Since we've gone this far, I'll summarize my "trick":
Is a married person looking at an unmarried person?
While marriage is binary, the choice between married person and unmarried person isnotbinary. There is a third option: not a person. Anne could be, for example, a dog. Hence the correct answer is C.
Uhh, dogs are unmarried. In which case Jack(married) is still looking at Anne(unmarried) and thus the answer would still be A.
Günter already posted the exhaustive explanation of the problem. What I found interesting about it is not the logic required to get the correct answer, since regardless of whether Anne is a dog, it is laughably easy to figure out the correct answer, but that It is not a Logic Puzzle and instead rather a Laziness Puzzle and that laziness, in this instance, correlates with intelligence.
This was framed as a logic puzzle in this thread, so I guess that part doesn't apply here.
Unfortunately, as Funfetus said, you posed it as a logic puzzle, which encouraged people to be less lazy. As stated in that same article,
how a question is asked dramatically affects the answer, and can even lead to a contradictory answer.
In my case, I'd say that the framing of the question, including the suggestion that a smart guy like you (Timo) got it wrong, led me to think yet more.
In my case, I'd say that the framing of the question, including the suggestion that a smart guy like you (Timo) got it wrong, led me to think yet more.
Thanks for the compliment (isn't there a thread for that;-) ), but yeah, like I stated above, I messed up the asking of the question.
Basically this also works for any amount of people between the first and last person. In essence this could be framed as a graph theory problem. You have a path in a directed graph and every node on that path must be either of two states, let's say State 1 and State 2. If the starting node of the path is in State 1 and the end node is State 2, there must be at least one edge on that path that goes from a node in State 1 to a node in State 2.
This can be proven via falsification. If we assume there there can't be any nodes in State 2 following nodes in State 1, thus all successors of a node in State 1 must also be in State 1. Since the starting node is in State 1, every other node on the path must be in State 1 as well. This is then contradicted by the end node being in State 2, thus proofing that the assumption is false. The same proof can be started from the end node as every predecessor of a node in State 2 would also have to be in State 2 and is contradicted by the starting node being in State 1.
I got A, proceeded to over think it, then proceeded to over-over think it, and decided that A must be right. That was a while ago, but only got round to posting now, once I'd read all the replies.
I still disagree with A. In Logic (capital L), a person may be married, unmarried, neither, or both. You cannot assume a person is married because they are not-unmarried, and vice versa.
a person may be married, unmarried, neither, or both
Umm no, you are either in a state of marriage or not in that state. It would be like asking you if you are male, you either are (that is your DNA says so) or you are not (be you female, asexual or whatever).
Observe:INCOMING HOTLINK! Let the left circle contain people that are married. Let the right circle contain people that are unmarried. There are 4 areas a person could be in: left circle, both, right circle, or no circle. Now, any one of these areas may or may not have any people in them, but we cannot assume a priori that they do not (or do, for that matter).
Umm no, you are either in a state of marriage or not in that state. It would be like asking you if you are male, you either are (that is your DNA says so) or you are not (be you female, asexual or whatever).
In logical terms, unmarried ≡ !married. Just because it's a logic puzzle, doesn't mean you don't use English. Un[p] ≡ !p in English. One cannot be in both sides of a binary and mutually exclusive state. Therefore, through logic and a simple syllogism, we can see that there are no people in the overlap. It would be more apt to have one circle, containing married people. Married is a positive condition, and unmarried is the default. It would be stupid to use a Venn diagram in this case.
I still disagree with A. In Logic (capital L), a person may be married, unmarried, neither, or both. You cannot assume a person is married because they are not-unmarried, and vice versa.
That is irrelevant - Jack is explicitly married, and George is explicitly not.
Unless Anne is some creature other than a person, this Schrodinger's marriage business is irrelevant, because if she qualifies for the tag married, be it or not in conjunction with other tags, she's looking at George, an explicitly unmarried person. If she qualifies for the unmarried tag, be it or not in conjunction with other tags, Jack is both looking at her, and is explicitly married.
I still disagree with A. In Logic (capital L), a person may be married, unmarried, neither, or both. You cannot assume a person is married because they are not-unmarried, and vice versa.
That is irrelevant - Jack is explicitly married, and George is explicitly not.
Unless Anne is some creature other than a person, this Schrodinger's marriage business is irrelevant, because if she qualifies for the tag married, be it or not in conjunction with other tags, she's looking at George, an explicitly unmarried person. If she qualifies for the unmarried tag, be it or not in conjunction with other tags, Jack is both looking at her, and is explicitly married.
Starfox is suggesting that Anne can qualify for neither the married tag nor the unmarried tag, which is plainly false. Even if Anne is a bitch, she qualifies as unmarried, but not an unmarried person.
Observe:INCOMING HOTLINK! Let the left circle contain people that are married. Let the right circle contain people that are unmarried. There are 4 areas a person could be in: left circle, both, right circle, or no circle. Now, any one of these areas may or may not have any people in them, but we cannot assume a priori that they do not (or do, for that matter).
