violate "if 3 then D" but it would NOT violate "if D then 3". "If D then 3" is what matters here.

[@БарриЛомов]

@@gavindeane3670 What if on the back of K we find D? As I remember, D - is used among Romam numerals/digits. D = 500.

[@gavindeane3670]

@@БарриЛомов Yes, Roman numerals would allow D on the back of a K. As would hexadecimal numbers. People (including me) have discussed those possibilities in the thread.

[@RoldanRR00]

So there's actually two rules here. One is being taken as immutable fact (letter on one side with a number on the other) and one is being verified (D-->3). If you are a logical person, wouldn't you want to verify if both statements are correct? Therefore I would flip all the cards over to see if the K had a letter on the other side and if the 3 had a number on the other side. The answer is so difficult because the question is actually counterintuitive.

[@adalbertus777]

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.

[@sharpnova2]

that was a ton of words to say nothing. you said literally nothing.

[@TheMofRider2]

​@@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.

[@und3rgroundman865]

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?).

[@brickviking667]

That was indeed the mistake I made.

[@StuermischeTage]

@@TheMofRider2 Why would you interpret "every D has a 3" as "every card with a 3 must have a D on the other side"?

[@dombo813]

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.

[@macdjord]

Then the first real customer turns one of the cards sideways, and the whole deck explodes.

[@paulstelian97]

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...

[@MrVirus9898]

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.

[@dickheadrecs]

just get the CI to check the cards while devs are sleeping 😴

[@martinhsl68hw]

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.

[@Gideon_Judges6]

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. 😂

[@CopyCat...]

You are correct tho 🙄

[@CopyCat...]

No you are not correct. Already given in the question that opposite side of alphabet is number.

[@nephalm5357]

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.

[@Gideon_Judges6]

​@@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.

[@CopyCat...]

@@Gideon_Judges6 given statement and rule are two different things. Statement is correct always. Rules can be violated only.

[@IMakeStuff92]

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!!

[@zantas-handle]

You nailed it - perfect.

[@johnbreitmeier3268]

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.

[@dermick]

Totally agree. This is very common with "brain twisters" and other puzzles.

[@johnbreitmeier3268]

@@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.

[@MartinBeerbom]

There's also the little word "over" in the puzzle. While the puzzles are logically equivalent, the "over" triggers people to think about the larger set, including the not-[number in puzzle] elements, which is necessary to get that you have to check the inverse rule.

[@dateland-twopalmspress755]

Right! I'm a professor of English and, I would mark this question "unclear -- restate"

[@foogod4237]

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.

[@MartinPoulter]

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.

[@foogod4237]

​@@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.

[@notrhythm]

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.

[@xianartman]

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.

[@PHIplaytesting]

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.

[@sung-ryulkim6590]

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.

[@QemeH]

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"

[@chrisengland5523]

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.

[@peter9477]

​@@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...

[@peter9477]

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.

[@QemeH]

@@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...

[@SmileyEmoji42]

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.

[@XJWill1]

Maybe they were hungry and just randomly selected answers to get it over with. What was their incentive to try to get it right?

[@SmileyEmoji42]

@@XJWill1 I suppose they should have had "I don't know" as an option

[@toni1140]

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.

[@leif1075]

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

[@jongyon7192p]

​@leif1075 if it has the letter F, then it's ok cuz other letters can have 3, too. Rule never disallowed that.

[@CasualTS]

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 🥰

[@SeemsLikeSomething]

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.”

[@panzermk8]

I was about to say something similar. I feel like computer science students would fare better on this.

[@HugRunner]

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.

[@jdamers3829]

Yeah I didn't realise the k couldn't have a d behind

[@davidshipley393]

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.

[@shawn951951]

You are absolutely correct. With the specific information provided, each card needs to be checked to make sure there is no D behind it.

[@scurtij]

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.

[@thswrestler160]

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.

[@michaelobrien1106]

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!

