Test Yourself: The Married Problem - 80% Get Wrong?

[ProfuselyQuarky]

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?

I saw this on YouTube and the claim is that 80% of people get this problem wrong. There are a lot of brilliant people here, so let's test to see if the % of people wrong is exceedingly less that 80% here on this forum. No Googling or Binging or Yahooing or Duck Duck Going for the answer. Or else, what would be the point?

Don't post the answer before a fair amount of people have voted, either :)

 

[axmls]

My answer:

Spoiler: Answer

if Anne is married, then a married person is looking at an unmarried person (Anne is looking at George). If Anne is not married, then a married person (Jack) is looking at an unmarried person (Anne). In both cases, the condition is satisfied.

 

[ProfuselyQuarky]

Ack! People, don't look at @axmls's SPOILER without voting first

 

[micromass]

Reminds me of this amazing proof http://www.cut-the-knot.org/do_you_know/irrat.shtml
As a constructivist, I have to answer that it cannot be determined even though I completely understand what the solution is supposed to be.

 

[ProfuselyQuarky]

Reminds me of this amazing proof http://www.cut-the-knot.org/do_you_know/irrat.shtml

Yes! I found the Married Problem while looking into this exact proof. It's very clever, isn't it?

 

[micromass]

Yes! I found the Married Problem while looking into this exact proof. It's very clever, isn't it? Have you voted? ;)

Clever and very unsatisfying since it doesn't tell you which the numbers are.

 

[ProfuselyQuarky]

Clever and very unsatisfying since it doesn't tell you which the numbers are.

Yes, true, but I still like it because it's something anyone can understand, so I can show it to all people I know who don't like math because they think it's too hard and boring (run-on sentence there). It makes them go, "whoa" and then I become slightly less ridiculed for enjoying numbers as much as they enjoy their video games and television.

 

[micromass]

Yes, true, but I still like it because it's something anyone can understand, so I can show it to all people I know who don't like math because they think it's too hard and boring (run-on sentence there). It makes them go, "whoa" and then I become slightly less ridiculed for enjoying numbers as much as they enjoy their video games and television.

How sad is a society in which a person would rather be ridiculed for doing math for hours than for playing videogames for hours...

 

[ProfuselyQuarky]

How sad is a society in which a person would rather be ridiculed for doing math for hours than for playing videogames for hours...

Hey, I'm sad for them!

 

[micromass]

Hey, I'm sad for them!

You shouldn't be. They're happy in their ignorance. You shouldn't be sad for yourself either, you seem to have found happiness in this situation. But consider those bright people who would enjoy math very much but dislike it in order to not be ridiculed. I think all of this is a great loss for society.

 

[ProfuselyQuarky]

You shouldn't be. They're happy in their ignorance. You shouldn't be sad for yourself either, you seem to have found happiness in this situation. But consider those bright people who would enjoy math very much but dislike it in order to not be ridiculed. I think all of this is a great loss for society.

Yes, okay. At least I have two parents, PF, and awesome YouTube channels to fuel my nerdiness

Anyway, back to the married problem. Two people have voted "Cannot be determined". If at least one of you are watching this thread, could you explain why you think there's no answer based on the info provided?

 

[micromass]

Yes, okay. At least I have two parents, PF, and awesome YouTube channels to fuel my nerdiness

Anyway, back to the married problem. Two people have voted "Cannot be determined". If at least one of you are watching this thread, could you explain why you think there's no answer based on the info provided?

You can click on "2 vote(s)" on the poll to see who voted it.

I voted "cannot be determined" in any case. I'm a constructivist.

 

[Evo]

Isn't this something that can easily be answered by just assuming Anne is unmarried? Is there something missing?

Anyway, back to the married problem. Two people have voted "Cannot be determined". If at least one of you are watching this thread, could you explain why you think there's no answer based on the info provided?

It cannot be determined without making an assumption about Anne.

 

[ProfuselyQuarky]

You can click on "2 vote(s)" on the poll to see who voted it.

Thanks, I didn't know that.

I voted "cannot be determined" in any case. I'm a constructivist.

You voted for the name of constructivism?? The point was to see if PF could score higher than the general public

Isn't this something that can easily be answered by just assuming Anne is unmarried? Is there something missing?
It cannot be determined without assuming Anne is unmarried.

What if she is married? What happens?

 

[micromass]

You voted for the name of constructivism?? The point was to see if PF could score higher than the general public

Well, you said 80% got the problem wrong. My point is that voting "cannot be determined" doesn't mean you got it wrong. What makes your answer wrong is the reasoning behind the answer, not the answer itself.

 

[Evo]

Thanks, I didn't know that.

You voted for the name of constructivism?? The point was to see if PF could score higher than the general public

What if she is married? What happens?

