Are You a Cognitive Miser?

By Sean Carroll | November 4, 2009 12:14 pm

Jack is looking at Anne, but Anne is looking at George. Jack is married, but George is not. Is a married person looking at an unmarried person?

A) Yes.

B) No.

C) Cannot be determined.

This is from this month’s Scientific American — article unfortunately costs money. It’s about “dysrationalia,” which is what happens when people with nominally high IQ’s end up thinking irrationally. A phenomenon I’m sure we’ve all encountered, especially in certain corners of the blogosphere.

And the answer is the first option. But over 80 percent of people choose the third option. Here’s the solution: the puzzle doesn’t say whether Anne is married or not, but she either is or she isn’t. If Anne is married, she’s looking at George, so the answer is “yes”; if she’s unmarried, Jack is looking at her, so the answer is still “yes.” The underlying reason why smart people get the wrong answer is (according to the article) that they simply don’t take the time to go carefully through all of the possibilities, instead taking the easiest inference. The patience required to go through all the possibilities doesn’t correlate very well with intelligence.

  • DP in CA

    Well, technically, Anne could be a canary, not a person, so the answer is technically C, but you got me good on the false reasoning, now I’m just trying to justify my wrong answer.

  • ian

    So experimentally, patience is obviously an important part of intelligence, because people with less patience are less good at rationally solving problems. No excuses needed!

  • mirror2image

    Interesting, that this question can not be posed in Russian, because word “married” is not symmetric in Russian (Or more exactly answer is C). Female married male and male married female are different words. One can infer that not-quite-smart but smart enough Russians foreseen this puzzle and organized their language in a such way as to not be caught.

  • Peter de Blanc

    Argh! I *think* I would have gotten it right, but I don’t *know* because I couldn’t avoid reading the answer, which you printed immediately below the question.

  • rec

    Patience doesn’t correlate with IQ because IQ values speed.

  • Bevy of Beauties

    It isn’t surprising that the pollsters deem irrational anyone who doesn’t want to waste time answering their stupid questions. But they shouldn’t be taken seriously. What’s in it for me? is the completely rational response to this kind of question.

  • Oded

    Bevy, you’re making excuses and you know it :)

    We’re all upset we got it wrong.. Damn I feel silly :)

  • Jumblepudding

    It’s possible that Anne is undergoing a trial separation, so if pressed, she wouldn’t know what to say as to the married/unmarried question, regardless of what the law says, so her marriage is, like Schroedinger’s cat, neither alive nor dead. The human heart is a complicated thing. This is why I chose C. Just kidding, I’m dysrational.

  • Eugene

    I chose A fairly quickly for the right reason and thought boy that was easy….mmmm perhaps too easy? Then I spent 5 minutes wondering if this is a trick question….so I am not dysrational.

    However, I am paranoid.

  • Romeo Vitelli

    Then again, Anne and Jack could each be in same-sex marriages. That way, whether or not they’re married could depend on which jurisdiction they’re in.

    Just my way to muddy the waters and to say that I’m bummed out by what happened in Maine.

  • bigjohn756

    It took me only a few minutes to get the correct answer…after I read the explanation.

  • Gavin Flower


    I too got the wrong answer.

    I now realize I was solving the wrong problem. The next step was to work out what I did wrong, and see what I can learn from this example.

    I was attempting to determine if Anne was maried, this is neither the question asked, nor is it relevant to answering the actual question.

    The question relates to a characteristic of the ‘system’ as a whole: does it contain a pair of objects that satisfies a given condition. There are 2 pairs we have information about, and Anne is in both of them. As implied in the explanation, the marital state of Anne is only relevant in determining which of the 2 pairs may satisfy the relationship. However, we are not asked which pair might satisfy the condition, nor exactly how many pairs satisfy the condition, rather if at least one pair satisfies the condition.

    I am a software developer, and sometimes tracking down bugs, or determining how to do something new, takes me longer than I would like – I suspect that this example indicates one cause of my problems.

    Hopefully, I can put this new insight into practice!

  • José

    Well, I don’t fully agree that “the patience required to go through all the possibilities doesn’t correlate very well with intelligence”. Of course there’s no point in going through possibilities that don’t help solving the problem (that’s where intelligence is a factor), but the number of possibilities one should go through has a lower limit bellow which it’s just lazy disregarding IQ, and an upper limit above which it’s not that intelligent to keep exploring them if solving the problem isn’t worth it.

    Patient correlates with IQ in the sense that one should stop trying if it’s not worth it, but stopping too soon I believe is more lazy than smart.


