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Which answer in this list is the correct answer to this question? (2017)

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Re: Which answer in this list is the correct answer to this question? (2017)

#121

Post by mannykannot »

colanderman wrote: post #86
Recursing wrote: post #57

Earlier quoted context omitted.

A less clever solution, using the wonderful z3 import z3 answers = [z3.Bool(f"answer{i}") for i in range(1,7)] implications = [ z3.And(answers[1:]), # All of the below z3.Not(z3.Or(answers[2:])), # None of the below z3.And(answers[:2]), # All of the above z3.Or(answers[:3]), # Any of the above z3.Not(z3.Or(answers[:4])), # None of the above z3.Not(z3.Or(answers[:5]))] # None of the above constraints = [z3.Implies(ans…

Not enough constraints. You must (EDIT: should? see discussion below) also constrain that there is exactly one `answer{i}` which is true, and all the implications should be equalities (else, for example, 6 is a valid answer, even though that would imply 5 is true and thus contradict 6). It just so happens that the first result Z3 finds is the correct one. But if you exclude that result with an additional constraint,…

> It just so happens that the first result Z3 finds is the correct one. But if you exclude that result with an additional constraint, it will find another.

Having an additional constraint would be a different question, would it not?

Re: Which answer in this list is the correct answer to this question? (2017)

#122

Post by nyhc99 »

cmonnow wrote: post #116
nyhc99 wrote: post #44

Earlier quoted context omitted.

So this one is an actual paradox, right? If they would accept both correct answers, then the answer would be 50%, but then if it's 50% those two correct answers would be incorrect.

answer - https://math.stackexchange.com/a/3437700/725808 The question displays a lack of understanding of language, especially the relation between a word and its meaning. More specifically, the relation between a noun and its pronoun. Suppose Question 1 was: > "What day is it today?" And suppose Question 2 was: > "Which answer in this list is the correct answer to this question? > Friday, Saturday, Sunday" If someon…

I think some of your premises are mistaken.

>>If I ask 'what is the weather in this city?' >>Does that question make sense without mentioning the city's name either before or after?

Yes, it does, if we're standing in a city when the question is asked. "This" would obviously refer to the city we're in. Likewise, in this instance, "this" obviously refers to the question that is currently being asked.

Re: Which answer in this list is the correct answer to this question? (2017)

#123

Post by cmonnow »

nyhc99 wrote: post #122
cmonnow wrote: post #116

Earlier quoted context omitted.

answer - https://math.stackexchange.com/a/3437700/725808 The question displays a lack of understanding of language, especially the relation between a word and its meaning. More specifically, the relation between a noun and its pronoun. Suppose Question 1 was: > "What day is it today?" And suppose Question 2 was: > "Which answer in this list is the correct answer to this question? > Friday, Saturday, Sunday" If someon…

I think some of your premises are mistaken. >>If I ask 'what is the weather in this city?' >>Does that question make sense without mentioning the city's name either before or after? Yes, it does, if we're standing in a city when the question is asked. "This" would obviously refer to the city we're in. Likewise, in this instance, "this" obviously refers to the question that is currently being asked.

I'm not saying that 'this' doesn't resolve to anything.

Of course it does. It's like pointing to something and asking 'what's this?'. Of course the act of pointing, or the act of standing in a city resolves 'this' to something else.

But the point is where 'this' resolves to something which has meaning.

A question makes sense, if it is understandable and answerable.

Q1: //TODO

Q2: what's the population of this city ?

Q3: what's the location of this city ?

...

Q22: what's the altitude of this city?

Q23: what's the weather in this city ?

Suppose I ask you "What is the answer to Question 23?".

You'll respond "what is Question 23?" (trying to resolve/concrete 'Q 23').

I'll reply "Question 23 is - 'What's the weather in this city?' ".

