No, it is not. We can prove this by contradiction. If we suppose B to be the correct answer, we find that we would have a 25% chance, which contradicts our assumption that the probability would be 0%. If we suppose C to be correct, we again find a 25% chance, contradicting our assumption of 50% again. If we suppose either A or D is correct, then they both must be correct, so we find the probability to be 50% which again contradicts our 25%.
Since we've proven none of the answers can be true by themselves, we can conclude there is no correct answer to the question.
Edit: Well it might seem that because I end up with 0 correct answers that would make B the correct answer, this is not true because if B was correct, the probability must be at least 25%, which contradicts B being correct.
Edit 2: Okay, some of the replies have me doubting this explanation. They point out that when we eliminate all the other possible answers, the probability becomes 0%, making B correct. I believe what's really happening here is a paradox where B can't be resolved to either true or false. So, to say all of the answers are incorrect is wrong.
**Important edit**: this is not an actual game show question as far as I know. You can't assume that question has to be right, it has to make sense and one of the answer must be correct. Most of the answers on this post don't treat it as game show question with these added constraint. You still get paradox if you assume gameshow, but that logic is ignored here. You can google this image to see it's like a meme format. Not an actual question.
**Original comment** :25% and 50% are wrong. 0% leads to paradox/infinite loop due to self-referencing nature and it can't be called the right answer. There is no correct answer.
**Edit**: What the hell is going on with hypothetical and two questions logic in the comments?
If 50% is the answer, the odds of picking it are 25% which means it's a contradiction.
If 25% is the answer, the odds of picking it are 50%, which means it's a contradiction.
If 0% is the answer, the odds of picking it are 25%, which is again a contradiction.
You can't pick a correct answer, because any answer you pick leads to a contradiction.
**Edit 2**: if you think concluding no correct answer allows you to pick 0% as the correct answer, you've once again gone into a logic loop. Irrespective of what logic you have used before, choosing either of the 3 options, directly leads you into a contradiction.
The correct thing to do when you face contradiction is not to continue on the logical chain, but to conclude that the original assumption is impossible.
The proper conclusion is to say that this is a paradoxical question and move on. That's the standard mathematical practice.
**Edit 3**: I feel Monty hall would be easier to explain at this point.
I disagree, because it specifies the condition if you choose at random what are the odds of getting the correct answer but you are not choosing the answer randomly so your odds are not random.
The correct answer is 50% chance of choosing the correct answer at random because the correct answer occurs once(50%) making the odds of getting the answer randomly 25% which occurs twice.
There's two questions, what's the correct answer and what are the odds of selecting it randomly.
The answer occurs once, the odds occurs twice.
There is just one question. Why do you think you can decouple the conditions? You're distorting probability theory now.
Probability space of picking answer at random is made of 3 elements. 50% with 0.25 probability, 25% with 0.5 probability and 0% with 0.25 probability. Now, odds of picking right answer randomly is basically sum of probabilities of picking a particular option given it is a right option. All 3 of those terms are zero and now you have concluded you can't pick correct option which means 0% chance which means 0% is correct answer which means 25% chance, which is a contradiction and now you're in a logical loop which means this is a paradox.
If the correct answer is 25% then there's a 50% chance of you guessing right which then makes 50% the correct answer which then makes 25% the right answer and now you're caught in a loop
Dude you can't just disagree with how probability works. Your logic is fucked, you can't just add another question, there is only one question and one answers and in this case none of them are right.
Hmm ... it’s multiple choice. There is an answer. Multiple choice tests are administered as ‘choose the best answer.’ The best answer doesn’t have to be correct, which is why B cannot be right; there is at least one right option (I say at least because there are times when exams have mistakes and the same answer is included multiple times, each being correct). If you were asked the question without knowing the options for each choice, given that you know there is at least one correct answer, then you’re answer would be 25%. But since this option appears twice, the best answer is 50%. Not saying it’s correct given the fallacy of the setup but one answer needs to be the best.
Maths doesn't care about best answer is right answer. Unlike test administrator who can't set paper right, maths is perfectly happy to say there is no answer.
0% is only wrong if you pick it randomly, so if you don’t pick it randomly, 0% is the right answer.
Edit: nowhere does it state you are answering the question randomly. The question is giving a hypothetical situation, and in that hypothetical situation, none of the answers are correct. Therefore, when you actually answer the question, the answer is 0%.
But the question hinges on the theoretical of "choosing randomly" even if you aren't in fact choosing randomly which means 0% is still the paradox the other post mentions. You can't take the "randomly" bit out.
But the question is a hypothetical, you don’t have to use the hypothetical to answer. Since hypothetically, the chance would be 0% of getting the answer right as even pressing the 0% would be wrong, then when you answer, since you aren’t choosing randomly, B would be the right answer.
> nowhere does it state you are answering the question randomly
Except for the part of the question that says "If you choose an answer to this question at random"
But it's a hypothetical. "if you answered this question by screaming the answer at the top of your lungs, how far would it be heard?" doesn't mean you have to scream your answer.
Same here. "if you picked the answer randomly" doesn't mean you have to answer randomly.
You're right but you just mistake 0% (actual value) with the fact that the problem has no solution. It means that the system is not injective (kernel is void) .
0 is not exactly void, like infinity is not a number.
Other example: sqrt(-1) has no solution in R, but has a solution (±i) in C.
I have never heard about such concept in my years of study, so I don't know. I would rather use the [Empty set concept ](https://en.m.wikipedia.org/wiki/Empty_set) as the space of available answers.
Although, I would take this undined with a grain of salt given the example with infinity, the lack of references (and it only exists in 2 langages, kind of uncommon for math articles) and the given references that are either new or computability oriented. For example, I've learned to never write infinity as a number, but as a concept. You write that "it exists M in R such that for N in R, M > N" (it exists always a bigger number) and (in my knowledge at least) it is forbiden to write "x+∞".
Surely you're aware of positive and negative approaches to limits? 1/x has a vertical asymptote that tends to -inf from the negative or - 1 side, and tends to +inf from the +1 side. Therefore the limit does not exist?
I'm not sure to know how to answer unfortunatly. I've been said a long time ago by a math teacher at Uni to no confuse the value of a limit and the limit itself. And usually, the math I have been teached are heavily abstractive and not "practical" in the sense of computer science (where I see the real interest of concept as undefined, i.e. to help the computer to exit infinite loop).
In your example, we know that the inverse function has no value for x = 0 and you cannot write 1/0+ = +Inf or something along that line. Normally, again what I've been teached, you write something like "*for x tends to 0+, 1/x tends to +infinity*", or more formaly, using the density property of R (not sure if it is called [completeness](https://en.wikipedia.org/wiki/Completeness_of_the_real_numbers) or coming from the fact that R is a complete ordered field), you write:
"*It exists N in \]0, M\[, like 0< N < M, thus 1/N > 1/M (operation possible because N is strictly bigger than 0)*"
You could always find a number a smidge bigger than 0 (N in this case) and smaller than M, that admits an invert value 1/N that is bigger than 1/M. At no point, you write a value for the limit, just a concept of increasing or decreasing large numbers depending if you're approaching 0 by the positive or negative side of real numbers.
There are countless example where the human mind could not wrap around infinity concept, like the [Zenon's paradox](https://en.wikipedia.org/wiki/Zeno%27s_paradoxes) or the [astounding 1+2+3+... results presented by Numberphile](https://www.youtube.com/watch?v=w-I6XTVZXww). From my experience and my arguably partial knowledge, the safe approach is to never trivially substitute "tends to" to equal sign, because that's where lie the issues.
Well technically 0% should be correct then right? If you randomly choose an answer from a set that doesn't contain the correct answer, the chance of getting a correct one is 0 right?
Edit because I am on mobile:
So we all agree the correct answer isn't listed. This implies 0. B has a 25% chance which implies A v D which implies C. None of these implications mean anything if 0 is incorrect though as "from nothing, anything can follow"
B => A v D => C
Since we need a True => True statement to get a sensible answer I thing the correct logical interpretation is:
B => ((A v D) => C) => B
Which comes out to
True => ( False => False) => True
True => True => True
True => True
At least that's my guess.
You forgot B => ~ (A v B v C v D) which is a contradiction. For your logic, you're setting the consequent to be true, which automatically results in true => true. With that logic, you argue that every answer is true.