  • Mickael P

    For those (like me) who got wrong on this one you can still have a look at a related New Scientist article ( ) which DON’T cost money.

  • Z

    Is a married person looking at an unmarried person?

    So we have two possible pairs, in the case of Jack and Ann we cannot tell since we don’t know if Ann is married in the case with Ann and Gorge same thing so the answer is C.

    To me this is a perfectly rational approach and I would have to have damn good reasons to ponder such questions any deeper than that. The explanation given in the post is certainly true in my case as I definitely view checking each case as way more effort then it’s worth, even though it did occur to me that it might be a tricky question it was still nowhere near the incentive I would need 😛

  • Brian

    >>>Well, technically, Anne could be a canary, not a person, so the answer is technically C, but you got me good on the false reasoning, now I’m just trying to justify my wrong answer.

    if anne is a canary, then she isn’t married, so a married person is still looking at an unmarried person. 😀

  • Brian

    This trick puzzle is an excellent illustration of the principle. And yes, where Sean says that patience doesn’t correlate very well with intelligence, I presume he means intelligence as it is traditionally measured by “IQ tests”.

  • PhilG

    I think that anyone who tries to make up excuses for not getting it right lacks integrity as well as intelligence – but there could have been two different Annes. :-)

  • Meredith

    Awesome. Only, in your explanation, you refer to Jack as John. This didn’t help my already spinning mind!

  • Ellipsis

    Yes, indeed Anne and George might both be canaries. However, even so, we can be essentially sure that somewhere in the world, a married person is looking at an unmarried person, so the answer is A.

  • Arun

    The psychometrician response would be that if these question does not correlate well with g, then it is not a good question.

  • The Science Pundit

    Having grown up on a steady diet of Raymond Smullyan books, I got the correct answer right away. Does that mean that I’m rational, or just that I’ve done so many logic problems that effectively parsing them is second nature to me?

  • Sean

    Meredith, I gave Jack back his nickname. Thanks for the catch.

  • spyder

    Like The Science Pundit, I have a large collection of books filled with these sorts of puzzles. I didn’t purchase any of them however. Due to the “changes” in the curricula of k-12 education in this country (NCLB?), there simply is no longer time to teach the children how to think rationally and logically through problem solving steps. Thus my collection came from books that were heading to the pulp plant, along with lots of other teacher workbooks and materials (that i passed on to my student teachers).

  • Neal J. King

    I’m one of the dumb people who got the answer right the first time, because the first thing I thought was, “Hmm, I wonder if this is like the Cretan-liar problem, where you can get a correct answer by studying the two cases?”

    In any case, who cares what the number on an IQ test is?

  • S.C. Kavassalis

    Very amusing. I like it (and still got it wrong at first too).

  • fh

    Got it wrong. And that even though I have been just solving logic puzzles involving lots of xor’s. I believe these puzzles are essentially hard because we don’t have a natural language concept for the xor operation, (this is really similar to xor at first glance, with the “if one is true the other isn’t and vice versa” concept). In this puzzle the additional difficulty is that there is a false lead. It’s intuitively easily misparsed into the kind of operations we know.


  • gr8googlymoogly

    I got it wrong. There is an upside – I’m gonna win some beers with this one. Thanks, Sean.

  • Michael

    Haven’t read the SciAm article, but I don’t see where “intelligence” or “patience” enter into this. It’s really a problem of reading–the puzzle traps you (it trapped me) by a syntactic sleight of hand; it’s worded to elicit a nearly automatic substitution of “George” for “unmarried person,” so that the question you think you’re answering becomes, “Is a married person looking at George?” (When I first read the puzzle, in fact, my reaction was that the “Jack” part was just there as a red herring.) To which the correct answer, of course, is C.

    In other words, the puzzle takes advantage of syntax, and of people who are unwary enough about logic puzzles as to apply their ordinary (and usually correct) syntactic expectations to it. It’s not a question of “dysrationality,” but about reading contexts and genre experience.

  • duh

    This always reminds me of the gordian knot…

    In any case, it is a two state system and the answer is A…but it is a load of cr*p

  • Koray

    Quote from the freely available article: “…But most researchers agree that, overall, the correlation between intelligence and successful decision-making is weak.”

    Good to know. I think.

    The trouble with the puzzle is that it’s too abstract, but phrased in everyday terms. We don’t often care about “an abstract married person”; we usually care about Anne or Jack in particular.

    There’s a similar logic puzzle regarding playing cards, which many people fail at. However, when phrased in terms of “card’ing alcohol purchasers” everyone gets it right. Sometimes we just don’t care enough.