[@Axman6]

This feels related to the phenomenon of people,being generally terrible at probability, until money becomes involved in the question.

[@jawstrock2215]

I don't think this shows a problem of logic. It's a reading comprehension problem, or a problem of inserting own bias/assumptions.

[@Ruchunteur]

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.

[@HiArashi13]

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.

[@57thorns]

I would be very scared if 10% of Computer Science fails this, but I am afraid that is also the truth.

[@SmileyEmoji42]

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

[@xXJ4FARGAMERXx]

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.

[@ravivdesai]

@@xXJ4FARGAMERXx wait, what does ,,, stand for?

[@ronald3836]

@@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".

[@davidmichaels307]

My mind also tested for the "is the letter on one side number on the other side rule being followed?" and came up with "yeah you gotta check all 4."

[@joshcantrell8397]

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.

[@Mattavilasa]

If only 10% of people are logical… How can society function at all? I ask myself this all the time.

[@rcb3921]

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.

[@GoldMoonGuy]

@@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.

[@user-qz2vu2wy6b]

that is a very logical doubt.

[@user-qz2vu2wy6b]

@@rcb3921 yes to make proper orders.

[@msydneyau]

It doesn't. Take a look around.

[@LiteBulb88]

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.

[@sidkemp4672]

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.

[@LeonardGreenpaw]

@@sidkemp4672 ZERO BREAKS ALL THE RULES

[@f5673-t1h]

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.

[@PhilBoswell]

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 🤣

[@sidkemp4672]

@@f5673-t1h 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.

[@aleyte1913]

This felt like one of the easier problems you posted.

[@Questerer]

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.

[@L17_8]

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.

[@hederahelix622]

@@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?

[@vez3834]

@@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.

[@hederahelix622]

@@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

[@Cats.In.Pyjamas]

What’s really irritating me about the response that “you need to turn all of the cards over because there might be misprints” is that: 1. It’s not a real set of cards, it’s a logic puzzle 2. Even if they were real cards and there were misprints, you STILL wouldn’t need to check all of the cards. You’re only being asked to check that all D cards have 3s; you wouldn’t need to check the 3 card because even if it’s broken the letters and numbers rule, that’s irrelevant to the question.

[@adamperdue3178]

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.

[@michaelclawson7343]

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.

[@keith6706]

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.

[@adamperdue3178]

@@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.

[@gavindeane3670]

@@adamperdue3178 The person you are replying to literally just described a system where one type of error is possible and the other isn't. When you understand what the failure modes are in your system, it's perfectly normal that you might check for one adverse outcome and not check for another.

[@kmbbmj5857]

@@gavindeane3670 The key point however is we don't know that from the information given. Keith6706 said "you could postulate." We could, but that is not a given in the problem; it's an assumption added by the reader. Which goes back to other comments that each person interprets the words based on their experience.

[@SimonClarkstone]

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!".

[@laurendoe168]

I facepalmed when it was revealed I need to check the 7. It was a "DOH!" moment for me.

[@050138]

Awesome

[@vxllabh09]

same man

[@FirstLast-rb5zj]

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?

[@Entropy67]

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.

[@anonymous.3458]

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.

[@mike1024.]

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.

[@MW-dh1ez]

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.

[@liamo4287]

your right, just because the d has a 3 behind it, doesn't mean the 3 has a d behind it

[@n085fs]

I swear I want to know the real statistic of how many people if hired at an M&M factory with the instructions to throw away any candy that has a 3, W, or E on it, would throw any away.

[@journeyofgreen3958]

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.

[@ThisCanBePronounced]

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.

[@ccmplayer87]

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.

[@sushovanpal6596]

To the point and elegant

[@c4t4ly5t]

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!

[@AnimationCPU-y2k24]

Actually, the cards are manufactured under 2 rules for his answer to be correct. 1) letter on one side with a number on the other side. AND 2) D=3. Based only on the one Rule that was stated, he would be incorrect.