Sorry, I clarified my answer. If you assume she's married, the answer is no. If you assume she is unmarried, the answer is yes. The real question is what is George doing?

 

[micromass]

Sorry, I clarified my answer. If you assume she's married, the answer is no. If you assume she is unmarried, the answer is yes.

That is not the correct answer, evo, even in constructivism.

 

[ProfuselyQuarky]

Sorry, I clarified my answer. If you assume she's married, the answer is no. If you assume she is unmarried, the answer is yes. The real question is what is George doing?

George is not married, so maybe he's looking for someone :P

But the question is not really supposed to be focused on George . . .

 

[Evo]

That is not the correct answer, evo, even in constructivism.

Works for me. My answer is that you cannot know without making an assumption, if that's wrong pfffft.

Sorry, I was just kidding about poor George.

 

[ProfuselyQuarky]

Works for me. My answer is that you cannot know without making an assumption, if that's wrong pfffft.

You HAVE to make an assumption. That's the point.

 

[micromass]

You HAVE to make an assumption. That's the point.

But are you allowed to make an assumption?

 

[ProfuselyQuarky]

But are you allowed to make an assumption?

That's how you solve the puzzle. You have to assume different scenarios before realizing that there is only one answer. Just like that proof you linked to. You're assuming that the answer is rational, but you never really know what the number is.

 

[SophiaSimon]

Spoiler: Spoiler

It's funny how such obvious things can elude us. I looked at this problem for a while thinking that there was going to be this obscure solution for which I would have to use probabilities to find. And no matter how many different ways I spun it, I could only guess the solution couldn't be determined, because there was a 1/2 probability that Anne was unmarried. Then, while sitting utterly confused, in a split second something clicked and I realized that it HAS to be true. :) Fun problem.

 

[micromass]

Spoiler: Spoiler

It's funny how such obvious things can elude us. I looked at this problem for a while thinking that there was going to be this obscure solution for which I would have to use probabilities to find. And no matter how many different ways I spun it, I could only guess the solution couldn't be determined, because there was a 1/2 probability that Anne was unmarried. Then, while sitting utterly confused, in a split second something clicked and I realized that it HAS to be true. :) Fun problem.

I wonder how many people would have gotten it right if we were also given the completely irrelevant piece of information that there is "1/2 probability that Anne was married" in the OP. It would have eluded a lot of people, I think.

 

[ProfuselyQuarky]

Spoiler: Spoiler

It's funny how such obvious things can elude us. I looked at this problem for a while thinking that there was going to be this obscure solution for which I would have to use probabilities to find. And no matter how many different ways I spun it, I could only guess the solution couldn't be determined, because there was a 1/2 probability that Anne was unmarried. Then, while sitting utterly confused, in a split second something clicked and I realized that it HAS to be true. :) Fun problem.

I wonder how many people would have gotten it right if we were also given the completely irrelevant piece of information that there is "1/2 probability that Anne was married" in the OP. It would have eluded a lot of people, I think.

Yes, it would have, I'm sure. People like to make things more complicated than it is. For instance, in the comments under the YouTube video, people were questioning, "What if Anne is divorced?" or "What if she is a widow?"

 

[micromass]

Yes, it would have, I'm sure. People like to make things more complicated than it is. For instance, in the comments under the YouTube video, people were questioning, "What if Anne is divorced?" or "What if she is a widow?"

What if she is being captured and kept in a box where she will - with probability 1/2 - sign the papers which would finalize the divorce with Schrödinger. Is the answer still "Yes" if we consider superposed people?

 

[micromass]

And what if Anne is a cat? You never specified that case. My case of "cannot be determined" is strengthened.

 

[ProfuselyQuarky]

Errr . . . um . . . are you suggesting that Anne is a feline who is married, unmarried, and filing for divorce at the same time, perhaps??

We better keep an eye on this Anne!

 

[micromass]

Clearly, your riddle didn't take into account QM and the fact that Anne might not be comfortable identifying herself as human. I declare you speciesist and theory-ist.

 

[SophiaSimon]

That's how you solve the puzzle. You have to assume different scenarios before realizing that there is only one answer. Just like that proof you linked to. You're assuming that the answer is rational, but you never really know what the number is.

Ahh, if it's rational then your done. If its irrational than you can use it as r or s. For the case of r=\sqrt{2}^\sqrt{2} and s=\sqrt{2} we get a rational number. Either way it works. It's all coming together now.

But then micromass comes along with Schrödinger and cats, and it all seems uncertain.

I actually also first thought, well I can't just assume that Jack is married and George is unmarried, because if Anne has a probability of being married or unmarried, then I can't be certain about Jack or George's status. However, I don't assume this is valid logic :P