You'll respond "well, what does 'this' refer to in Question 23?" (trying to resolve/concrete pronoun 'this')

I'll reply "this refers to the city in Question 22"

You'll respond "well, what is Question 22?' (again trying to resolve/concrete 'Q 23')

I'll reply "Question 22 is - 'What's the weather in this city?' "

You'll respond "well, what does 'this' refer to in Question 22?" (again trying to resolve/concrete pronoun 'this')

So-on, so-forth.. until we reach Question 2, referring to Question 1.

Now, If I define question 1 to be - 'What is the capital of USA?'. Then, by chaining, you can answer Question 23.

But if it do not define question 1, you can't answer Question 23, because I have not given you enough information to resolve pronoun 'this' in 'this city'.

That is the case with OP's question. In order to answer a question, the question must be answerable. In order for a question to be answerable, it must be understandable. In order for a question to be understandable, all pronouns in it must be resolvable to a valid question.

Do you agree that the question 'what is his height?' - is unanswerable IF the asker is not pointing to anyone, or there is no one else in the room, or there is no prior context - because the pronoun 'this' is unresolved ?

Re: Which answer in this list is the correct answer to this question? (2017)

#124

Post by kingludite »

dtjohnnyb wrote: post #17

Similar one I enjoyed in the Naive Bayes article from yesterday https://blog.floydhub.com/naive-bayes-for-machine-learning/ Multiple Choice: If you choose an answer to this question at random, what is the chance you will be correct? A) 25% B) 50% C) 60% D) 25%

Normally 25% but since there are 2 answers with 25% this cant be correct. There is only one answer with 50% but if that is the correct one there would be only 25% chance.

Therefore it must be C) 60%

Re: Which answer in this list is the correct answer to this question? (2017)

#125

Post by nyhc99 »

cmonnow wrote: post #123
nyhc99 wrote: post #122

Earlier quoted context omitted.

I think some of your premises are mistaken. >>If I ask 'what is the weather in this city?' >>Does that question make sense without mentioning the city's name either before or after? Yes, it does, if we're standing in a city when the question is asked. "This" would obviously refer to the city we're in. Likewise, in this instance, "this" obviously refers to the question that is currently being asked.

I'm not saying that 'this' doesn't resolve to anything. Of course it does. It's like pointing to something and asking 'what's this?'. Of course the act of pointing, or the act of standing in a city resolves 'this' to something else. But the point is where 'this' resolves to something which has meaning. A question makes sense, if it is understandable and answerable. Q1: //TODO Q2: what's the population of this city ?…

I don't agree with that. The pronoun "this" does not appear in the example question you just provided. There's a difference between "this" and "his" and the difference is how they resolve contextually.

And in the OP's question, it's obvious that "this" resolves to the current question that it appears in. It seems like you want to say that this is not obviously the case simply because the question is unanswerable. Yet I'm not convinced that you didn't invent this requirement yourself. Anyone reading the OP's question would clearly understand to what the "this" is referring.

Re: Which answer in this list is the correct answer to this question? (2017)

#126

Post by MrManatee »

sunstone wrote: post #120

It seems all of the answers assume "You cannot assume there is only one correct answer." However in "...answer in this list is the correct answer..." to my mind the word "the" requires only one correct answer. If it was worded '...a correct answer...' or '...one of the correct answers...' ok sure, there can be more than one. But as it stands there can only be one correct answer so the "correct" answers so far, are ba…

Regardless of the interpretation it's not a false premise. The uniqueness of the answer is just an assumption that we don't need.

Suppose the question was instead: "What is the unique real number x for which x^3 = 8?" We can guess and verify that x = 2 is a solution. And if we're allowed to assume that this equation has a unique solution, then that's enough. But if we work a little harder, then we don't actually need that assumption: we can prove that x = 2 is the unique solution.

Similarly, in the original problem we could guess and verify that FFFFTF is a solution. And if we're allowed to assume that the solution is unique, then we're done. But again, if we work a little harder, then we don't need that assumption: we can prove that FFFFTF really is the only solution.