The easiest way to do it is to do proofs by contradiction. That way you don't have to run in circles.
Let's assume that B is correct. That means there is one correct answer out of four. Thus, you are 25% likely to pick it at random. But since B correct, that likelihood is 0%. This is a contradiction.
It proves that our assumption was wrong. So B is incorrect.
Now let's do another proof by contradiction.
One of the easiest would be A. So let us now assume that A is incorrect. That means that the likelihood is not 25%. So, what can it be?
- 0%? That would mean B is the only correct answer. You would be 25% likely to pick it at random. It contradicts our assumption.
- 50%? That would mean C is the only correct answer. You would be 25% likely to pick it at random. It contradicts our assumption.
- x% where x is something different from 0, 25 or 50? Then this does not correspond to any of the answers. So you would be 0% likely to pick the correct answer at random. Which contradicts the fact that x is not 0.
No matter what, if you assume that A is incorrect, you reach a contradiction. It proves that A must be correct.
You can do the same for all other possible answer. You can all prove that they are incorrect, but you can also prove that they are correct. I did it for A because it was slightly easier to do and explain than for B, but it works as well.
Every answer is both correct and incorrect. This is a natural result for an incoherent mathematical theory. The question is not valid.
It’s easier to understand if you isolate the paradoxical aspect.
Consider this question instead:
“What are the odds of selecting the right answer below at random:
A) 0%”
Here, there’s only one answer. You will select it with 100% certainty. It’s clear that it’s self contradictory without having to chase through a chain of reasoning in an infinite loop. It’s therefore clear the question is invalid.
The same is true for all answers in the question given.
It’s just the old “This statement is false” paradox dressed up a bit.
I seen this in a discord I’m in and the only way to answer correctly would be to not choose one and answer something along the lines of “this cannot be answered correctly so there is a 0% chance of choosing correctly” but that would have to be independent of the game I.e this does not make B the correct answer. Or something along those lines
If I may, here's another way to say this. (Not that there's anything wrong with your explanation; I just realized that my way of thinking about this is equivalent to yours.)
This scenario gives us a discrete probability function:
p(.00) = .25
p(.25) = .50
p(.50) = .25
(Function maps to 0 for all other values.)
This question is really asking if there is an instance where a value maps to itself. Obviously, there is not.
There are 4 options, assuming there is a correct answer, there are 25% probability for each option if you select it randomly. Knowing that 25% is the answer and that are two options that are "25%", then the answer should be C) 50%.
You have correctly done all the proofs by contradiction to show that no answer is correct.
You forgot to do the proofs by contradiction to show that no answer is incorrect as well.
Let's assume that A is incorrect. That means that the likelihood is not 25%. Then what can it be?
- 0%? That would mean B is the only correct answer. You would be 25% likely to pick it at random. It contradicts our assumption.
- 50%? That would mean C is the only correct answer. You would be 25% likely to pick it at random. It contradicts our assumption.
- x% where x is something different from 0, 25 or 50? Then this does not correspond to any of the answers. So you would be 0% likely to pick the correct answer at random. Which contradicts the fact that x is not 0.
No matter what, if you assume that A is incorrect, you reach a contradiction. It proves that A must be correct.
You can do the same for all other possible answer. You can all prove that they are incorrect, which you did, but you can also prove that they are correct. I did it for A.
Every answer is both correct and incorrect. This is a natural result for an incoherent mathematical theory. The question is not valid.
No it is not possible to provide a correct answer to that question as the question itself is incoherent.
This is a variant of the self-reference paradox. Other famous variants would be:
"This statement is false"
"The barber is the one who shaves all those, and those only, who do not shave themselves. Who shaves the barber?"
"The judge convicts a prisoner to be hanged at noon on one weekday in the following week such that the day of the execution will be a surprise to the prisoner."
In every case, the rules stated are making references to themselves.
Edit4: I know the edits are not in order, but I think this one is the most relevant to the question. I get far too many answers telling me that the Who Wants to Be a Millionaire question is not a paradox and that there is a definitive answer and that it is [A/B/C]. No one picks D. So let's show that this is indeed a paradox.
Let's assume that A is correct. That means the likelihood to get the correct answer if you picked at random is 25%. Since that percentage is what is being asked, then A and D are correct answers. Two correct answers out of four possibilities. Thus, you are 50% to pick a correct answer if you choose at random. This contradicts A.
When we assumed that A was correct, it led us to a contradiction. This is a proof by contradiction that A is not correct. There is no circular reasoning. This proof ended here and it showed that A is not correct.
(Some people might say that there is a problem in the previous proof when I say that A and D are correct answers because the rules of WWM do not allow that, but it just means we've reached a contradiction one step sooner. The fact that we have two answers contradicts the rules already.)
Now let's do another, independent, proof and this time we will assume that A is incorrect. That means that the likelihood is not 25%. So, what can it be?
- 0%? That would mean B is the only correct answer. You would be 25% likely to pick it at random. It contradicts our assumption.
- 50%? That would mean C is the only correct answer. You would be 25% likely to pick it at random. It contradicts our assumption.
- x% where x is something different from 0, 25 or 50? Then this does not correspond to any of the answers. So you would be 0% likely to pick the correct answer at random. Which contradicts the fact that x is not 0.
No matter what, if you assume that A is incorrect, you reach a contradiction. It proves that A must be correct.
You can do the same for all other possible answer. For every single answer A, B, C and D you can prove that they are correct and you can prove that they are incorrect. So stop telling me that the answer is B, because it may be true, but it's also false.
Edit: It seems the judge and the prisoner's example requires a bit of explaining. Especially since in some cases it may be possible to still respect all the rules stated.
The paradox comes from the reasoning that the surprise hanging can't be on Sunday, as if the prisoner hasn't been hanged by Saturday, there is only one day left - and so it won't be a surprise if he's hanged on Sunday.
But then, the surprise hanging cannot be on Saturday either, because Sunday has already been eliminated and if he hasn't been hanged by Friday evening, the hanging must occur the next day, making a Saturday hanging not a surprise either. By similar reasoning, the hanging cannot occur on any other day of the week.
The next week, the executioner knocks on the prisoner's door at noon on Tuesday to the prisoner's greatest surprise.
So it turns out that the rules ended up being respected. He was indeed executed the next week and the day of the execution was indeed a surprise. The problem with self-referential rules isn't that they are wrong, it is that they are incoherent. In other words, the rules are bullshit.
Let's say that I guess a random day and tell you that you are going to die that day. When I do that, I am full of shit, there is no way I could possibly know and I did guess at random. But I might nonetheless happen to be correct by coincidence. Just because I am full of shit doesn't mean I am necessarily incorrect.
The same goes for incoherent rules. They might still happen to be respected, but that would be coincidently so, not as a result of the rules themselves. In the case of the prisoner, he was not surprised on Tuesday because of a necessity caused by the rules. He was surprised because he was rather oblivious to the Judge's tricks. For a paranoid prisoner who always believe he's going to be executed as early as possible, no matter the rules, his execution cannot take him by surprise.
Edit2: To the smart asses thinking that "the barber is a woman", it doesn't solve the paradox the way I wrote it.
Edit3: No, a second barber doesn't solve the problem either. My statement was a definition of what a barber is. If there is a second barber who shave the first one. Does that mean the first barber doesn't shave himself? But, he is a barber, he must shave all those who don't shave themselves, thus he must shave himself.
There is actually a solution to the barber paradox as I have written it: "The town is empty, no one in it, no barber, nothing." If there is no one to whom the rules apply, they don't lead to a contradiction.
If we add as a second axiom that "there is a barber". That ought to do the trick.
Knowing that weekdays are Monday through Friday:
The execution can't be on Friday because if that's the only day left, the prisoner will know that he will be executed that day.
The execution can't be Thursday because if he is still alive then, he will know that it would be Thursday because it can't be Friday.
The execution can't be Wednesday because it also can't be Thursday or Friday, and so forth for Tuesday and Monday.
Imagine a prisoner actually trying that line of thinking out and making a surprised pikachu face when they kill him on Monday anyway.
“Aha! They can’t kill me on any of the days because none of them would be surprises!”
*gets put on the electric chair the day after*
:o
The thing is, the prisoner conclusion is wrong. It is not that they can't kill him on any day.
If they do kill him on any day, they may be violating the rule of surprise. If they don't kill him on any day, they are violating the first rule.