  • CoffeeCupContrails


    Not enough patience – I’ve known this for a long time. It’s the reason I scored perfect in my GRE Quants and not so much on verbal – the last multiple choice exam I took. I think reading loads of information on an hourly basis makes you scan and pick up flavors of an article or piece rather than pay really close attention. Information overload.

    At least, ‘intelligent’ people like me have a sense of ‘why do I sense that I’m gonna get this easy one really wrong?’ in the back of our minds after we read the choices – based on the context of an intelligent blog posting seemingly easy questions. Didn’t think as much on the citizenship questions couple of weeks ago – just picking up facts is easier than processing them maybe.

    But yes, Anne could’ve been a Chipmunk.

    You should put the answer in the comments for posts like this, Sean. It comes highlighted anyway here on discover and my RSS reader doesn’t pick up comments.

  • TimG

    I got it right, since I carefully talked through both possibilities. I wonder if getting it right correlates better to high grades in school than it does to high IQ scores. I know I did well in school because I was the kind of geek who triple checked his homework . . . but that kind of anal retentiveness probably isn’t as useful on a speed based IQ test. (I’ve never taken one so I can’t say for sure.)

  • DP in CA

    Michael may have a point about the syntax being the trick. Imagine the puzzle presented a different way: someone lays a red playing card on the table in front of you, face up, then covers half of it with a face-down card, then covers half of the second card with a face-up black card in such a way that the third cards is not covering any part of the first card, and asks you “Is a black card covering a red card?” You’ll probably immediately see that the answer has to be “yes” regardless of the color of the face-down card. When you’re looking at the three overlapping cards, you’re not dealing with syntax or word meanings, and coming up with the correct answer by considering both combinations is easy.

  • Kennric

    Michael: No, its still a matter of patience. The cues of syntax and language are time-saving devices, a patient person would see that this is a logic puzzle and would take the time to sieve out the actual logical cases, not just take the syntax and toss out an answer.

    I got it wrong, knew I was getting it wrong because the answer seemed so obvious, but did not have the patience to work out how and why, I clicked through instead. But at least I was aware that I was abdicating a rational analysis. Yes, it is a trick question, a language trick, but the patient rational thinker would take the time to unravel the language and understand the logic.

    Oh, and patience is not the opposite of laziness, how much time you devote to a problem is a cost/benefit kind of calculation. Scientists all over the place deal with far trickier, more confusing and syntactically sneakier problems all the time, and they get them right because that is their job, whereas thinking hard about a silly question in a blog post is not.

  • wordmoose

    I got the right answer because I was taught to go through the possibilities in this sort of problem by Ray Smullyan’s wonderful books of logic puzzles.

  • Stephen

    How is having to think through two cases patience? It’s amazingly sloppy thinking otherwise. But then I’m a computer programmer by trade and a scientist by training so this sort of thing is pretty much second nature (it’s akin to debugging).

    Oh, and I got it right and am amazed anyone didn’t!

  • J.J.E.

    This does not strike me as a matter of patience, but a matter of training. Maybe that’s just a semantic distinction though.

    True, it probably took me several times as long (20 seconds instead of 3 seconds or whatever the times actually are, I didn’t measure the time) to determine the correct answer as it took others to guess the wrong one. But really, as far as problems go, the “brute force” method isn’t all that time consuming, and hence doesn’t require much patience. If only people were trained for this sort of thing in the same way they are trained for other tasks (like basic arithmetic or tying shoes), then it wouldn’t seem so “patience” based.

    When confronted with a multiple choice question that requires one to think in unfamiliar ways, it is easy to pick the wrong answer. I think this type of question is a very different class of question than the Monty Haul problem or the “what speed would you need to travel on a return trip to average 2x the speed of the 1st half?” types of question. However, all 3 showcase solutions that require unfamiliar ways of thinking.

    Stumbling when answering such questions out of the blue isn’t an evidence of lack of patience, but rather a lack training. They are trick questions insofar as they probe rarely used mental “muscles”. But maybe I’m just biased a bit. I’m scientist who programs a lot, so like Stephen says, maybe I’m already trained to do this sort of thing.

  • Lord

    The ambiguity is whether Ann’s only choices are married or unmarried. Often they are not and she may be categorized differently, unmarried meaning never married, divorced having been married, remarried after having been divorced. While the assumption she has only two choices is not unreasonable, it is still an assumption.

  • capitalistimperialistpig

    In any case, who cares what the number on an IQ test is?

