Paradox

[lemmingllama]

Just try to solve this. HAHAHAHAAHAHAHAHAHAAHAHA!!!!!

[Katongo]

If we assume that we can only choose one answer for the question, we have four answers hence out of four we have 1 in 4 chances to get one of the answers at random. But only three out of 4 are partly right answers to the question therefore we have 3 in 4 chances to get the answer partly right, but of course we can not get the correct answer of the question hence its a Paradox because there is no answer to the question

other Paradox i have come across.

1. The first statement, states that it is true that the second statement is true, the Second statement states that it is false that the first statement it true

2. When Pinocchio say's that his nose is going to get longer, If his nose gets longer his telling the true but of course his nose only gets longer when his telling a lie.

3. Unstoppable force hits an unmovable wall

4. When someone say's Today is Opposite day, if today is opposite day the person saying it is wrong and if the say today is opposite day and it is not opposite day the would be also wrong.

[shyguysteve]

a paradox is like irony.

when something is defined in completeness but come into contact with which it can no longer be defined as is.

sorta like, humans imperfections equaling perfection.

our flaws make us perfect, but perfect has no flaws.

[CaNzCo]

Um, this question is not quite a complete paradox. There is no way to answer that question since there is no way to know how many, if any correct answers there are. Because of the percentages, we are supposed to think the question is about probability, however there is really nothing in the question that actually correlates with the answers. This might lead to people believing it is 0% since there is no way to answer this question, but just because we don't know if there is a correct answer doesn't mean there isn't one.

My verdict is that this is in fact a trick question.

[Alegend1994]

This confused me a lot, especially since I had an answer typed out my explanation only to find a flaw at the end. So really it doesn't matter which one you choose because you will always be simultaneously correct and incorrect, the whole reason for it being a paradox.

I do love the ideas of paradox's.

[swill48]

The answer is 50% because the corect answer is 25%, and as there are two 25% answers one therefore has a 50% chance of picking the correct answer..........Paradox... aaaarrrrrgh

[Warrenjans]

So we have 4 Answers

Normally there is 25% chance of a correct guess.

so the answer at the start would be A and D.

But that means there is a 50% chance to get the right answer.

So the answer now becomes B. BUT, that means there is a 25% chance of it being correct

bringing us back to the fact that the answer is A and D

If we were to choice C with 0% chance then there is still a 25% chance of the answer being correct with a random guess. Meaning A and B.....

Meaning there is no way to answer this question with out resorting to the following:

Drawing an Elephant in front of choice D

causing us to be unable to read choice D

Thus making the correct answer A (Somehow)

[AaronScythe]

1 in 4 chance regardless of what the actual answer is, so 25%

This even accounts for the chance of 50% being a correct answer, as there is still only 1 choice

The answer changes, the fact you have one choice out of 4 does not, so its stuck at flat 25% chance.

[Kyle_Dimetri]

I...... can't.......undersatand

[Lenalee33]

O.o I think some one divided by zero because that's way to confusing for me

[Kasoivc]

1 in 4 chance regardless of what the actual answer is, so 25%

This even accounts for the chance of 50% being a correct answer, as there is still only 1 choice

The answer changes, the fact you have one choice out of 4 does not, so its stuck at flat 25% chance.

Now to follow up on this, we assume there there is only ONE answer, as in some cases it will be stated that a specific multiple choice has multiple correct answers. Regardless, we assume there is only one answer because it does not state that there are multiple answers. Otherwise, it's not our fault for an incorrect answer, but the tester lacked in providing fair question.

[RikuoAmero]

It's not a paradox, because you haven't asked the question you were originally going to ask. The question up there is asking you about an answer you're supposed to have given to a different question. What that question is, I have no idea.

[DrumRoll]

the below statement is false

the above statement is true

[† Mute point]

The first question has a simple answer. None of the above. Because If A and D were different, then you would have a 25% chance. With them being the same you have a 33.3% chance due to having only 3 answers. If you take out C because it is not possible to have 0% probability, then the anwser is B: 50%

[Dae314]

The question defines itself which is the root of the problem. To answer the question means to define the question in such a way that your answer is wrong. This may lead you to believe that 0% © is the correct answer, but then you'd be wrong (since that's the nature of what I just described).

If the answers were considered only by their value (not their letter) then put into a set as Mute would have it then we could just drop one of the 25% answers and say it's 33.3%, but we aren't dealing with a set. We're dealing with a list of ordered pairs and we need to treat it as such.