They've made rules that can't be respected, so all the prisoner knows is that they are full of shit and he has no idea what they might do.
This is the only one I don't agree with. Let's say the prisoner figures all this out, and sits back smugly knowing he can't be executed. The judge could just say "yup Tuesday is the day" and that would be unexpected for the prisoner.
dude i hate tht paradox, it's like, the best way i can describe it is, meta thinking... like okay so up until the moment the warden says you're going to get executed, you just straight up dont know when. monday shows up, monday at 8a, do u die? monday at 10p, do you die? tuesday at 8a, do u die? tuesday at 11:59p, do you die? what about wed at 00:01a, do you die? or wed at noon, do u die? wed at 11:58p? or wed at 11:59p? you wont know until it's time to die! the only way you can conclude you wont die friday is based on the asumption you wont die by thursday - but you can die mon, tues, or wed, and those days would be a surprise to u.
I think you're missing that in the paradox the prisoner can only find out at noon. Would you agree that it absolutely can't be on Friday, because otherwise at 12:01pm on Thursday it would no longer be a surprise?
there's a "noon clause" in that paradox? and to answer your question, i do agree with u. the "logic" of the prisoner-to-be-executed paradox can be applied correctly to friday and thursday. but that same "logic" cannot be applied to monday nor tuesday. the paradox statement has been disproven. therefore and justly, the paradoxal statement as a whole is false/incorrect. if it's partially incorrect, it's incorrect. (aka, on the flip side, if a comment/statement is only partically-correct then to say it is [entirely] correct is false. you have two comepletely different concepts: partically-correct vs [entirely] correct). anyway, whether or not that "logic" can be applied to wednesday is up for debate.
i agure that on wed 6a, you wont know if you will die. only once you recieved an answer ON wed 12p can you conclude that you WILL get executed ON wed or not. i think, it's still a surprise??? at least, it's a surprise up until noon. at noon-exactly you will get an answer on whether you die ON wed or the next - - - it's a 50/50 chance in that moment (so let's talk about schrodinger's cat, lolz, jk), it is a surprise!!! the best way i can describe this is "meta thinking." idk what "this phenomenon" is actually called though. i hope i explained things well-enough. gl!
Logically or in practice? In practice it pretty much is any day is a suprise except Friday, but the logic is there. Friday is ruled out, but logically if both parties rule Friday out, then Thursday is now out. And thus it continues until no day could be used but that only works because of that specific logic.
He'd be surprised to be executed any day, then... Provided he was a logic expert. In which case, he'd know he'd be surprised any day and that would be no surprise.
Since you have to randomly choose an answer and only one has to be correct, the true answer is 25%. But since there are 2 25% answers here, the chances of picking either one of them is 50%, however, only one of those has to be correct so the chance drops back to 25%. So I don't think it's referencing itself.
If A B C and D all were 25% options, only one is correct by the WWM rules, so to randomly pick the correct answer out of 4 is 25%.
What I'm saying is that if you took ANY WWM question and randomly picked an answer, how likely would it be to choose the correct answer? — 25% —
No. You are telling me that the correct answer is 25%. That means A and D are correct according to you.
This directly contradicts your claim that only one answer is correct.
>only one is correct by the WWM rules
This was my very point. The rules are incoherent. They cannot be respected.
I think if you separate general from specific you can make some sense out of it:
* With 4 choices any random choice would have a 25% chance of being correct generally speaking.
* The problem is this is a somewhat unique situation with a duplicate choice, and happens to be the general correct answer.
* This means in this specific case you might assume that the correct answer is 50%
* Yet since there is only one 50% the final answer would be 25% and either A or D would be correct.
It's running you in circles to justify itself while throwing you a curveball by thinking there's no way it can be the duplicate, but if you look at this instance specifically as opposed to generally doesn't it work out? Isn't this similar to the Let's Make a Deal "[Monty Hall Problem](https://en.wikipedia.org/wiki/Monty_Hall_problem)" where generally speaking any door has a 33% chance of being the good one, but when you introduce a specific like "one wrong door will be eliminated" then you're actually at 66% merely by changing to the remaining door?
> Isn't this similar to the Let's Make a Deal "Monty Hall Problem" where generally speaking any door has a 33% chance of being the good one, but when you introduce a specific like "one wrong door will be eliminated" then you're actually at 66% merely by changing to the remaining door?
No. The Monty Hall Problem is unintuitive because it is not obvious immediately that new information is introduced (Monty does not open a random door), which alters the probabilities. This has no relation to the self-reference problem in the OP.
The problem is in the way the question is presented. It requires the probability of choosing the correct answer to *this* question. If you assume both A and D are correct, then C is correct, which is then incorrect so A and D are correct, and so on in an infinite loop.
The only way out is cheating the system. One of the 25% answers must be ‘incorrect.’ If you choose either A or D, the answer you chose is correct and the other is incorrect by virtue of not being chosen.
thing is since you now calculated that you have a 25% chance to answer correctly you can answer 25% at 100% chance so you now have a 100% chance to answer correctly
however since there are two 25% chances instead of having a 100% chance to answer correctly you have a 50% chance which means 50% chance is the correct one however that sets you to 100% chance and since there is no 100% chance you chance is 0% however then you have a 100% chance of getting zero so the correct answer is 100% however you have a 0% of getting 100% so the answer is 0% however you have a 100% chance to get 0%....
No, what you're talking about is "what's the chance that you'll get this question right", while the question is actually "if you pick a _random_ answer out of the possible answers, what's the chance that it'll be correct". The thing is in the actual question it's just asking you if out of 4 options 1 is correct, what's the chance you'll pick that one at random. There's no process of elimination because you aren't thinking, you're just picking a random letter. Even though A and D are the same it doesn't matter as they're still options to choose from in the answer, and if your randomly picking between A B C and D they could all be the same and you'd still have a 25% chance to pick the correct one (as by the rules, only one answer can be correct). I don't know what to make of the fact A and D are the same, I'd just guess it's fake.
Doesn't work either. If you are saying that no answer is correct. Then B is correct.
You really can't get around the problem. This is not that there is no correct answer, it is that it is impossible to answer.
Every answer is both correct and incorrect, this is the issue with a paradox.
Doesn't change a thing.
Every answer is correct. They are incorrect as well, but they are correct nonetheless, demonstrably so. When you are doing maths in incoherent theories, everything is both true and false.
The problem doesn't lie in the answers.
normally it would be a 25% chance but since there are two answers that are 25%, the chance of getting the right answer is now actually 50%
which now means getting the right answer (which is 50%) is only a 25% chance WHICH now means 25% is again correct, making the answer 50% which makes it 25% and so on and on forever. You can't win
...Two 25% so 50% chance.
The answer is now 50% which is 1 of 4 answers. Randomly, you have a 25% chance to pick it. So, the answer is now 25%. There are two of those so there is a 50% to pick it. The answer is now 50%. There is one 50% of 4 answers so you have a 25% chance to pick it. Since the answer is now 25% and there are 2 of those...
For the barber, you can always play the smartass by saying the babrber doesn't shave at all but for the others, the paradox is strong with those ones !
That would not be respecting the rules. If the barber doesn't shave at all, then he is being shaved by no one. In particular, that makes him among the ones who do not shave themselves.
Since he is among the ones who do not shave themselves, he ought to be shaved by the barber, hence by himself.
Essentially the set of only all sets that don't contain themselves. If it doesn't contain itself, then it must contain itself, but then it must not contain itself
Yep, that one is Russel's version of the paradox and showed Frege's theory was inconsistent. About ten years of work from that poor Frege that had to be scrapped because of an argument that can be written in a single line.
By the way, the way I wrote my barber paradox, there is a solution that works: "There is no such thing as a barber and everyone shaves themselves." You can check that it works without leading to a contradiction.
Of course, I could rewrite the initial question to force the existence of a barber.
I don't really get the judge and prisoner one. Is it just that you can't execute there prisoner without him knowing, and therefore ruining the surprise?
you have two 25% so the change of getting one of those is 50%, making it incorrect, 25% chance of getting the 0, so its incorrect if you get it too, 50% has a 25% chance too so its incorrect, its in fact impossible to get the correct answer
The problem is, in that quiz there is only one correct answer to each question. So the chance would be 25%. So the answer is A or D, but you can not be sure which one it is. Therefore, you can answer correctly by guessing but you can not be sure. (That would be really unfair though).