[@gametimewitharyan6665]

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

[@dire_prism]

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 :)

[@nobodysfool2232]

Yes exactly, my mind went straight to “if and only if” equivalence D3. But the rule is just one-way implication D=>3

[@jonorgames6596]

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.

[@jakolu]

The only thing that maybe could be confusing was whether or not one needed to check that every card had a letter on one side and a number on the other side. If we assume that is true (which is we get from the first statement), then the logic to solve this is very straightforward in my opinion.

[@thomasdooley5904]

The problem is that the question is not asked in such a way as to illicit the response they are looking for.

[@empathyisonlyhuman7816]

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.

[@UpYourArsenal]

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).

[@marklonergan3898]

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.

[@xxxmachsevenxxx2440]

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.

[@cartersmith9842]

​@@xxxmachsevenxxx2440what are you talking about

[@akuunreach]

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.

[@master_sergik]

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 🤦🏻‍♀️🤭

[@jotun5383]

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.

[@Nuclearburrit0]

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?

[@francojosemuertes4273]

​@@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.

[@Nuclearburrit0]

@francojosemuertes4273 that's a different rule besides the one I said was unambiguous that was stated separately

[@DasHemdchen]

@@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.

[@tranquilcoast]

Ah I didn’t get it. This brings me back to my formal logic class. When you present it with conditional statements it makes sense! I conflated the D>3 and 3>D

[@l.w.paradis2108]

Remember: it's like the difference between "only the good die young" and "all the good die young." 😊

[@leif1075]

Yes but you can argue the wording of the question is ambiguous.

[@dielaughing73]

​@@leif1075you'd be wrong, though. It's simply that people tend to miss unstated conditions. That doesn't mean they're not clearly implied though.

[@leif1075]

@@dielaughing73 no I can validly argue the wording is a tad ambiguous.

[@dielaughing73]

@@leif1075 go ahead and argue that in a job interview with the person who wrote the wording with great care to test who is capable of understanding certain types of communication and exercising certain thought processes. They will simply mark you down as "Failed Logic Test". But at least you'll feel like they were the ones who were wrong and not you. I'm sure that will keep you warm at night. I'll say it one last time: everything needed to correctly answer these tests is contained in the test. It's a test of using the information provided _and nothing else_. Wilfully misinterpreting the problem statement, or adding extra details or complications of your own imagining, is one of the ways to get it wrong. Stubbornly insisting they're a matter of interpretation is a glaring red flag of an inflexible mind. If you're ever given one of these tests in a setting with any stakes, I'd suggest asking questions to clear up any uncertainty in the wording or interpretation of the question. A well-phrased question will receive a definitive answer, and you can get on with trying to solve the problem rather than look for clever-clever loopholes. Understanding the constraints of a problem is central to being able to solve it effectively.

[@kylon1235]

The first and fourth cards. If the 3rd card (the 3) has a D on the other side, the rule is upheld. But even if it has another letter, the rule is still upheld, so that card is irrelevant. You just need to check the D to see if the flip side is a 3, and check the 7 to make sure the flip side is NOT a D.

[@jasonjanes9756]

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!

[@DanEBoyd]

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.

[@Bibibosh]

This was a fresh new idea. Loved the video. Logical puzzles in mathematics helps the brain overcome difficulties in life!

[@aidanm.655]

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.

[@drahcirnevarc9152]

Where did you do your degree? I did a Philo MA & PhD at Bristol, and taught logic to undergrads there for several years.

[@ianbelletti6241]

The answer is the D and the 7 cards. The rule is not worded to include the reverse proposition. Therefore, if the card has a 3 it isn't required to have a D on the other side and the rule doesn't cover the K card.

[@logangodofcandy]

All cards can have D on the other side.

[@ezion67]

This is a test of linguistic capability to parse the statement, not of the logic. Law students might "outsmart" math or physics students on this one. Instruct people to carefully consider the question before answering and most likely you get other results.