    Employers – from Google to the Army to WalMart to the NFL. They all test for IQ since almost nothing* correlates better with job performance. And schools – SAT, GRE, LSAT are all mainly tests of IQ, even though they all deny it.

    *The exception is demonstrated performance of the work required – which is why the NFL measures that as well.

  • Bee

    I’m waiting for the day when giving the wrong answers will be used as an indicator for high IQ.

    (In case anybody wants to know, I had read what the right answer is before I switched on my brain.)

  • Sara

    Oh no, I got it right. Of course I had to draw a diagram first. Does that mean I’m not smart?

  • Charon

    What I find interesting is that, as with many kinds of complicated thinking, this can be taught (not that this is particularly complicated, but the point remains).

    I got it right quite easily, which I attribute to a lot of good math courses in college. (A certain kind of basic real analysis problem presents itself nicely to proof by categorization – doing a>0, a=0, a<0 separately, for a in the reals. There are plenty of other examples.)

    This is of course why we physicists spend so many damn years in university. Even the ones much smarter than I.

  • Stephen Bahl

    Kenric: But once one falls into the trap, patience is not a way out. One can keep reading each part of the problem over and over and keep (erroneously) substituting “George” for “an unmarried person.” I know I’ve done that in the past, albeit not with this exact problem. Even when I knew the right answer, I couldn’t arrive at it despite numerous careful repetitions, all because I was stuck in a mode of unconsciously transposing one thing over another. I became very frustrated, trying to split the problem into as many pieces as I could and examine each piece and check and doublecheck and triplecheck and look for any inconsistency I could, but it didn’t help because there was a square somewhere that I was inexplicably calling a circle despite evidence to the contrary sitting right in front of me every time I went over it.

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  • Peter Coles

    I think the correct answer is C. Where does it say that Jack, Anne and George are persons?
    Horses can be “married” when they are harnessed in pairs..

  • Lab Lemming

    “Employers – from Google to the Army to WalMart to the NFL. They all test for IQ since almost nothing* correlates better with job performance.”

    Don’t think too fast, or you might assume that the above statement implies a good correlation.

    But the terms of reference for most intelligence tests require them to be quick** to administer and quick to assess, so it is not surprising that they show a bias towards quick thinkers over thorough ones.

    ** compared to, say, the timescale of research publication.

  • GAC

    Ironically, I dismissed the “Yes” answer as being the irrational choice because I came to that choice on the assumption that Anne was married to Jack and then said … wait a minute, it doesn’t say that.

    So apparently my mathematical logic gets polluted with social experience and assumptions (like an assumption that married people will be together most of the time), and then I overcompensate without actually understanding the abstract question.

  • SFJP

    Well, after 1 second of deep though, confident in my High IQ, I answered C. Then I submitted the problem to my automated theorem prover I wrote when I was a researcher in applied logic. And it gave me the answer A. I was ready to go into a long debugging sequence to understand why this usually robust and complete theorem prover went wrong when I read its proof that was perfectly valid. You know what, I’m already depressed that an elementary automated chess player I wrote 30 years ago can still beat me, but I’ve never been a grand master of this game, but that my own theorem prover could do that to me, a professional logician, is really too much… Please, restrict yourself to physics news….

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  • marcel

    I’m surprised that the programmers claim that their training in debugging protects them from this error. I have an emprical, even dialectical, approach to debugging: study the problem for awhile, several steps where I make a change or two and rerun the program to get a better idea of what is going on, study some more, try changing and rerunning the program some more, etc. Rarely do I just sit down and try to work out every case. Probably not patient enough.

  • Nick

    Some comments I put on Sean’s FB account – must remember the blog. I like the syntax suggestion too – ‘is not’ directs away from the married-unmarried binary.

    1) These cognitive deficits are highly context dependent. E.g.:

    Jack is looking at Pat but Pat is looking at Georgette. Jack’s male but Georgette is not. Is a male looking at a female?

    I bet a lot more people would get that right. Some categories are much easier to reason about.

    My example is supposed to show that you can’t analyse these deficincies simply in terms of the form of the problem. It’s not so much laziness as misidentifying the kind of problem – and not so much stupidity as having a ‘heuristic’ for some other important kind of problem hard wired. It takes effort and training to overcome the innate misidentification of the problem (again in part caused by the specific categories involved – marital status vs gender); hence the cognitive cost. I guess the heuristic was selected for at some stage – who knows, perhaps day to day it still gets enough right to be more useful than taking the time to think things through! Of course for big things it could be catastrophic but is there any evidence that this defect still applies in life or death situations rather than the unreaistic toy examples we been discussing?