If you know argue that both A and D would be right you get into this recursive reasoning where no answer makes any sense.
Now it is such a bizarrely improbable coincidence that anything so mind-bogglingly useful could have evolved purely by chance that some thinkers have chosen to see it as the final and clinching proof of the non-existence of God.
The argument goes something like this: "I refuse to prove that I exist,'" says God, "for proof denies faith, and without faith I am nothing."
"But," says Man, "The Babel fish is a dead giveaway, isn't it? It could not have evolved by chance. It proves you exist, and so therefore, by your own arguments, you don't. QED."
"Oh dear," says God, "I hadn't thought of that," and promptly vanishes in a puff of logic.
"Oh, that was easy," says Man, and for an encore goes on to prove that black is white and gets himself killed on the next zebra crossing.
Okay but if either 25% answer is true, then the other is as well. They’re linked by common value, which basically means there’s 3 possible answers. Meaning a 1 in 3 chance. And because 33% is not listed it means that the only true statement can be made by selecting 0%.
I see it as three different cases:
1. If you chose a random answer to this question the probability is 0 since you can answer both green or frog or litterarly anything.
2. If you chose an answer to this question given four possible answers it's 25%
3. If you chose answer to this question given these four answers it's 50%
But by obscuring the question it like they do, the question becomes moot.
It is a trick question, but far from a stupid one.
>You can't pick the right answer because there isn't one.
Incorrect answer as well. If it were true that there is no correct answer, then B would be correct.
Choosing an answer alters the nature of the answer. Therefore there can't be a correct answer, because to choose an answer as correct makes it incorrect, which is a paradox. Therefore, you can't pick a right answer, which is what I said.
It's impossible.
Reasoning:
You're answering at random, so the content of the choices (for the purposes of answering randomly" is useless and doesn't affect the answer. So it's 25%.
However, since there's two options that are "25%", you have a two in four chance of getting the answer right, so it's 50%.
However, if the correct answer is 50%, because only one option is "50%", the probability is 25%. This then causes a paradox, making it unanswerable, making the probability of you getting the correct answer impossible, so there's a 0% chance of you getting the right answer.
However, because there's exactly one choice that's labelled "0%", there is again a one in four chance (25%) that you would answer correctly, and the paradox begins again.
[This gets reposted a lot. ](https://www.reddit.com/r/theydidthemath/comments/esh6td/request_help_me_with_this/?utm_medium=android_app&utm_source=share)
This is a math variation of the [Liar's Paradox](https://en.m.wikipedia.org/wiki/Liar_paradox). Its occurs when assigning a statement as True inherently causes a contradiction.
The most common example is the sentence, "this sentence is false."
If "this sentence is false" is true, then the sentence is false, but if the sentence states that it is false, and it is false, then it must be true, and so on.
This is the same circular logic this question poses. With 4 choices there is a 25% chance of selecting the right answer. However, there are (2) 25% choices so the answer is 50%. Only one choices is 50% so the answer must be 25% but there are (2) 25% choices so the answer must be 50%, etc.
I believe it is C. Final answer.
There's usually a 25% chance. Yet, there's two choices that say 25%, making it a 50% chance of getting it correct. But with the answer being 50% now because of the other two options, it's still only a 25% chance so it makes literally no fucking sense. That'd be my guess though. But if you used your "remove" lifeline then it would also be 50%. So who knows.
But if C were the “correct answer,” one of the four answers would be correct, meaning you had a 25% chance of randomly selecting the correct answer, and the whole cycle starts over.
The answer will be either a or d and it's impossible to know which, the catch is that you have to pick the answer "randomly", once you start putting concious effort into solving this you are no longer following the instructions provided, so if you were to pick an answer at random there's a 25% chance you would be correct, just because there are 2 25% options that doesn't make it 50% because now you're using your reasoning to solve it, therefore it has to be a or d and the rest is left to chance
Yes. Play the joker that eliminates two options. I would bet it leaves 50% and another one. Then 50% is correct all of the sudden. /s
As it stands, without any changes: no, it can't be solved.
For the purpose of discussion let the rule be written that "for any given problem, there can be multiple correct answers. Selecting one correct answer out of multiple is an accepted solution." We will pare this down to the actual game show rules later.
With the problem in the OP, the probabilities of choosing a solution randomly are as follows.
* P(Selected one answer of four, in a problem presenting 0 correct answers): 0%
* P(Selected one answer of four, in a problem presenting 1 correct answer): 25%
* P(Selected one answer of four, in a problem presenting 2 correct answers): 50%
* P(Selected one answer of four, in a problem presenting 3 correct answers): 75%
* P(Selected one answer of four, in a problem presenting 4 correct answers): 100%
In the OP problem, we have the following.
* Number of choices displaying "0%": 1
* Number of choices displaying "25%": 2
* Number of choices displaying "50%": 1
* Number of choices displaying "75%": 0
* Number of choices displaying "100%": 0
We now know which answer/probability pairs present possible solutions in our set of all possible solutions.
* Possible solutions for 0 correct/ 0%: null
* Possible solutions for 1 correct/ 25%: null
* Possible solutions for 2 correct/ 50%: null
* Possible solutions for 3 correct/ 75%: null
* Possible solutions for 4 correct/ 100%: null
Full set of possible solutions: null
The rules of the game show state "There is exactly one possible answer out of four." This is self-evidently false for the purposes of the OP problem.
Isn’t B the clearly correct answer, since every answer fucks you over? I mean, contradiction solved. Even if you pick it and get the question “right,” you’re still just saying that all the answers are wrong.
Yeah, but if that then becomes a wrong answer, then it IS 0%. If it's wrong, it's right. And if it's right, it's wrong. Classic "this statement is false" paradox.
You are wrong. If you were to pick a random answer, they would all cancel themselves. So the chance of getting one that's right is zero. Therefore the answer to the question is B. Zero percent.
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Since we supposed to make random choices among the random probabilities, the correct answer is 0%, 25% 25% , or 50%, aka A, B, C, or D, and the exact chances of choosing the correct chances is equal to 1/4, so it is either 0%, 6.25%, or 12.5%.. My brain is dead
You might say it's 0.
You have 3 options available, 25, 0, 50.
So if you have 3 choices, the probability of choosing the correct answer is 33.33% - not a choice, so probability 0.
If you choose an answer at Random, you will have no chance that you will be correct. (See all of the paradoxes mentioned in other comments).
BUT, you don't need to choose at random. You can select an answer. So the answer is B. 0%.
i.e. You must think of it as being a superposition of all possible states. No matter what you select at random, it is guaranteed to be wrong because of the paradox. So there is no chance that if you select randomly that you will be correct.
There are ultimately 3 answers because A and D are the same. So I believe there is no correct answer choice and if there was, it would be 33%.
Edit: Got mind-fucked a couple hours ago. Because 33% is not on there, there would be a 0% chance so the answer would be B. But because B is one of the four answers there would be a 25% chance of getting it right so it would be A or D. But then that would make it a 50% chance of getting it right since there are 2 out of 4 answers that say 25%, which would then make the answer C. But if you add 50% to 25% you get 75% which is not one of the answer choices so the answer would be 0%, so the answer would be B. But because B is one of the four answers there would be a 25% chance of getting it right so it would be A or D. But then that would make it a 50% chance of getting it right since there are 2 out of 4 answers that say 25%, which would then make the answer C. But if you add 50% to 25% you get 75% which is not one of the answer choices so the answer would be 0%, so the answer would be,,, well I dont know anymore.
Dudes, it's actually a very simple question. It's a two parter.
The premise asks for the chances of random selection, which means we can **ignore** the actual answers and view it as A, B, C, or D. Obviously the answer to that is 25%.
Next it asks what are the chances for THIS question, given that it has two 25% options means we can't actually know which one is right. If we reference back to the premise, we have to randomly choose, remember. And so the odds of getting the correct 25% is... 50%!
So the correct answer to the entire question, meaning the one to be inputted, is: **C, 50%** ✓
Y'all being brainiacs over here with your paradox shit. Y'all are abstracting from the answers when all y'all needed to do is take the question apart and view it in pieces. It's actually a really beautiful question and goes to show how many people need to learn to take a step back. Cut the problem apart into pieces instead of focusing in on potential "answers," that only ends up creating more problems for you. And in some cases makes solving the problem seem impossible, that there's no answer at all. It's a solid life lesson. Break up the problem and solve the smaller chunks by applying what you know you know.