What? If the left circle is married and the right circle is unmarried, then the circles don't cross. There are not four states, there are two. It CANNOT be both. It CANNOT be neither. You're complicating this in a totally illogical way. A Venn diagram has absolutely no place here.
@ Starfox: Come on, that's just stupid. You are trying to find the intersection of a group and it's complement. In a Venn diagram you only have a single circle. Everything inside the circle is "married" and everything outside the circle is "unmarried". There are no two circles.
I re-read the puzzle and have not read any other responses. My thinking is this: Whether Anne is married or not is irrelevant. If she is married, she is looking at George who is unmarried. If she is unmarried, then Jack (who is married) is looking at an unmarried person. Thus, a married person must be looking at an unmarried person within the framework of the question.
There are not four states, there are two. It CANNOT be both. It CANNOT be neither.
I guess I don't really know what to say besides it can. Rules of formal logic and all. Call the two circles "married" and "single" if you want. It just so happens that in English they are the complement of each other, but one cannot assume that.
I guess I don't really know what to say besides it can. Rules of formal logic and all. Call the two circles "married" and "single" if you want. It just so happens that in English they are the complement of each other, but one cannotassumethat.
Suddenly I can't understand a word you're saying because I've decided to abandon any and all knowledge of the English language in order to perform a "logical" analysis...
Unmarried = not married, under the very clear definition of "not" in the field of logic; the complement of "Anne is married" is "Anne is unmarried". If you wish to consider different possible meanings of English terms, perhaps we should consider alternative meanings for the word "is" as well?
There are not four states, there are two. It CANNOT be both. It CANNOT be neither.
I guess I don't really know what to say besides it can. Rules of formal logic and all. Call the two circles "married" and "single" if you want. It just so happens that in English they are the complement of each other, but one cannotassumethat.
Oh come on. If you are going to do this kind of BS we also have no clue what "looking at" means in the context of that problem. You also still have to give an explanation of how a person can both be married and unmarried at the same time or be neither at once to give your two circle model any sense.
Simple matter of fact is that unmarried is everyone that is not married. It is precisely the complement of being married. It doesn't matter that "it happens that in English they are the complement of each other" because the problem is formulated in english! You are essentially asking us to read something into it that isn't written there and ignore what in fact is written there in as plain a language as plain can be.
I guess I don't really know what to say besides it can. Rules of formal logic and all. Call the two circles "married" and "single" if you want. It just so happens that in English they are the complement of each other, but one cannot assume that.
Three guesses to the forums as to what would've been said by forumites if I had stated what Starfox is stating, other than what has been stated to Starfox (i.e. "you're an idiot").
Comments
This can be proven via falsification. If we assume there there can't be any nodes in State 2 following nodes in State 1, thus all successors of a node in State 1 must also be in State 1. Since the starting node is in State 1, every other node on the path must be in State 1 as well. This is then contradicted by the end node being in State 2, thus proofing that the assumption is false. The same proof can be started from the end node as every predecessor of a node in State 2 would also have to be in State 2 and is contradicted by the starting node being in State 1.
I tried asking this same puzzle to a friend yesterday. It took him a bit, but he got the right answer as well.
I much prefer my pedantry over Anne not needing to be a person.
The two choices are mutually exclusive sucka
Let the left circle contain people that are married. Let the right circle contain people that are unmarried. There are 4 areas a person could be in: left circle, both, right circle, or no circle. Now, any one of these areas may or may not have any people in them, but we cannot assume a priori that they do not (or do, for that matter).
Yeah, maybe in the real world. This is logic.
Unless Anne is some creature other than a person, this Schrodinger's marriage business is irrelevant, because if she qualifies for the tag married, be it or not in conjunction with other tags, she's looking at George, an explicitly unmarried person.
If she qualifies for the unmarried tag, be it or not in conjunction with other tags, Jack is both looking at her, and is explicitly married.
Even if Anne is a bitch, she qualifies as unmarried, but not an unmarried person.
EDIT: Fuck, it's A, isn't it?
I re-read the puzzle and have not read any other responses.
My thinking is this:
Whether Anne is married or not is irrelevant. If she is married, she is looking at George who is unmarried. If she is unmarried, then Jack (who is married) is looking at an unmarried person. Thus, a married person must be looking at an unmarried person within the framework of the question.
2 cases:
1) Anne Married: Married Anne looking at unmarried George
2) Anne Unmarried: Married Jack looking at unmarried Anne
Unmarried = not married, under the very clear definition of "not" in the field of logic; the complement of "Anne is married" is "Anne is unmarried". If you wish to consider different possible meanings of English terms, perhaps we should consider alternative meanings for the word "is" as well?
Simple matter of fact is that unmarried is everyone that is not married. It is precisely the complement of being married. It doesn't matter that "it happens that in English they are the complement of each other" because the problem is formulated in english! You are essentially asking us to read something into it that isn't written there and ignore what in fact is written there in as plain a language as plain can be.