    I came up with a suggestion about the problem riding in to work this morning, in between dodging trucks. That is, the way the question is posed suggests that it is a kinship problem, and so the natural thing to do is to try solving it with kinship heuristics (I think it’s more than reasonable to suppose we evolved to have those), which of course are useless here – again, the ‘cost’ is in finding another approach to the problem, not in sorting through the possibilities – something much higher. So, as you described it, the Sci Am article sounds pretty much wrong to me.

    Finally, a random speculation. Maybe some people are both smart and stereotypically impractical because these heuristics have less of a grip on their thought processes – because they suffer from a cognitive deficiency (relative to some problem scenarios)!

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  • onlines

    Based on, “The patience required to go through all the possibilities doesn’t correlate very well with intelligence.” Should i consider myself stupid since i said “Yes”?

  • Plato

    This example is a bad analogy to the majority of problems faced in the real world. In the real world, “Anne” is usually not in a yes or no state (2 options; married or unmarried), but is instead in one of many unknown states. From conditioning, our behavior has been molded to not try and figure out all of the possible states for “Anne” or a minor problem like this one since this is usually not possible and a waste our time. Making the possible false assumption that “Anne” is in one of two states (married or unmarried) will usually give you more false conclusions in the real world than the number of false conclusions that come from running into the above problem. Now if getting the wrong answer to this problem actually had a negative outcome on your life, then I am sure more people would have taken the time to work out all of the possibilities and get the correct answer.

  • Neal J. King

    The analogous examples described in:
    #34, DP in CA
    #53, Nick

    show that a change of interpretation of the entities and the actions they do makes the problem much easier to get right quickly.

    It reminds me of another logic puzzle, which was difficult to figure out when the entities were labeled as “A”, “B” and “C”, but easy to sort out when they were described as “Alice”, “Bob” and “Carol”. (I don’t remember the specific details of the puzzle.) In that case, it seemed that the use of the names plugged into a mental module that we all seem to have for processing relationships: Probably a useful mental capability for operating within a social group!

    Whereas in the case of this puzzle, somehow the invocation of that module gives a misleading push to one’s direction of thought. Perhaps because there is NO social/behavioral connection between the status of being married and the action of looking at someone else.

    However, there IS an obvious tie-in between being male/female and the action of looking at someone else (also male/female). So in that case, the invocation of the mental module might help.

    In the case of the cards covering each other, there is no social aspect at all, so the mental module is not invoked at all: Hence, no confusion.

    The relation between these tests and “intelligence”? Well, the most common application of intelligence is dealing with other people, so it makes sense that intelligence is correlated with the activity of the mental module. In the instant case, this module is hurting performance on this test. So intelligence SHOULD be negatively correlated with this test.

    The people who did well on this test are either weak in the mental module (“dumber”), or else somewhat alienated from other people (“socially dumber”). I probably fit into the second sub-category.

  • Alex R

    Someone using classical logic would of course derive the answer (A) to this question. However, I must note that someone using intuitionistic logic would get the answer (C). Intuitionistically, let A = “Anne is married”, and B = “a married person is looking at an unmarried person”. We know that A implies B (since then Ann is looking at George), and we also know that not-A implies B (since then Jack is looking at Ann) — but intuitionistically, we can’t derive B from these two statements. (If we could, we could derive excluded middle, which is not an intutionistic theorem.)

    Another way of thinking about this is that intuitionistic derivations should be “constructive” — we should be able to find an example of a married person looking at an unmarried person. But if we don’t know Ann’s marital status, we can’t come up with such an example.

  • Koray

    Alex R, yes, that’s also what I meant in my reply, but I didn’t want to use the logic jargon. Nobody should beat themselves up too much for missing an existence proof in this context; we don’t as much care about “there exists a married person” as “this particular married person”. I believe if the question was phrased differently (e.g. with live wires and bombs, etc.) I am guessing more people might get it right.

  • Mayhem

    Sheesh, I’m feeling stupid BECAUSE I got it right. -_- Should I feel that way cause I stoped to read again, or should I feel good because I stopped and read again? I’ve heard that IQ doesnt necesarily go hand in hand with intelligence, but still. Thats a depressing read.

  • gwennyth

    Anne could be in a domestic partnership.

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  • John

    Listen, Ann is divorced. She no longer believes in marriage and is likely to start playing for the other team. Jack is married and thinks she’s cute but all he can do is stare, since he is married. Annoyed, Ann looks at George who is a clueless middle-aged man who ponders trick questions for enjoyment.