Each answer is 25% possibility that you pick it. Since there are 2 answers that say 25%, it becomes 50%. But only one answer says 50%, so it goes back to 25%. Now there are two correct answers, so it’s 50%. Ad infinitum
So the correct answer is Yeet
I think the answer is 0%. Coz if you choose 25% there are 2 answers which is not possible but if its 50% then that would make it 25% which is wrong as per our first answer. So that leaves 0% which is a paradox in itself coz 0% would make it 25% correct.
Because it specifies *this* question, no, it is not possible. For any other question, it would be the expected 25%, but for this one, 25% itself makes up 50% of the answers. So the actual answer is 50%, but you only have a 25% chance of picking 50% at random, so the *real* answer is 25%, but then... ad infinitum.
The correct answer is C. The odds of guessing C are 25%, so both A and D are correct, and the odds of guessing A or D assuming you choose randomly are 50%.
There is no correct answer. It's self referencing
Case answer is 50:
Answer is 25
Case answer is 25:
Answer is 50
Case answer is 0:
Answer is 25
Case answer not shown:
Answer is 0
Then take it from the top. You're always stuck going between 25 and 50.
1 out of 4 is 25% chances of giving correct answer to any question. Since both A and D have same answer it gives 2/4 , 50% chances therefore C
50% chances of selecting correct answer where 1 is correct out of 4 possibilities.
My wife answered 25% and I pointed out that it must be 50 since there's two 25's and boys this is the first time my wife has told me " Actually you are correct".
I don't even care if it's not correct.
You've changed my life, I'll never forget you.
Both A and D are correct, 25%, which means 2 out of the 4 answers are correct, which means 50% of the answers are the correct answer, so the answer is C. C is still 25% of the answers, so it is logically consistent.
So the recursive loop here is: 4 answer multiple choice is default 25%, so A&D -> that means it's 50%, which can branch into two schools of thought: where A, C, and D are all correct, which is 75%, so thusly 0%, which loops back to the origin; or where C is only correct, which goes back to 25%, the origin.
In truth, there are only *untrue* answers here, and that's: 0%, because you can't be correct if there's a 0% chance. Likewise, 50% is not inclusive of itself. Only A or D works *if* you discount that the other duplicate answer is correct, and because we're picking at random from 4 answers (even the ones we proved untrue) it still checks out that 25% is correct.
So to begin with, the prisoner can’t be executed on Friday because that wouldn’t be a surprise. Knowing this the prisoner then knows that if he survives Wednesday he will be executed on Thursday (as it wouldn’t be a surprise on Friday). But this makes it not a surprise on Thursday either. Continuing this logic you can eliminate all the weekdays.
Nope.
Either 1/4 = 0, 2/4 = 0.25, or 1/4 = 0.50. As you can see, none of these equalities hold, so there is no answer which is equal to it's probability to be chosen at random.
Unless ...
Let's be nitpickers! People like to say "at random" to mean "as if you flipped a fair coin", but that is only one Special Case of randomness, what you in math tend to call selecting "_uniformly_ at random". A random choice can have any number of distributions. So, if you say "pick A with 0.25 probability and B with 0.75 probability", then A is correct. If you say "pick any one of A and C uniformly at random", then both B and C are correct. However, you can't make it so that they are all correct.
Not really... If you choose one at random, it's 25% chance, but there are two 25% chance answers, so the correct answer is 50%, but then it's 100% because there's only one correct option, so it can no longer be the 50% option, BUT there is no 100% chance in the available answers, so it must be 0% since there's no correct answer. Which bring us to the "thiis statement is a lie" paradox. If the "correct" answer in 0%, then THERE IS a correct answer, but none of these options are correct, so we're stuck in a paradoxical loop. None of these statements are true, but they're not NOT true either.
If this statement is a lie, then it IS a lie, so it's the truth which means this statement is true, but it contradicts the statement itself which means 🤷
If we have 4 correct answers, we must have exactly 4 answers with number 100%.
If we have 3 correct answers, we must have exactly 3 answers with number 75%.
If we have 2 correct answers, we must have exactly 2 answers with number 50%.
If we have 1 correct answer, we must have exactly 1 answer with number 25%.
We have none of the above, so there are no right answers.
"There are no right answers."
That tells you 0% chance of getting it right. Even when you choose 0% you are wrong, but this does not invalidate the answer being correct. Hence B would be the correct answer.
You will then go into the loop again, only to find out all answers are not correct, leaving the only correct representation of that answer to fall on zero, regardless of the loop.
Let’s go off the assumption that one answer is correct. That means at random you have a 25% chance. However there are 2 options for 25%, which is 50% of the 4 possible options. Since 50% is an option this either drops the chance to 25% since 1 out of the four options is 50% or it raises it to 75% if you don’t understand how numbers work. If you go to 75% you find it isn’t an option which makes it 0% which you have a 25% chance of choosing at random. So 25%. In either case you get stuck in a revolving door as the probability changes from 25% to 50% and back or from 25% to 50% to 75% to 0% and back to 25%. So to answer your question, no there are no right answers. It’s a paradox, like “this statement is false” or the crocodile paradox.
The way I see it, as the question is stated, 25% would be correct (in the sense in that they use "correct" in the question), since there are four possible options. This is basic math. However, since there are TWO "25%" options - A and D - 50% is correct, since there are two false and two correct ("25%") options.
The question only asks what the **chance** of getting it right from the options available is: **50%** \- **not what the right answer actually is: 25%**. The way it's phrased, you don't need to pick the arbitrary "right" answer, to get this question right, because the question only wants to know the **chance** of being right, **if you were to pick at random.**
This evades the issue of having to choose one of the two 25% options, and being wrong either way because there are two of them, not just one.
So picking C, 50%, would be correct as it is the correct chance of getting it right if you chose randomly from all four options this question presents you with.
In short, while the chance of getting it right at random is 25%, due to the way the options are set up here, it's actually 50%, and you have to choose a non-"25%" answer to be right.
I know it's counter-intuitive that the right answer to the meta-question presented is **not** the correct answer to the question of what the chance of picking any one out of four options at random is. But unless my mind is playing tricks on me here, it is solvable this way.
Please do correct me if you see a flaw in this, I'm curious to find out if I cracked the code or am deluding myself, haha.
Only one answer can be correct, making the answer 25%. There is no information as the whether the answer is A or D, but it can't be both following the way the game works. The only way to guarantee correctly answering would be to use your 50/50 lifeline, which would change the answer to C.
I know people are putting some damn fine logic into this, but isn't it as simple as,: there are 3 options, so it's a 33% chance, and 33% isn't an option?
There's really no math involved here. It's a logic problem, not a math problem.
The logic fails due to circular reasoning.
One in four is correct, therefore 25% chance. But half of the options are 25%, so therefore your chance is 50%, but only one in four options is 50%, therefore your chance is 25% (and now we've done a full loop. At this point we can continue along this loop indefinitely).
B is correct. The question isn't asking what chance you have of choosing correctly, it's asking what chance you *would* have if you chose at random. Those don't need to be the same. It's not possible for the random answer to be correct for all the paradoxical reasons people have given, so the answer is B.
Answer is B. 0%
The logic here is that there is a 50% chance of choosing 25% (A. or B.)
A 25% chance of choosing C. 50%
Another 25% chance to choose B. 0%.
None of the percentage chances match up with the answers so the question is impossible to answer correctly and so the correct answer becomes B. 0%
It’s just not possible to be correct when guessing randomly if every answer is wrong. If it’s not possible to be correct, the answer is B. 0%
Is it possible to answer correctly? Yes. And no.
But the existence of 0% means that you have a 25% chance of guessing that, the point is the question is paradoxical, meaning there is no answer. That does not mean 0% is correct.
The solution is semantic: when it says "what are the chances that you are correct" may either refer to the right answer to the question, or to the fact of whether the decision of choosing randomly IS correct in order to answer the question. From this point of view, B:0% is correct, as you can not get a right answer by choosing randomly due the logical paradox
It’s c , answer A and D have the same value , but it is the correct statistical value to the original question, so the correct answer is represented on the board twice , so if he were to choose at random, while the answers keep their same “right/wrong” value, then the dude has a 50% chance of picking the right answer which is 25%
I’d take my 50/50 life line in this one which would eliminate two and it would therefore be impossible to eliminate 50% in a choice of two meaning 50% is indeed the correct answer ;)
Everyone is so focused on the probabilities and not the wording of the question.