Re: Which answer in this list is the correct answer to this question? (2017)

#127

Post by cmonnow »

nyhc99 wrote: post #125
cmonnow wrote: post #123

Earlier quoted context omitted.

I'm not saying that 'this' doesn't resolve to anything. Of course it does. It's like pointing to something and asking 'what's this?'. Of course the act of pointing, or the act of standing in a city resolves 'this' to something else. But the point is where 'this' resolves to something which has meaning. A question makes sense, if it is understandable and answerable. Q1: //TODO Q2: what's the population of this city ?…

I don't agree with that. The pronoun "this" does not appear in the example question you just provided. There's a difference between "this" and "his" and the difference is how they resolve contextually. And in the OP's question, it's obvious that "this" resolves to the current question that it appears in. It seems like you want to say that this is not obviously the case simply because the question is unanswerable. Yet…

I've given clearer examples in updated answer here - https://math.stackexchange.com/a/3437700/725808

Basically, OP has not provided a base case for his recursive question. As a result, it goes on infinitely, ending up in stackoverflow.

Re: Which answer in this list is the correct answer to this question? (2017)

#128

Post by nyhc99 »

cmonnow wrote: post #127
nyhc99 wrote: post #125

Earlier quoted context omitted.

I don't agree with that. The pronoun "this" does not appear in the example question you just provided. There's a difference between "this" and "his" and the difference is how they resolve contextually. And in the OP's question, it's obvious that "this" resolves to the current question that it appears in. It seems like you want to say that this is not obviously the case simply because the question is unanswerable. Yet…

I've given clearer examples in updated answer here - https://math.stackexchange.com/a/3437700/725808 Basically, OP has not provided a base case for his recursive question. As a result, it goes on infinitely, ending up in stackoverflow.

>Because there are still unresolved pronouns in (Q2).

When something is self-referential and resolves to itself, that's the end of the recursive process. There's no need to produce a Q2 that is Q layered inside itself. You go and substitute the entire sentence in place of "this" and form some unresolveable chain of recursion but you do it for no apparent reason. If these were statements in a programming language your expansion might make sense, but not in the context of spoken english language.

Re: Which answer in this list is the correct answer to this question? (2017)

#129

Post by cmonnow »

nyhc99 wrote: post #128
cmonnow wrote: post #127

Earlier quoted context omitted.

I've given clearer examples in updated answer here - https://math.stackexchange.com/a/3437700/725808 Basically, OP has not provided a base case for his recursive question. As a result, it goes on infinitely, ending up in stackoverflow.

>Because there are still unresolved pronouns in (Q2). When something is self-referential and resolves to itself, that's the end of the recursive process. There's no need to produce a Q2 that is Q layered inside itself. You go and substitute the entire sentence in place of "this" and form some unresolveable chain of recursion but you do it for no apparent reason. If these were statements in a programming language your…

I've updated the answer again with hopefully clearer examples.

You're getting stuck because you're used to only 1-level resolution/replacements for pronouns, because that's what we're used to in daily speak.

But I've given a concrete 2-level example, where you will question your own stance of "that's the end of the recursive process", and help you expand the logic to 3-levels deep, 4-levels, 5... to infinity.

Re: Which answer in this list is the correct answer to this question? (2017)

#130

Post by krasi0 »

Recursing wrote: post #107
colanderman wrote: post #86

Earlier quoted context omitted.

Not enough constraints. You must (EDIT: should? see discussion below) also constrain that there is exactly one `answer{i}` which is true, and all the implications should be equalities (else, for example, 6 is a valid answer, even though that would imply 5 is true and thus contradict 6). It just so happens that the first result Z3 finds is the correct one. But if you exclude that result with an additional constraint,…

I can't edit, but you're right, implications should be bidirectional (expressed in z3 using == instead of z3.Implies) You can limit the number of true answers with "atMost" "atLeast" and "PbEq" I mostly wanted to show off how cool z3 is (especially with python imho), the subtleties of the wording of the problem itself don't seem too important

Could you please post the `fixed` solution in a separate gist? Thanks!
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