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.
Very amusing. I like it (and still got it wrong at first too).
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.
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I got it wrong. There is an upside – I’m gonna win some beers with this one. Thanks, Sean.
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.
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
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.
D’OH!
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.
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.)
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.
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.
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.
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!
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.
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.
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.
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.)
Oh no, I got it right. Of course I had to draw a diagram first. Does that mean I’m not smart?
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.
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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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..
“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.
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.
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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