[@NisseHult101]

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?

[@bruc1555]

I was wondering about this too

[@HypherNet]

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.

[@davidirvin8885]

So it wasn't a rule at all. It was a statement. That's all that accounts for the given anwer.

[@ayporos]

I wonder if they polled students that had recently finished a course of Logic 101 how they'd fare. :D

[@guyincognito7211]

If you find a mathematician that gets this wrong, then they're not a mathematician, they're just some dude that does calculus

[@johncrwarner]

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

[@antiprime4665]

Why is your comment written like a poem

[@johncrwarner]

@@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.

[@DanteJayce]

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!

[@Slade_the_dragon_slayer]

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).

[@DanteJayce]

@@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!

[@MrBalor89]

@@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.

[@Slade_the_dragon_slayer]

@@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.

[@AlexYaroff]

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.

[@rogerfroud300]

Taking the cards one at a time... The D card must be turned over, because it could be any number, so you need to check. The K card is irrelevant because it isn't a D card. The 3 card is irrelevant because any letter could be on the other side, including a D, but the rule doesn't say that all cards with a 3 on one side must have a D on the other, so it doesn't matter. If it was a D then the rule we're checking for would be followed, so there's no need to check. The 7 card needs to be checked though, because it could be a D on the other side, and you won't know the rule has been broken until you check. So in short, you only have to check the D and the 7

[@TinyZu]

I reckon the less you clarify the wording, the more people get this wrong because you leave them too much room to ask questions. "Was it supposed to be a reliable fact that cards have a letter on one side and a number on the other?" This is why people want to check whether the card with K has the letter D on the other side. "Why is the rule written in such a way that D and 3 appear interchangeable?" I guarantee you, more people would get this right if the rule emphasized that it only cares about one specific sequence, like this: "If a card has a D on one side, it must have a 3 on the other side."

[@rylinwilliams1393]

The simpler solution is that mathematicians are merely bad at linguistics. I've seen this problem a million times, Mathematical questions on tests and other worksheets are terribly phrased and often moronically worded. There were even a few SAT questions that were so poorly worded that none of the answers on the multiple choice would reflect the actual question the prompt was asking. People are not illogical, but function in forms of logic. The conversational form of logic is different from the function of mathematical prompts, as they do not use common linguistic characteristics. The question "Every card that has a D on one side has a 3 on the other." Falls into the category of not enough information. The tense of the rule lacks any verbiage on emphasizing the fact that D is only related to 3 but 3 is not related to D. And although by gross technicality the question asks that, there is no emphasis or emotion present, nor is there tense. Thus, a person would read it as static and will misinterpret the question, as it is not understandable to common linguistics, rather than actually get the question as it stands wrong. 75% is the clearer answer as the drinking age is more culturally understood. Therefore, it makes the understanding of the subject matter have greater clarity through the use of cultural customs, and the question can afford to be without the changed linguistic cues. In short, mathematicians should take courses on language if they ever want to make proper prompts. Further, they should learn from statisticians on the problem of phrasing and the creation of bias or misunderstandings on surveys and other prompts.

[@randomxgen6167]

Sorry, but I think you need to retake a language course. If someone pointed to a parking lot and said "hey look, every truck that has a trailer attached has been painted green", would you write a 10-line paragraph detailing how they're wrong when you spot a green truck that has a boat attached? Hopefully not, because they didn't say anything non-trailer trucks painted green, the same way the question didn't say anything about non-D letters having 3. And before you try to say I changed the syntax, I didn't. Besides the "hey look", it's still in the form of every [subject] that has [property] has [other property].

[@macrobeastie2923]

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.

[@georgesheffield1580]

As usual in this series of podcast

[@DIGGERfromAR]

How is it "inadequately specified?" Steven Pinker presented this in a talk many years ago. He also used a real world example, checking identification for drinking age in a bar, and the results were improved. It highlights the above average intelligence required to create or comprehend abstracts over concretes. EDIT: I see he did that also.