Now the question itself as I mentioned earlier is recursive in that choosing a "correct" answer affects the correctness of that answer. So the real question that this is asking is "Which answer can you choose to be correct such that the subsequently defined question is correctly answered by the answer you chose to be correct?" If we assume the condition that ONLY one letter (A,B,C,D) can be correct then we can do a case analysis of the problem and hopefully find a "solution".

To begin, since there can be ONLY one answer as per the precondition I defined then immediately A and D are eliminated since calling either "correct" means the other is also correct. This causes a contradiction with the precondition and so A and D cannot be considered for solutions under the precondition. That leaves only B and C as possible correct answers to the question (remember, I redefined the question as stated above). Choosing C to be correct immediately makes you incorrect since saying it is correct that there is a 0% chance of getting the question correct creates a contradiction. Therefore B must be correct right!? But no, choosing B to be correct means that there must be at least 2 correct answers, and that creates a contradiction with the precondition.

What did I just do there? I just proved (by contradiction) that the precondition that ONLY one letter (A,B,C,D) can be correct is not a valid precondition for this problem. That means that there MUST be either no correct answer or multiple correct answers. However, in proving that the precondition I defined above does not hold for this problem, I also proved that no correct answers is impossible since that causes another contradiction since 0% © would be an answer. Therefore, the only case for this problem is one in which multiple answers (A,B,C,D) are correct.

Based on the above information, I postulate that the answers B and C are the correct answers to this problem. At first you might think that A and D must be the correct answers since the only logical way 2 or more answers to a question can be correct is by having their value be the same. However, this case causes a multiple answer contradiction since A and D being correct means the correct answer to the question is B. But how can B and C be correct when their values are different? Well that gets a bit sticky (this is where my formal logic begins to break down somewhat). You see, it may at first seem that choosing C to be correct in and of itself creates a contradiction, but this only holds for the single answer scenario. Choosing C alone to be correct should actually answer the question BECAUSE I proved above that there must be more than one answer to the question (choosing only C means you missed an answer). B may also at first seem to cause a contradiction, but again this is only for the single answer scenario. In the 2 or more answer scenario, there must be at least 2 answers. If we choose B to be correct then we can have 2 answers (B and C) and B is therefore correct. Basically by choosing both B and C to be correct you create 2 equivalent states of the question, and in both states, B or C hold to be correct.

Therefore, I theorize that the answer to this question is B and C.

edit:

Wait a second wtf just happened? That just might be a valid logical answer to this paradox . I think I just blew my own mind........

[lemmingllama]

The question defines itself which is the root of the problem. To answer the question means to define the question in such a way that your answer is wrong. This may lead you to believe that 0% © is the correct answer, but then you'd be wrong (since that's the nature of what I just described).

If the answers were considered only by their value (not their letter) then put into a set as Mute would have it then we could just drop one of the 25% answers and say it's 33.3%, but we aren't dealing with a set. We're dealing with a list of ordered pairs and we need to treat it as such.

Now the question itself as I mentioned earlier is recursive in that choosing a "correct" answer affects the correctness of that answer. So the real question that this is asking is "Which answer can you choose to be correct such that the subsequently defined question is correctly answered by the answer you chose to be correct?" If we assume the condition that ONLY one letter (A,B,C,D) can be correct then we can do a case analysis of the problem and hopefully find a "solution".

To begin, since there can be ONLY one answer as per the precondition I defined then immediately A and D are eliminated since calling either "correct" means the other is also correct. This causes a contradiction with the precondition and so A and D cannot be considered for solutions under the precondition. That leaves only B and C as possible correct answers to the question (remember, I redefined the question as stated above). Choosing C to be correct immediately makes you incorrect since saying it is correct that there is a 0% chance of getting the question correct creates a contradiction. Therefore B must be correct right!? But no, choosing B to be correct means that there must be at least 2 correct answers, and that creates a contradiction with the precondition.

What did I just do there? I just proved (by contradiction) that the precondition that ONLY one letter (A,B,C,D) can be correct is not a valid precondition for this problem. That means that there MUST be either no correct answer or multiple correct answers. However, in proving that the precondition I defined above does not hold for this problem, I also proved that no correct answers is impossible since that causes another contradiction since 0% © would be an answer. Therefore, the only case for this problem is one in which multiple answers (A,B,C,D) are correct.

