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.
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.
I got it right with no problem
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.
#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.)
SO FUNNY,I LIKE HIGH IQ people!
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@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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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.
@ #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.
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…
#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.
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.
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 .
@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.
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.
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.
Apropos of absolutely nothing, there is a great new cartoon at xkcd: “Sympathy tips for physicists”
http://xkcd.com/660/
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 ???
>>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.
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?
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.