[@embee187]

No kidding. Thumbnail was inaccurate and lead to confusion for me

[@KazmirRunik]

Maybe the thumbnail was incorrect before. Right now, the thumbnail does give the correct set of constraints for you to get the correct answer.

[@mathmannix]

That was easy, but also fun! Great video!

[@Yupppi]

I believe the difficulty is that once you realize that the instruction only says something about D, and you also see the 3 and think it doesn't matter if there's D or not D anyway. And then you think you have for sure exhausted the options and call it for good without considering the last option to be sure. For me for example I just wanted to quickly have a solution and watch the video, I didn't bother to check rigorously and when it seemed like I had a simple answer, I stopped thinking even the little bit I was thinking before and pressed play. I wasn't eager to have guaranteed correct answer, I was eager to have an answer and watch the rest to get on.

[@thecarman3693]

Like you I was thinking along similar lines. Here was my comment: I think what's causing logical thinkers to dismiss the 7 card is having the 3 card in there. Why? Because they will rightly assume that it's possible to have other letters opposite the 3, and hence believe they outsmarted the test and feel done. If on the other hand you only presented 3 cards, D, K and 7, I think more than 10% will ask to have the 7 card checked. Just my 2 ¢.

[@BLior96]

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.

[@PfyscheStyx]

As a history student I’m proud to be in the 8%

[@marcel-jt3dy]

In what part of history might that 8% reside?

[@ollllj]

gotta love the 9% that did not check the d-card.

[@flippinnoodlers298]

*9% jk lol

[@Kyrinson]

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.

[@sodavalve4829]

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

[@briant7265]

You're waaaaay overthinking the problem.

[@TarnishedProductions]

​@@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.

[@pmkaboo2446]

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.

[@fire-vk8dn]

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.

[@chimyshark]

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!!!

[@fixups6536]

And they say we are safe for now because AI is not able to generalize... :)

[@TarnishedProductions]

man, all this writing about training and thought-process, and i just figured it out because it seemed obvious to me

[@chimyshark]

@@TarnishedProductions consider it a gift bro

[@nigelnightmare4160]

I think the problem with the first set is people assume that if all D's = 3 then the reverse is also true, that all 3's = D.

[@zoltanboros8963]

I made that mistake. Then I realized that logical thinking includes not making assumption beyond the definition.

[@alinceusan]

Well obviously D, but probably 7 as well. If the 7 card has D on its back, then the rule doesn’t work. If there is a GENERAL RULE that is ALWAYS RESPECTED (every card has letters and nubers, no card with two letters) then checking D and 7 is enough. We could also check K and if on the back there is D then the rule also breaks. So again, if every card has one number and one letter, D and 7. If that is not guaranteed, we would need to check K as well. If on the 3 card there is something else than a D, that wouldn’t be a problem because all D imply 3 doesn’t mean that all 3 imply D. Some memories from logic lecture in high school

[@3dplanet100]

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!💯

[@multiwebinc]

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.

[@mohitrawat5225]

@@multiwebinc Its not a rule but a statement. Don't overcomplicate things

[@teacherman6347]

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.

[@kenhaley4]

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."

[@mohitrawat5225]

Its not the rule. Its the statement. You can't just assume things on your own.

[@petersmythe6462]

So: You need to turn over D because it may have a 3. You do not need to turn over K because the rules don't affect it. You do not need to turn over 3 because it is definitely following the rules whether or not they apply to it. You need to turn over 7 because it is has a D on the other side, it is breaking the rules. So flip D and 7 and you're good.