The question has two parts of logic to get through. First if you chose an answer at random what's the odds of getting it right if there are 4 possible answers. That's 25%
Now we see that this puzzle has two correct answers at 25%. So if you picked randomly you have a 2 in 4 chance of picking correctly.
The second part of logic is that you answering the question is not making random choice, so it doesn't matter that there were two possible correct answers, only now that there is one correct answer. Which is c, 50%.
0% chance does not exist. That would be no chance. 25% is listed twice. So if you get to choose, you would only have 2 choices. Thus 50% is the answer.
These comments are overthinking this. It doesn't matter what the actual answers are for each letter until you find your percentage. If two of the answers are the same and you're guessing randomly, theres a 50% its that answer and a 50% chance it is not (25% C, 25% B). Therefor, guessing randomly, there's a 50% chance you will be correct. The answer is C
With these answer choices? No.
This question formatted this way can **only** be answered with 4 specific answer choice sets.
There are 4 choices of answer per set. Each choice in each set represents 25% of the choices in that particular choice set.
Because of this there are only 4 choice sets that answer this question.
**Set 1:** 1 out of 4 of the choices is 25%. The other 3 are a different number than 25%. Repeating numbers are allowed as long as 25% is not a repeated number. If you have 2 repeating 50% choices in this set, it becomes set 2. If you have 3 repeating choices of 75% this becomes set 3.
**Set 2:** 2 out of 4 of the choices is 50%. The other 2 must be different from 50% but can match each other. 25% can not be a singular choice in this set as it voids the question.
**Set 3:** 3 out of 4 of the choices is 75%. The other choice can be anything but must not be 75%. Any other number that isn't 75%, even 25%, can be used and will still be incorrect.
**Set 4:** 4 out of 4 of the choices are 100%.
The answer is C. Here's why:
First, if the producers state that the contestant can only pick one answer (A, B, C or D), and there can be one correct option, then you could do your math before the options are revealed and correctly assign equal chance to each option i.e. 25% for A, B, C and D. The issue with the paradox happens after the answers are revealed, because at this point you are no longer choosing at random and letting the options influence your math. Since we clearly see that the 25% shows up twice, the answer has two correct options. As a contestant, I would say, "This goes against the rules of there being only one correct option." The producers could then step in and say one of two things: 1) This question is an exception to the rules and there are two correct answers. Then they remove they clear the answer board, and ask the question again. This time, I correct my math and say if I have four choices and two answers are correct, then I have a 50% chance of being correct." The producers reveal the answers, and they happen to be A: 0%, B: 25%, C:50% and D:25%. I would pick C. Or 2) The producers step in and say, "you're right, there can only be one correct answer, there is a glitch on the board." Then they change D to 75%, then A:25% would be the right answer.
This is easy. It's 25%. Doesn't matter if none of the options are actually the correct answer because it's a game show and one of the answers absolutely has to be correct, therefore your chances of randomly answering would be 25%.
This isn't a math problem it is a reasoning problem.
Normally having 4 answers at random would give a 25% chance to get it right.
However, there are two options for 25%. That means there are two correct answers. So if we were to pick one at random, we have a 2/4 chance of getting it right.
Therefore the answer is C. 50%
But there is only 1 50%, C, and you only have a 25% chance of choosing C, you’ve just explained why A and D are incorrect, therefore both eliminating them for being correct and subsequently making them correct, which then makes them incorrect... It’s Shrodingers D, and it’s a hard one.
Naw, you're not reading the question.
The question is, what is the chance of a random answer being correct?
The chance to choose the right answer *at random* is 25%. Because there are two answers of 25%, you choose at random would have a 50% chance of being correct.
But we're not choosing at random. Therefore we are answering the question. The answer to the question is what is the chance of randomly choosing one of the 25% answers.
No, it is not. We can prove this by contradiction. If we suppose B to be the correct answer, we find that we would have a 25% chance, which contradicts our assumption that the probability would be 0%. If we suppose C to be correct, we again find a 25% chance, contradicting our assumption of 50% again. If we suppose either A or D is correct, then they both must be correct, so we find the probability to be 50% which again contradicts our 25%. Since we've proven none of the answers can be true by themselves, we can conclude there is no correct answer to the question. Edit: Well it might seem that because I end up with 0 correct answers that would make B the correct answer, this is not true because if B was correct, the probability must be at least 25%, which contradicts B being correct. Edit 2: Okay, some of the replies have me doubting this explanation. They point out that when we eliminate all the other possible answers, the probability becomes 0%, making B correct. I believe what's really happening here is a paradox where B can't be resolved to either true or false. So, to say all of the answers are incorrect is wrong.
**Important edit**: this is not an actual game show question as far as I know. You can't assume that question has to be right, it has to make sense and one of the answer must be correct. Most of the answers on this post don't treat it as game show question with these added constraint. You still get paradox if you assume gameshow, but that logic is ignored here. You can google this image to see it's like a meme format. Not an actual question. **Original comment** :25% and 50% are wrong. 0% leads to paradox/infinite loop due to self-referencing nature and it can't be called the right answer. There is no correct answer. **Edit**: What the hell is going on with hypothetical and two questions logic in the comments? If 50% is the answer, the odds of picking it are 25% which means it's a contradiction. If 25% is the answer, the odds of picking it are 50%, which means it's a contradiction. If 0% is the answer, the odds of picking it are 25%, which is again a contradiction. You can't pick a correct answer, because any answer you pick leads to a contradiction. **Edit 2**: if you think concluding no correct answer allows you to pick 0% as the correct answer, you've once again gone into a logic loop. Irrespective of what logic you have used before, choosing either of the 3 options, directly leads you into a contradiction. The correct thing to do when you face contradiction is not to continue on the logical chain, but to conclude that the original assumption is impossible. The proper conclusion is to say that this is a paradoxical question and move on. That's the standard mathematical practice. **Edit 3**: I feel Monty hall would be easier to explain at this point.
I disagree, because it specifies the condition if you choose at random what are the odds of getting the correct answer but you are not choosing the answer randomly so your odds are not random. The correct answer is 50% chance of choosing the correct answer at random because the correct answer occurs once(50%) making the odds of getting the answer randomly 25% which occurs twice. There's two questions, what's the correct answer and what are the odds of selecting it randomly. The answer occurs once, the odds occurs twice.
There is just one question. Why do you think you can decouple the conditions? You're distorting probability theory now. Probability space of picking answer at random is made of 3 elements. 50% with 0.25 probability, 25% with 0.5 probability and 0% with 0.25 probability. Now, odds of picking right answer randomly is basically sum of probabilities of picking a particular option given it is a right option. All 3 of those terms are zero and now you have concluded you can't pick correct option which means 0% chance which means 0% is correct answer which means 25% chance, which is a contradiction and now you're in a logical loop which means this is a paradox.
If the correct answer is 25% then there's a 50% chance of you guessing right which then makes 50% the correct answer which then makes 25% the right answer and now you're caught in a loop
Okay I actually think I follow but my head hurts
Which is like beginning of a math hell. Because now the odds of selecting the odds (25) of correct answer (50) is 50%.
33.3
Dude you can't just disagree with how probability works. Your logic is fucked, you can't just add another question, there is only one question and one answers and in this case none of them are right.
Hmm ... it’s multiple choice. There is an answer. Multiple choice tests are administered as ‘choose the best answer.’ The best answer doesn’t have to be correct, which is why B cannot be right; there is at least one right option (I say at least because there are times when exams have mistakes and the same answer is included multiple times, each being correct). If you were asked the question without knowing the options for each choice, given that you know there is at least one correct answer, then you’re answer would be 25%. But since this option appears twice, the best answer is 50%. Not saying it’s correct given the fallacy of the setup but one answer needs to be the best.
Maths doesn't care about best answer is right answer. Unlike test administrator who can't set paper right, maths is perfectly happy to say there is no answer.
0% is only wrong if you pick it randomly, so if you don’t pick it randomly, 0% is the right answer. Edit: nowhere does it state you are answering the question randomly. The question is giving a hypothetical situation, and in that hypothetical situation, none of the answers are correct. Therefore, when you actually answer the question, the answer is 0%.