Based on the above information, I postulate that the answers B and C are the correct answers to this problem. At first you might think that A and D must be the correct answers since the only logical way 2 or more answers to a question can be correct is by having their value be the same. However, this case causes a multiple answer contradiction since A and D being correct means the correct answer to the question is B. But how can B and C be correct when their values are different? Well that gets a bit sticky (this is where my formal logic begins to break down somewhat). You see, it may at first seem that choosing C to be correct in and of itself creates a contradiction, but this only holds for the single answer scenario. Choosing C alone to be correct should actually answer the question BECAUSE I proved above that there must be more than one answer to the question (choosing only C means you missed an answer). B may also at first seem to cause a contradiction, but again this is only for the single answer scenario. In the 2 or more answer scenario, there must be at least 2 answers. If we choose B to be correct then we can have 2 answers (B and C) and B is therefore correct. Basically by choosing both B and C to be correct you create 2 equivalent states of the question, and in both states, B or C hold to be correct.

Therefore, I theorize that the answer to this question is B and C.

edit:

Wait a second wtf just happened? That just might be a valid logical answer to this paradox . I think I just blew my own mind........

So close... You have come at this problem with a great deal of patience and time, this answer is probably one of the best that I have seen in over a year for this Only thing is, the question that is asked at the top states that you are picking one at random, and so you are unable to actually choose two answers.

My personal answer for this would be that it must be an indefinate, so that the real answer is a 0/0, thus making it so that the answer is either 0 or infinate. This state would then encompass all answers and none, thus making it so that any answer that you randomly pick is in fact correct, since they are all correct at the same time.

As for people who are posting about this, it is not a traditional paradox, yet by analysing it then you are able to determine that any answer chosen as correct is in fact incorrect, unless it can be both incorrect and correct. A traditional paradox are things like Xeno's Paradoxes.

[Dae314]

A different person on another forum came up with the undefined answer also:

So we have our probability space W = {a, b, c, d}. By the classical problem (assuming each answer is uniformly weighted) the answer is 0% assuming none are correct, 25% assuming one is correct, 50% assuming two are correct etc. Lets call these evets C and C' as we are assuming that one cannot be correct and not correct at the same time and so CuC' = W.

So what events fit into C? This is where the problem arises. Since we don't know the size of C then we don't know what elements fit in C. c cannot be a member of C or P© > 0, a can be a member of C if there are no other elements in C but the same goes for d and since a and b are 'equal' you can't really have one without the other. Since no other elements can exist in C and b cannot be the only element in C, none of the combinations of {a, b, c, d} equals to C, even the empty set thus the set C is undefined.

So basically, the set of correct answers is not defined.

Tuturu~!

When I concluded that there must be multiple answers, I validated going after a multiple answer solution by looking back at the problem description:

Choose an answer

Choosing an answer does not necessarily rule out choosing multiple answers as "an answer" because technically when you do so you define a set of answers to be your answer (one set). If you try to force the single answer precondition on to the problem, you invalidate the problem as I proved above . I'm pretty much redefining the word "answer"

[zx0]

The question is unanswerable as it refers to itself and is therefore undefined.

[Dae314]

Just because a question refers to itself doesn't mean it's invalid. Had the answers been A) 25%, 0%, C) 500%, D) -3.14%, then A would be a correct answer . The invalidity comes from having the precondition "can only pick 1 answer" which leads to contradictions in every case.

An even simpler question that's easily answerable but refers to itself would be:

"True or False? True is a possible answer to this question."

Anyway, Lemming, you (or me) should post more interesting paradoxes :3. I looked up Xeno's stuff as you recommended, but I also found one on the paradox wiki page about logical implication that I think is pretty cool ^^. Or should we just make a thread for each one (Paradox II, III, IV, ...) ?

[lemmingllama]

Just because a question refers to itself doesn't mean it's invalid. Had the answers been A) 25%, 0%, C) 500%, D) -3.14%, then A would be a correct answer . The invalidity comes from having the precondition "can only pick 1 answer" which leads to contradictions in every case.

An even simpler question that's easily answerable but refers to itself would be:

"True or False? True is a possible answer to this question."

Anyway, Lemming, you (or me) should post more interesting paradoxes :3. I looked up Xeno's stuff as you recommended, but I also found one on the paradox wiki page about logical implication that I think is pretty cool ^^. Or should we just make a thread for each one (Paradox II, III, IV, ...) ?

Different pages, unless they are directly related to one another. That makes for more discussion. Lets revitalize Mako! And there are really just an infinate number of paradoxes if you think about it. Xenos are really fun though, prove that nothing moves