[@Tyrian3k]

My answer is as follows: First I reworded the condition into more explicit terms: "If side A is D, then side B must be 3." The D needs to be flipped over because it *must* have a 3 on the other side. The 7 needs to be flipped because it *mustn't* have a D on the other side. The K is entirely irrelevant to the condition. The 3 is irrelevant, because we are only checking that every D has a 3 on the other side, not that every 3 has a D on the other side.

[@roskoced6598]

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.

[@Moowe291]

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?

[@kevino4846]

@@Moowe291 👎

[@AkilanNarayanaswamy]

I'm less surprised at the first one. But the second one, how do 25% of people mess that up?

[@zantas-handle]

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.

[@punditgi]

This video is so logical. I love it! 😊🎉

[@briant7265]

People tend to way overcomplicate simple stuff. D: Need to ensure the other side is 3. K: Not a D. Don't care. 3: Other side doesn't matter, D or not. 7: Need to ensure other side is not D.

[@zantas-handle]

Elegantly expressed my friend.

[@seanmurphy8458]

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.

[@hymnz]

This is one of the tests I generally put in front of programmer during my hiring process. Efficient programming requires shortest path to solution.

[@hymnz]

@JonaasK it is more to do with efficiency testing. Someone who can arrive at a solution effectively can always become better programmers.

[@i.setyawan]

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. 😂

[@050138]

Arithmetic and Logic are interrelated but slightly different areas of Math

[@kevino4846]

I think your last sentence applies to most of us😉🤯

[@kevincassidy7233]

If it has a "D," then has a "3." Contrapositive- if it doesn't have a "3," then it doesn't have a "D." Check every card that has a "D" to make sure that it has a "3" on the other side. Check every card that has a number other than "3" to make sure that it doesn't have a "D" on the other side.

[@ramiel555]

I think that it's framed in a way that is slightly misleading 'each letter has a number' makes it sound like one letter and one number are tied together

[@Tiqerboy]

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.

[@hippophile]

Me too. But then I studied and researched maths at university, and logic is pretty basic to maths.

[@Tiqerboy]

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.

[@Delta_Red]

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.

[@kareem_xyz]

I got confused because I thought the rule meant that “Every card that has a D on one side, has a 3 on the other side, and the opposite is true.”

[@MrSergecj]

Yes, but why did you make that assumption? Thats exactly the test for logic. Making that assumption is not thinking logically, what this test is actually is testing. If I fall out of the window I will have a broken leg. That does not mean that if I have a broken leg, I fell out of the window. It could be the reason, but there are many more reasons to break the leg.

[@acantilado]

I bet a lot of people fail just by simply not reading the question correctly. It’s easy to mistakenly assume you are only allowed to choose 1 option. It would be good to know what % fail this test if you control for that

[@artmcnamera7984]

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.

[@waltergold3457]

The question is badly worded - it should read: "The rule is that every D card must have a 3 on its back - however, every 3 card need not have a D on its back." That's why the puzzle's other iteration is so easy to solve - we can deduce for ourselves, without a vague and clumsy explanation, what the rule is. Academics aren't necessarily writers.

[@nathanaelculver5308]

I disagree. “Every 3 does not need to have a D” is not a rule, it’s just explanatory. But a part of the test of logic is for the player to understand that “If D then 3” does _not_ entail “If 3 then D”. The rule “If D then 3” is not clumsy or vague. It’s only the (mistaken) assumption that it’s equivalent to “If 3 then D” that makes it so.

[@sushovanpal6596]

Your 1st statement actually implies the 2nd one (and the converse )using mathematical logic..so they are equivalent

[@davidsmith7653]

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.

[@onesquirrel2713]

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.

[@zantas-handle]

0:03 - "every card has a letter on one side and a number on the other side". That's pretty clear I'd say!

[@davidsmith7653]

@@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.

[@Baekstrom]

The problem gets a LOT easier if you, like me, have already seen another video explaining this exact riddle 😀

[@TarnishedProductions]

"this is easy if you already know the answer" lol

[@colorlessink]

I got it right but I get why mathematicians chose some of the other answers. They definitely like to overthink and look at all probable scenarios. I chose D7 as that's the minimum to get the rule right. But even I was like Am I wrong? after i clicked on the video and looked at the top comment.