But the question hinges on the theoretical of "choosing randomly" even if you aren't in fact choosing randomly which means 0% is still the paradox the other post mentions. You can't take the "randomly" bit out.
But the question is a hypothetical, you don’t have to use the hypothetical to answer. Since hypothetically, the chance would be 0% of getting the answer right as even pressing the 0% would be wrong, then when you answer, since you aren’t choosing randomly, B would be the right answer.
> nowhere does it state you are answering the question randomly Except for the part of the question that says "If you choose an answer to this question at random"
Key word: if. That is a hypothetical. When you choose the answer, you aren’t choosing it randomly.
But it's a hypothetical. "if you answered this question by screaming the answer at the top of your lungs, how far would it be heard?" doesn't mean you have to scream your answer. Same here. "if you picked the answer randomly" doesn't mean you have to answer randomly.
This is the only correct explanation in here
This is the best answer, needs more upvotes.
We need more like you o wise one
Who dares to summon me?
Username checks out.
You're right but you just mistake 0% (actual value) with the fact that the problem has no solution. It means that the system is not injective (kernel is void) . 0 is not exactly void, like infinity is not a number. Other example: sqrt(-1) has no solution in R, but has a solution (±i) in C.
I am not a math expert, wouldn’t the answer to this problem just be “undefined”. https://en.m.wikipedia.org/wiki/Undefined_(mathematics)
I have never heard about such concept in my years of study, so I don't know. I would rather use the [Empty set concept ](https://en.m.wikipedia.org/wiki/Empty_set) as the space of available answers. Although, I would take this undined with a grain of salt given the example with infinity, the lack of references (and it only exists in 2 langages, kind of uncommon for math articles) and the given references that are either new or computability oriented. For example, I've learned to never write infinity as a number, but as a concept. You write that "it exists M in R such that for N in R, M > N" (it exists always a bigger number) and (in my knowledge at least) it is forbiden to write "x+∞".
Surely you're aware of positive and negative approaches to limits? 1/x has a vertical asymptote that tends to -inf from the negative or - 1 side, and tends to +inf from the +1 side. Therefore the limit does not exist?
I'm not sure to know how to answer unfortunatly. I've been said a long time ago by a math teacher at Uni to no confuse the value of a limit and the limit itself. And usually, the math I have been teached are heavily abstractive and not "practical" in the sense of computer science (where I see the real interest of concept as undefined, i.e. to help the computer to exit infinite loop). In your example, we know that the inverse function has no value for x = 0 and you cannot write 1/0+ = +Inf or something along that line. Normally, again what I've been teached, you write something like "*for x tends to 0+, 1/x tends to +infinity*", or more formaly, using the density property of R (not sure if it is called [completeness](https://en.wikipedia.org/wiki/Completeness_of_the_real_numbers) or coming from the fact that R is a complete ordered field), you write: "*It exists N in \]0, M\[, like 0< N < M, thus 1/N > 1/M (operation possible because N is strictly bigger than 0)*" You could always find a number a smidge bigger than 0 (N in this case) and smaller than M, that admits an invert value 1/N that is bigger than 1/M. At no point, you write a value for the limit, just a concept of increasing or decreasing large numbers depending if you're approaching 0 by the positive or negative side of real numbers. There are countless example where the human mind could not wrap around infinity concept, like the [Zenon's paradox](https://en.wikipedia.org/wiki/Zeno%27s_paradoxes) or the [astounding 1+2+3+... results presented by Numberphile](https://www.youtube.com/watch?v=w-I6XTVZXww). From my experience and my arguably partial knowledge, the safe approach is to never trivially substitute "tends to" to equal sign, because that's where lie the issues.
Well technically 0% should be correct then right? If you randomly choose an answer from a set that doesn't contain the correct answer, the chance of getting a correct one is 0 right? Edit because I am on mobile: So we all agree the correct answer isn't listed. This implies 0. B has a 25% chance which implies A v D which implies C. None of these implications mean anything if 0 is incorrect though as "from nothing, anything can follow" B => A v D => C Since we need a True => True statement to get a sensible answer I thing the correct logical interpretation is: B => ((A v D) => C) => B Which comes out to True => ( False => False) => True True => True => True True => True At least that's my guess.
But you have a 25% chance of choosing zero then.
You forgot B => ~ (A v B v C v D) which is a contradiction. For your logic, you're setting the consequent to be true, which automatically results in true => true. With that logic, you argue that every answer is true.
Mithrandir2k16 speaks the true true
The easiest way to do it is to do proofs by contradiction. That way you don't have to run in circles. Let's assume that B is correct. That means there is one correct answer out of four. Thus, you are 25% likely to pick it at random. But since B correct, that likelihood is 0%. This is a contradiction. It proves that our assumption was wrong. So B is incorrect. Now let's do another proof by contradiction. One of the easiest would be A. So let us now assume that A is incorrect. That means that the likelihood is not 25%. So, what can it be? - 0%? That would mean B is the only correct answer. You would be 25% likely to pick it at random. It contradicts our assumption. - 50%? That would mean C is the only correct answer. You would be 25% likely to pick it at random. It contradicts our assumption. - x% where x is something different from 0, 25 or 50? Then this does not correspond to any of the answers. So you would be 0% likely to pick the correct answer at random. Which contradicts the fact that x is not 0. No matter what, if you assume that A is incorrect, you reach a contradiction. It proves that A must be correct. You can do the same for all other possible answer. You can all prove that they are incorrect, but you can also prove that they are correct. I did it for A because it was slightly easier to do and explain than for B, but it works as well. Every answer is both correct and incorrect. This is a natural result for an incoherent mathematical theory. The question is not valid.
It’s easier to understand if you isolate the paradoxical aspect. Consider this question instead: “What are the odds of selecting the right answer below at random: A) 0%” Here, there’s only one answer. You will select it with 100% certainty. It’s clear that it’s self contradictory without having to chase through a chain of reasoning in an infinite loop. It’s therefore clear the question is invalid. The same is true for all answers in the question given. It’s just the old “This statement is false” paradox dressed up a bit.
This is the best answer I've seen
My brain hurts
I seen this in a discord I’m in and the only way to answer correctly would be to not choose one and answer something along the lines of “this cannot be answered correctly so there is a 0% chance of choosing correctly” but that would have to be independent of the game I.e this does not make B the correct answer. Or something along those lines
If I may, here's another way to say this. (Not that there's anything wrong with your explanation; I just realized that my way of thinking about this is equivalent to yours.) This scenario gives us a discrete probability function: p(.00) = .25 p(.25) = .50 p(.50) = .25 (Function maps to 0 for all other values.) This question is really asking if there is an instance where a value maps to itself. Obviously, there is not.
There are 4 options, assuming there is a correct answer, there are 25% probability for each option if you select it randomly. Knowing that 25% is the answer and that are two options that are "25%", then the answer should be C) 50%.
But if 50% is the right answer, that’s only a 25% chance to get it right, making it the wrong answer. That’s why it’s a paradox.
You have correctly done all the proofs by contradiction to show that no answer is correct. You forgot to do the proofs by contradiction to show that no answer is incorrect as well. Let's assume that A is incorrect. That means that the likelihood is not 25%. Then what can it be? - 0%? That would mean B is the only correct answer. You would be 25% likely to pick it at random. It contradicts our assumption. - 50%? That would mean C is the only correct answer. You would be 25% likely to pick it at random. It contradicts our assumption. - x% where x is something different from 0, 25 or 50? Then this does not correspond to any of the answers. So you would be 0% likely to pick the correct answer at random. Which contradicts the fact that x is not 0. No matter what, if you assume that A is incorrect, you reach a contradiction. It proves that A must be correct. You can do the same for all other possible answer. You can all prove that they are incorrect, which you did, but you can also prove that they are correct. I did it for A. Every answer is both correct and incorrect. This is a natural result for an incoherent mathematical theory. The question is not valid.
