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 Schrodinger. 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 Schrodinger 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

 

[ProfuselyQuarky]

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.

Hey, hey go easy . . . this is not my riddle, I just took it from someone else who probably took it from someone else who probably took it from someone else who probably took it from someone else who probably took it from someone else who probably took it from someone else who probably took it from someone else who probably took it from someone else ...

Let Anne call herself what she wants. Cat, dog, horse, capybara . . . the sky’s the limit!

@micromass let me see you create a new riddle with all of these considerations.

 

[micromass]

Hey, hey go easy . . . this is not my riddle, I just took it from someone else who probably took it from someone else who probably took it from someone else who probably took it from someone else who probably took it from someone else who probably took it from someone else who probably took it from someone else who probably took it from someone else ...

Let Anne call herself what she wants. Cat, dog, horse, capybara . . . the sky’s the limit!

@micromass let me see you create a new riddle with all of these considerations.

So you don't think cats are allowed to marry? You make me sick.

 

[ProfuselyQuarky]

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, it was already stated the status of Jack and George, but nothing was said about Anne except that she was looking at George

 

[ProfuselyQuarky]

So you don't think cats are allowed to marry? You make me sick.

Nope, sorry

 

[ProfuselyQuarky]

@collinsmark @Psinter @Merlin3189 @Infinitum

Why don't you think the answer cannot be determined?

 

[Psinter]

@collinsmark @Psinter @Merlin3189 @Infinitum

Why don't you think the answer cannot be determined?

I did not even replied to this thread. I'm unaware of how you even know I voted. I'm like: *wut* Anyway...

You need evidence to reach a conclusion. If a married person is accused of looking at an unmarried person, the judge will ask who are these people. If no one says anything the case is closed as the judge cannot sentence a ghost or sentence a tangible person for looking at a ghost (or so I think).

Another analogy I used was:

• If you ask a scientists to solve something, they experiment and get all the data. They won't reach a conclusion based on assumptions. If they do, it is still a hypothesis or theory. Nothing has been proved. And if you tell them: make assumptions. The correct reply should be: "No, I won't make assumptions and pass it as proved. I must get empirical evidence before passing it as proved."

Since we have no solid evidence, we cannot determine. That was my logic.

Now if I'm told that the answer to the question is just for theory purposes then I can come up with answers by plugin values at each person at however I seem fit. If it's theory I can even scramble the sentence and make Jack look at George.

 

[micromass]

I did not even replied to this thread. I'm unaware of how you even know I voted. I'm like: *wut* Anyway...

You need evidence to reach a conclusion. If a married person is accused of looking at an unmarried person, the judge will ask who are these people. If no one says anything the case is closed as the judge cannot sentence a ghost or sentence a tangible person for looking at a ghost (or so I think).

Another analogy I used was:

• If you ask a scientists to solve something, they experiment and get all the data. They won't reach a conclusion based on assumptions. If they do, it is still a hypothesis or theory. Nothing has been proved. And if you tell them: make assumptions. The correct reply should be: "No, I won't make assumptions and pass it as proved. I must get empirical evidence before passing it as proved."

Since we have no solid evidence, we cannot determine. That was my logic.

Now if I'm told that the answer to the question is just for theory purposes then I can come up with answers by plugin values at each person at however I seem fit. If it's theory I can even scramble the sentence and make Jack look at George.

Spoken like a true constructivist

 

[ProfuselyQuarky]

I did not even replied to this thread. I'm unaware of how you even know I voted. I'm like: *wut* Anyway...

@micromass spilled the beans. He said … I mean she … nevermind (maybe micromass is a cat) Anyway, you can click the number of votes on the poll and it tells who voted what. It’s all public for the world to see.

You need evidence to reach a conclusion. If a married person is accused of looking at an unmarried person, the judge will ask who are these people. If no one says anything the case is closed as the judge cannot sentence a ghost or sentence a tangible person for looking at a ghost (or so I think).

Another analogy I used was:

• If you ask a scientists to solve something, they experiment and get all the data. They won't reach a conclusion based on assumptions. If they do, it is still a hypothesis or theory. Nothing has been proved. And if you tell them: make assumptions. The correct reply should be: "No, I won't make assumptions and pass it as proved. I must get empirical evidence before passing it as proved."

Since we have no solid evidence, we cannot determine. That was my logic.

Impressive logic and way of thinking, @Psinter

Constructivism or not, there is definite answer. We can answer yes or no with (almost) purely the information given. We are given enough information about Jack and George. We know who Jack is looking at and we know his marital status. We know George’s marital status, and it doesn’t really matter who he is looking at for the purposes of this riddle. We know that Anne is looking at George, however, we lack the knowledge of whether she is married or not. That’s all we need to know. No matter how we twist and turn the information, we can determine the answer and be sure that it is correct.

Spoiler: click if you want the supposed “solution”

The marital status of Anne is the only factor that we have to play with.

If Anne is married, then the statement in question (a married person is looking at an unmarried person) holds true because Anne is looking at George, who is not married. However, if Anne is not married, then the statement holds true yet again because Jack (who is married) is looking at Anne. It doesn’t matter whether George is looking at Jack or anything of that sort. Regardless, the answer is yes, a married person is looking at an unmarried person.