  • Mai

    Wonderful discussion. Much better than the puzzle itself.
    The only additional point I would like to emphasize is that changing your way of thinking about such puzzles is what graduate school is all about today in the U.S.A. Critically thinking through medical data that may be contradictory, complimentory or neither is key to good medical decision making. (While avoiding those heuristics, which scare me silly!)
    Training IS the difference on whether or not this is answered correctly. Training is what gives you the tools to separate the social paradigm out from the problem as well as objectify the individuals Iyes, while isolating us and perhaps making us socially “dumber” it is a useful skill) and use a A,B, C schema instead of getting wrapped up in extraneous detail. I guess I am saying…while intelligence may not be correlated with patience, speed IS important when dealing with a roomful of Patients. So, intelligence or training, I still think it is a fair test.
    I guess I am just saying, respect those who have worked hard to develop these skills in order to serve you. It might just save your life…
    Yes, quite obviously, I got it right.

  • Mark

    I agree with those who say it’s not really about patience. I think it’s simply more efficient to skip the thinking and read the readily available answer.

    (No, I don’t really think that. Yeah, I got it wrong too. Dammit.)

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  • kikito

    I really thought Anne could be a donkey or a mannequin or something.

    If it would have said “The three of them are real people” then I would have probably thought a bit more.

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  • RichardW

    I think the reasoning that most of us probably went through was something like this…

    We don’t know whether Anne is married. Therefore we don’t know (A) whether Jack is looking at an unmarried person, or (B) whether a married person is looking at George.

    So far that’s correct. But then we continue… Since we don’t know either A or B, we don’t know whether either of them is true.

    But that step is not logically valid. We can know (A OR B) without knowing either A or B. To put it another way, we can know that one of them is true without knowing which one.

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  • Janne

    I took the right answer but started to feel skeptical about it later on.

    Anyway, I think you can disagree about fundamental issues. Do you agree or disagree?

  • Z

    Lol at @49 SFJP.

    Based on reactions I have to say the problem is designed to make everyone feel bad, if you picked C you got owned by a simple puzzle, if you picked A your intelligence is being questioned if you picked B not only you got it wrong your heuristics which the problem exploits to induce wrong answer is not working.

    Sean stop alienating your readers 😛 BTW which one did you pick?

  • Cody

    Yeah, I got it right but now I’m questioning my intelligence.

    Though a few points: it does say that 80% of people got it wrong, so it can’t be only above-average intelligence people answering incorrectly (unless, did they only give it to high intelligence people?)

    And also it doesn’t say patience is anti-correlated with intelligence, just not strongly correlated. Though it seems the more I believe myself to be “smart”, the more likely I am to make silly mistakes (my ego seems extremely detrimental to my intelligence.)

  • znz

    It’s a philosophical question.

    Not all schools of mathematical philosophy (e.g. intuitionists as per Brouwer) accept the law of the excluded middle, i.e. that either A or not A.

    Actually, that is true, but I still don’t think it applies here, because we know that for being married or , the law of the excluded middle does apply.

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  • John R Ramsden

    I posted the question as a poll on the UK IT Contractors’ Forum which I frequent, and sure enough the results showed a large majority of “can’t be determined”. (The name change is an in-joke specific to that forum.)

    Someone there asked if there were any other problems that can disproportionally lead intelligent people astray in the same way, and the only one I can think of is the Monty Hall problem. Almost everyone, even world-class mathematicians like J E Littlewood and Paul Erdos, gets that wrong at first.

  • http://facebook Sherita

    I got it right with no problem

  • Brian Too

    I wasn’t that invested in the puzzle and came to a quick and wrong answer.

    The thing is, I’m still not that invested in the puzzle. So what if I got it wrong? I suspect that’s true of many or even most of the people here.

  • Neal J. King

    #76, John R Ramsden:

    You claim that the Monty Hall problem “disproportionately” leads intelligent people astray.

    Do you have any evidence for that?

    It’s my impression that that problem fools virtually everyone, because the result is so unintuitive. You really have to crank out the probabilities before you can be sure of the correct answer.

    (After you’ve done it the hard way, you can formulate a “simple” argument – but it doesn’t sound any more convincing than the more intuitive arguments that lead to the wrong answer. There really is no replacement for case-by-case examination for that one.

    The only reason I could imagine that unintelligent people could be said to “do better” on that problem would be that they would give up right away. But I don’t even think that’s likely.)



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  • Ralf Muschall

    @Alex (#58): That was exactly my idea after I failed (i.e. guessed C and started to search an excuse). Might it be that the human brain implicitely uses some weaker (intuitionist or whatever) axiom system unless one is explicitely trying to calculate exactly? This looks like an interesting topic in cognitive psychology.