[@marsovac]

Truth is you need to check every card because of manufacturing defects you might have a letter on both sides and that will also make the rule fail.

[@yasminesteinbauer8565]

I do not agree with this solution. The cards are not just made according to one rule. Another rule is that each card has a number on one side and a letter on the other. If I assume that the manufacturer of the cards is so unreliable that I consider that they do not follow the rules, I have to check the compliance of each rule and therefore each card. Who says the K card doesn't have a D on the other side? Why would the manufacturer follow one rule with 100% certainty and not the other? If I distrust the manufacturer I have to consider that every other rule has been broken as well. This means that the given task does not describe the logic constellation of the solution.

[@waltergold3457]

Agreed, Yasmine. And to top it off, the puzzle is worded, deliberately or not, in a misleading way. As I've just commented in the main thread, it's never stated that a 3 card needn't have a D on its back. That's why the puzzle's other iteration is so easy to solve.

[@jsmith498]

You phrased the question badly. How do you know that the K card doesn't have a D on the other side? You have no choice but to turn it over. If it's 100% guaranteed that the cards all have letters on one side and numbers on the other then that needs to be made clear at the beginning. Misprints can happen.

[@ayo-whats-this]

Bro stop it. You're just making a stretch here.

[@michelerusconi]

Bro have you watched the video? "Every card has a letter on one side and a number on the other side" Don't cope only because you didn't got it correctly

[@rubengarciaquismondo]

Stop giving excuses. This problem consists of very basic mathematical reasoning i solved it in 1 second. Idont believe anybody got it wrong i just dont believe it its too easy

[@abhisekchoudhury2661]

The question itself states that there is a letter on one side and number on the other. The question was accurately phrased. Stop making rubbish excuses.

[@tschantz]

I really hate “logic” problems like this. The rules are never explained well. It’s just a shell game, a trick. Nothing to do with actual math or logic.

[@AB-yz7bo]

Diddums

[@bulovapsb]

The problem was not a math problem, but it was definitely a logic problem. There was a condition: all cards have a letter on one side and a number on the other, and a rule: every card with a D on one side must have a 3 on the other. Then the narrator explains the solution about as clearly as possible. What more of an explanation would qualify as “explained well” to you?

[@Cory93NS]

the problem is it is deceptive and the question that is needed to be answered is vague, you may assume some details wrong, its not specified while asked. so because of that, the answer shown is one of the possible answers, depending on the logic used. it doesnt say that you cant have a duplicate of something, nor does it say you can etc.

[@Chomp_Fllangin]

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.

[@sm64guy28]

Ok, I feel like only 10% got it because the prompt is extremely confusing. I hadn’t understood the question asked correctly

[@БарриЛомов]

Actually, the second variant of the problem (beer and age) though it sound "logically equivalent" to the first (letters and digits) one, it has a HUGE difference. And that is - PHRASING. In second variant in video you get "age OVER 20", which means "from 20 and up to infinity", thus in human perception you divide the infinity of number into only TWO categories - over 20 and less 20. While in the first variant - human mind must look for a certain point out of an infinity of other higher AND lower points (a dot on an eternal line between infinity less and infinity more), that dont fit. So. In second variant - there is a BIG FENCE and we are looking on 2 areas of numbers, while in first variant - small dot among infinity of other dots. Have anyone tried to change the 2nd variant to something like "only men of age 30 - no more, no less - are allowed to drink whiskey of special sort". Or something like this. Wanna bet it will significantly decrease the number of people who will solve it - be much less than 75%? P.S. D is used in roman numerals and equals 500. Thus, it can be on both sides of cards, so you need to check card K too. :)

[@gavindeane3670]

D is a hexadecimal digit too 🙂