**To the question of whether Anne is cat or capybara or nonhuman, no, animals can’t be married in real life so that idea is eliminated. You can argue, “So if Anne is a cat, she is unmarried”. Well, that still makes the answer yes.

 

[gjonesy]

It cannot be determined without making an assumption about Anne.

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

That's the problem you can't make a decision based on the assumption only, based on available information I voted Yes.

 

[ProfuselyQuarky]

That's the problem you can't make a decision based on the assumption only, based on available information I voted Yes.

Even after considering all *plausible* assumptions, the answer is still the same.

 

[gjonesy]

Even after considering all *plausible* assumptions, the answer is still the same

BINGO

 

[ProfuselyQuarky]

BINGO

 

[gjonesy]

The only 3 provable facts are:

Jacks married and looking at Anne
Anne is looking at George
George isn't Married

Consider all the possibilities and the answer is obvious.

 

[Infinitum]

@collinsmark @Psinter @Merlin3189 @Infinitum

Why don't you think the answer cannot be determined?

@Psinter brings up great points.

I do not intend to derail, but I actually sent micromass a message right after I voted for this question, as it made me realize how certain discussions with him had influenced my thoughts as a constructivist, long ago.

As a constructivist, I have to answer that it cannot be determined even though I completely understand what the solution is supposed to be.

How interesting. Although it has been quite a while, it appears that I have independently followed in the footsteps of my former mentor, in one aspect at least.
...Thanks!

In any case, I will only present two of the many reasons why the answer cannot be determined.

Spoiler

Firstly, to re-iterate the question itself,

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?

We are given enough information about Jack and George.

Not necessarily. The question does not even specify whether Jack, Anne and George are persons. They could be robots. There is no reason to assume robots cannot marry.

(Fun fact, actually: http://www.dailymail.co.uk/news/article-3142129/First-robot-wedding-Japan-takes-place.html)

The second point is the binary state of being married or unmarried. This need not be true. One could argue that there are three states to marriage, that is, married, unmarried, or marrying.

**To the question of whether Anne is cat or capybara or nonhuman, no, animals can’t be married in real life so that idea is eliminated. You can argue, “So if Anne is a cat, she is unmarried”. Well, that still makes the answer yes.

While you assume the question imposes bounds of realism, there is no compulsion by the question to do so. Also, it is possible that Anne is a cat (and implicitly unmarried), and cats are not people, while the question asks whether a married person is looking at an unmarried person.

 

[ProfuselyQuarky]

The only 3 provable facts are:

They don't even have to be proven--that information is given to everyone. The tricky part is the logic . . . and then you have all those proclaimed contructivists who keep suggesting different things and saying that the answer cannot be determined because of information not, such as the species of the subjects.

 

[gjonesy]

They don't even have to be proven--that information is given to everyone. The tricky part is the logic . . . and then you have all those proclaimed contructivists who keep suggesting different things and saying that the answer cannot be determined because of information not, such as the species of the subjects.

My logic is that they MUST be persons, marriage is a human concept since AI hasn't been invented and marriage implies a legal contract between people. I have to stick with the simple obvious conclusion.

 

[ProfuselyQuarky]

While you assume the question imposes bounds of realism, there is no compulsion by the question to do so. Also, it is possible that Anne is a cat (and implicitly unmarried), and cats are not people, while the question asks whether a married person is looking at an unmarried person.

The question based on the situation of Jack, Anne, and George. You're saying that the puzzle tells us all those things about the three beings and then asks a question that has nothing to do with them? I'm getting confused . . .

 

[micromass]

The question based on the situation of Jack, Anne, and George. You're saying that the puzzle tells us all those things about the three beings and then asks a question that has nothing to do with them? I'm getting confused . . .

Come on, you don't honestly think you could post a puzzle on PF and not get all kinds of smartass answers such as mine

 

[ProfuselyQuarky]

Come on, you don't honestly think you could post a puzzle on PF and not get all kinds of smartass answers such as mine

Well, I suppose not. I’ve been here at PF for only a month and I gather that most of the recognized members here are witty, cunning, argumentative, bold, and brilliant all at the same time.

It makes this place irresistible.

 

[Infinitum]

The question based on the situation of Jack, Anne, and George. You're saying that the puzzle tells us all those things about the three beings and then asks a question that has nothing to do with them? I'm getting confused . . .

That assumption never commented on the status of Jack and George, both of whom may be (or for the sake of this argument, are) persons. So the question is still valid and has to do with the given beings. Only that Anne may be a cat.

On a side note, given the choices of (a) Yes (b) No and (c) Cannot be determined, it is entirely logical for the question to ask something completely unrelated which can be put into (c), but of course, it would not make it a very exciting question.

Come on, you don't honestly think you could post a puzzle on PF and not get all kinds of smartass answers such as mine

EDIT: In all fairness, I completely understand the "supposed solution". I simply believe that there there are more ways to look at the solution, given the question.