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  • Alan Kellogg

    …If Anne is married, she’s looking at George, so the answer is “yes”; if she’s unmarried, Jack is looking at her, so the answer is still “yes.”…

    Say what? I think we’ve got a case of assumptionitis here. Let’s go over what facts we have.

    Jack is married.

    George is not.

    Jack is looking at Anne.

    Anne is looking at George.

    Question: Is a married person looking at an unmarried person?

    Going by the facts available, without over analyzing the problem, we don’t know. Anne’s marital status is not specified, much less hinted at. To say she is married or not requires guessing, and that is prone to error. To conclude she has to be married because she’s looking at an unmarried person is to assume something that may not be so.

    Call me a strict constructionist, but I go by the information available; and if the available information says nothing about a subject or a subject’s state, then I don’t consider what isn’t there. And in this case the question says nothing at all about Anne’s marital status. In short, people are making assumptions because the authoritative answer says she is married while using some faulty reasoning of its own.

    In short, this thread is an example of Appeal to Authority as Dysrationalia. Remember, the author of a piece isn’t always right.

  • Alan Kellogg

    And then I realize I engaged in a bit of Dysrationalia. In short, I had the wrong answer because I jumped to conclusions. Let’s look at the problem another way.

    Anne is looking at George, who is unmarried.

    Jack, who is married, is looking at Anne.

    It doesn’t matter whether Anne is married or not, because if she is then it would be a married person, Anne, looking at an unmarried person, George. Whereas if she is unmarried then it would be a case of a married person, Jack, looking at an unmarried person, Anne. To say Anne has to be married because she’s looking at the unmarried George is a mistake, because we are dealing with three people not just two.

    Anne’s marital status has nothing to do with the case, it’s an irrelevancy. What matters is the marital status of George and Jack. So long as we know that they are, respectively, unmarried and married, Anne can be either without substantially affecting the answer to our question.

    So, to make this succinct, is a married person looking at an unmarried person? Answer, yes.

    At greater length, because we have a married person—Jack—and an unmarried person—George—-involved Anne’s marital status has nothing to do with the case. So if she’s married the fact she’s looking at George means a married person is looking at an unmarried person. While if she is unmarried means that Jack—who is married—is looking at the unmarried Anne.

  • J.J.E.

    @ #79

    I think the Monty Haul problem can be expressed very intuitively in such a way that can even defy the intuitive (but wrong) answers.

    1) The probability of being right before removing a door is 1/3;
    2) If you don’t switch, the probability of being right remains unchanged;
    3a) (the correct answer) If you switch, the probability of being right is the complement of staying (ie 2/3), so you should switch;
    3b) (bad reasoning/right answer) If you switch, the probability of being right is 1/2, which is greater than the probability of being right if you stay (1/3), so you should switch.

    The key is establishing #2. Of course, if you’ve successfully established #2, then the intuitive (but wrong) reasoning in #3b (if you switch, the probability of being right is 1/2) should be very suspect. But even if you can’t convince somebody of that, as long as you can establish #2 and you can establish 1/2 > 1/3, then you’re home free, although you feel dirty for having used faulty logic.

  • Cory

    I got this wrong, but what about the person staring at Jack, Anne and George? What’s his or her deal? If Jack, Anne and George fall in the forest…

  • Neal J. King

    #87, J.J.E.:

    Yes, as you’ve shown, there IS a correct line of reasoning.

    But you’ve also shown two other lines of reasoning that are wrong, but which look just as plausible.

    The only way that I could be sure of the right answer was to look into & count the very specific cases: Then one can identify the correct way of looking at it.

    And, further to the point that I raised: according to the wiki article on the Monty Hall problem, it seems to stump people universally. No mention is made of any special error-rate for higher-IQers.

  • John

    I got this right pretty quickly and easily when reading the article (New Scientist version)- because of the context of the question (an article on reasoning and mistakes people make etc) I knew to take that extra second to think about it a bit more carefully. Because I did this and because it triggered familiar experiences with logic puzzles, math etc, I found it straight-forward. Visualizing the basic arrangement before enumerating possibilities also seems to help me with these sorts of things.

    I think that more than anything this kind of puzzle/article shows the importance of reflecting on your own thinking habits and trying to improve them, rather than trying to get the right answer first up. In the past I have made a lot of silly mistakes on tests etc when trying to go too quickly – only by realizing this problem and directing conscious effort towards recognizing when to slow down did I stop myself making these mistakes (as much). I think that learning when to control your thinking more carefully is a crucial skill to work on.

  • JaroslawG

    My first reflex was to consider Ann as a filter for a beam because the question is formulated in a nice transitive way :
    J -> A -> G .
    If Ann has the same state like Jack then she is transparent and Jack looks at George , e.g a married person looks at an unmarried person
    If Ann has the opposite state to Jack then she is opaque and Jack can only see her , e.g a married person looks at an umarried person .

    Hence as Ann can only have these 2 polarisations , I said myself the answer is A .

  • monty

    @all those talking about the monty hall problem.

    This problem only works if you know beforehand that you are *always* going to be offered the chance to change doors. If this isn’t stated beforehand, then its easy to imagine a scenario where changing doors is not in your favour, i.e. if the host only offers you the chance to change when he knows you’ve picked the winning door. The failure to say that you will always have the option to change your door before the door-picking has started, means that any probability calculations are meaningless.

  • pete

    If Anne is married then YES. If Anne is not married then YES.
    If Jack is married then YES. If Jack is not married then YES.
    If George is married then YES. If George is not married then YES.
    ……….likes brains that value dull loops.

  • Haelfix

    The first post in this thread is the technically correct response. If Ann is a canary, then she isn’t a ‘person’.

    I got the A answer after about 2 seconds of thinking about it, but I paused for awhile thinking there must be a catch somewhere (something along the lines of ‘what could Ann be’). Its a typical problem with overanalyzing a question that often plague IQ test results.

  • Neal J. King

    Apropos of absolutely nothing, there is a great new cartoon at xkcd: “Sympathy tips for physicists”

    I admit to getting it “very wrong”: I was thinking about separating mother/child pairs.

  • ^^

    i still dont get it…why is the answer not ???

  • chris

    >>if anne is a canary, then she isn’t married, so a married person is still looking at an unmarried person.

    since when is a canary a person??

    and for exactly this reason C is the correct answer – sorry SciAm.

    (my math teacher in school had trick questions like this to teach us never to assume things that were not given. the canonical example goes like this: there are 4 children and 3 lollies. Anne, Bernard and Chris each ave one lolly. Does David have one? of course you can’t tell, since noone specified David was one of the four.)


    Unless of course if Anne is gay then whether or not she’s married depends on what state she’s standing in at any given time.

  • Arsenic

    I, like several others, thought “C,” realized that it had to be a trick question, gave myself another 10 seconds of thought and got A for the right reasons.

    This is obviously because of my training at recognizing and overanalyzing logic problems when I know I’ll feel particularly stupid if I get it wrong. What I wonder is: Would I have gotten the problem without training in tricky logic questions of this sort otherwise? Was the crucial thing about my past experience the training itself or the capacity to realize I needed to think longer?

  • Blue

    Nice one.

    I got it (option C) wrong too, and like some of the above I looked at the answer too soon!!!

    Also, I suspect Jack’s marriage is in trouble.

  • Dadude

    I thought C. I didn’t read all the posts, I’m too impatient. The reason for my choosing C was that we do not know where George is looking. He might be looking at his nails, himself, Jack. Hence we don’t have enough info to answer the question.

  • PeneErectus

    All of you are trying to arguing about “What I choose C”… Next time only say, oh shit! is really A? and don’t try to autosatisfy yourselves saying to you “Eh eh, I have a Scientific reason to choose C”. Next time, simple say, nice game bro.


  • Neal J. King

    #102, PeneErectus:

    Well, I did choose A.

    But I still think it’s an interesting question as to why many people chose C: It suggests some ideas about how people think.

    You can learn something about a system from its failures, as well as from its successes…

  • Raman HK

    But cant Anne still be in a LIVE-IN relationship… Consider all the options.. So its C

  • Zequez

    Nice, so, I’m smart =D xD

  • James

    The answer is C). We do not know if Ann is a person. Therefore, we cannot determine the answer. To say A) is to make an assumption and therefore to be wrong.

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  • Jack

    Hi, Im Jack, I was not looking to Anne, I was looking to George, but I felt embarrased to recognise it at first… so I lied. Oh! The answer is still “YES”, it doesn’t change nothing….


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Cosmic Variance

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About Sean Carroll

Sean Carroll is a Senior Research Associate in the Department of Physics at the California Institute of Technology. His research interests include theoretical aspects of cosmology, field theory, and gravitation. His most recent book is The Particle at the End of the Universe, about the Large Hadron Collider and the search for the Higgs boson. Here are some of his favorite blog posts, home page, and email: carroll [at] .


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