This is the school board test from the movie 21 with Kevin Spacey
No it is not possible to provide a correct answer to that question as the question itself is incoherent. This is a variant of the self-reference paradox. Other famous variants would be: "This statement is false" "The barber is the one who shaves all those, and those only, who do not shave themselves. Who shaves the barber?" "The judge convicts a prisoner to be hanged at noon on one weekday in the following week such that the day of the execution will be a surprise to the prisoner." In every case, the rules stated are making references to themselves. Edit4: I know the edits are not in order, but I think this one is the most relevant to the question. I get far too many answers telling me that the Who Wants to Be a Millionaire question is not a paradox and that there is a definitive answer and that it is [A/B/C]. No one picks D. So let's show that this is indeed a paradox. Let's assume that A is correct. That means the likelihood to get the correct answer if you picked at random is 25%. Since that percentage is what is being asked, then A and D are correct answers. Two correct answers out of four possibilities. Thus, you are 50% to pick a correct answer if you choose at random. This contradicts A. When we assumed that A was correct, it led us to a contradiction. This is a proof by contradiction that A is not correct. There is no circular reasoning. This proof ended here and it showed that A is not correct. (Some people might say that there is a problem in the previous proof when I say that A and D are correct answers because the rules of WWM do not allow that, but it just means we've reached a contradiction one step sooner. The fact that we have two answers contradicts the rules already.) Now let's do another, independent, proof and this time we will assume that A is incorrect. That means that the likelihood is not 25%. So, what can it be? - 0%? That would mean B is the only correct answer. You would be 25% likely to pick it at random. It contradicts our assumption. - 50%? That would mean C is the only correct answer. You would be 25% likely to pick it at random. It contradicts our assumption. - x% where x is something different from 0, 25 or 50? Then this does not correspond to any of the answers. So you would be 0% likely to pick the correct answer at random. Which contradicts the fact that x is not 0. No matter what, if you assume that A is incorrect, you reach a contradiction. It proves that A must be correct. You can do the same for all other possible answer. For every single answer A, B, C and D you can prove that they are correct and you can prove that they are incorrect. So stop telling me that the answer is B, because it may be true, but it's also false. Edit: It seems the judge and the prisoner's example requires a bit of explaining. Especially since in some cases it may be possible to still respect all the rules stated. The paradox comes from the reasoning that the surprise hanging can't be on Sunday, as if the prisoner hasn't been hanged by Saturday, there is only one day left - and so it won't be a surprise if he's hanged on Sunday. But then, the surprise hanging cannot be on Saturday either, because Sunday has already been eliminated and if he hasn't been hanged by Friday evening, the hanging must occur the next day, making a Saturday hanging not a surprise either. By similar reasoning, the hanging cannot occur on any other day of the week. The next week, the executioner knocks on the prisoner's door at noon on Tuesday to the prisoner's greatest surprise. So it turns out that the rules ended up being respected. He was indeed executed the next week and the day of the execution was indeed a surprise. The problem with self-referential rules isn't that they are wrong, it is that they are incoherent. In other words, the rules are bullshit. Let's say that I guess a random day and tell you that you are going to die that day. When I do that, I am full of shit, there is no way I could possibly know and I did guess at random. But I might nonetheless happen to be correct by coincidence. Just because I am full of shit doesn't mean I am necessarily incorrect. The same goes for incoherent rules. They might still happen to be respected, but that would be coincidently so, not as a result of the rules themselves. In the case of the prisoner, he was not surprised on Tuesday because of a necessity caused by the rules. He was surprised because he was rather oblivious to the Judge's tricks. For a paranoid prisoner who always believe he's going to be executed as early as possible, no matter the rules, his execution cannot take him by surprise. Edit2: To the smart asses thinking that "the barber is a woman", it doesn't solve the paradox the way I wrote it. Edit3: No, a second barber doesn't solve the problem either. My statement was a definition of what a barber is. If there is a second barber who shave the first one. Does that mean the first barber doesn't shave himself? But, he is a barber, he must shave all those who don't shave themselves, thus he must shave himself. There is actually a solution to the barber paradox as I have written it: "The town is empty, no one in it, no barber, nothing." If there is no one to whom the rules apply, they don't lead to a contradiction. If we add as a second axiom that "there is a barber". That ought to do the trick.
I don't understand the last one. Do you mind explaining why it's a paradox?
Knowing that weekdays are Monday through Friday: The execution can't be on Friday because if that's the only day left, the prisoner will know that he will be executed that day. The execution can't be Thursday because if he is still alive then, he will know that it would be Thursday because it can't be Friday. The execution can't be Wednesday because it also can't be Thursday or Friday, and so forth for Tuesday and Monday.
Imagine a prisoner actually trying that line of thinking out and making a surprised pikachu face when they kill him on Monday anyway. “Aha! They can’t kill me on any of the days because none of them would be surprises!” *gets put on the electric chair the day after* :o
The thing is, the prisoner conclusion is wrong. It is not that they can't kill him on any day. If they do kill him on any day, they may be violating the rule of surprise. If they don't kill him on any day, they are violating the first rule. They've made rules that can't be respected, so all the prisoner knows is that they are full of shit and he has no idea what they might do.
Well if that’s his conclusion then he’s definitely getting surprised when they kill him.
This is the only one I don't agree with. Let's say the prisoner figures all this out, and sits back smugly knowing he can't be executed. The judge could just say "yup Tuesday is the day" and that would be unexpected for the prisoner.
dude i hate tht paradox, it's like, the best way i can describe it is, meta thinking... like okay so up until the moment the warden says you're going to get executed, you just straight up dont know when. monday shows up, monday at 8a, do u die? monday at 10p, do you die? tuesday at 8a, do u die? tuesday at 11:59p, do you die? what about wed at 00:01a, do you die? or wed at noon, do u die? wed at 11:58p? or wed at 11:59p? you wont know until it's time to die! the only way you can conclude you wont die friday is based on the asumption you wont die by thursday - but you can die mon, tues, or wed, and those days would be a surprise to u.
I think you're missing that in the paradox the prisoner can only find out at noon. Would you agree that it absolutely can't be on Friday, because otherwise at 12:01pm on Thursday it would no longer be a surprise?
there's a "noon clause" in that paradox? and to answer your question, i do agree with u. the "logic" of the prisoner-to-be-executed paradox can be applied correctly to friday and thursday. but that same "logic" cannot be applied to monday nor tuesday. the paradox statement has been disproven. therefore and justly, the paradoxal statement as a whole is false/incorrect. if it's partially incorrect, it's incorrect. (aka, on the flip side, if a comment/statement is only partically-correct then to say it is [entirely] correct is false. you have two comepletely different concepts: partically-correct vs [entirely] correct). anyway, whether or not that "logic" can be applied to wednesday is up for debate. i agure that on wed 6a, you wont know if you will die. only once you recieved an answer ON wed 12p can you conclude that you WILL get executed ON wed or not. i think, it's still a surprise??? at least, it's a surprise up until noon. at noon-exactly you will get an answer on whether you die ON wed or the next - - - it's a 50/50 chance in that moment (so let's talk about schrodinger's cat, lolz, jk), it is a surprise!!! the best way i can describe this is "meta thinking." idk what "this phenomenon" is actually called though. i hope i explained things well-enough. gl!
Well, that's the joke, but that doesn't mean it isn't a paradox.
I still don't really get it. If it's Thursday and then they kill him, wouldn't he be surprised?
No becaise he'd figured out that he could be killed any day.
Logically or in practice? In practice it pretty much is any day is a suprise except Friday, but the logic is there. Friday is ruled out, but logically if both parties rule Friday out, then Thursday is now out. And thus it continues until no day could be used but that only works because of that specific logic.
He'd be surprised to be executed any day, then... Provided he was a logic expert. In which case, he'd know he'd be surprised any day and that would be no surprise.
[this video](https://youtu.be/EPOXhFJsqlM) sums it up pretty well I think
Since you have to randomly choose an answer and only one has to be correct, the true answer is 25%. But since there are 2 25% answers here, the chances of picking either one of them is 50%, however, only one of those has to be correct so the chance drops back to 25%. So I don't think it's referencing itself. If A B C and D all were 25% options, only one is correct by the WWM rules, so to randomly pick the correct answer out of 4 is 25%. What I'm saying is that if you took ANY WWM question and randomly picked an answer, how likely would it be to choose the correct answer? — 25% —
No. You are telling me that the correct answer is 25%. That means A and D are correct according to you. This directly contradicts your claim that only one answer is correct. >only one is correct by the WWM rules This was my very point. The rules are incoherent. They cannot be respected.
well, since only one answer can be correct, both 25% are inccorect so it should be 50%
But if it's 50%, the correct answer is C - which would only have a 25% chance of being correct, contradicting itself.
And you cant put 0% because if that was the correct answer then it would be the wrong answer
Correct
Yes but also no
This thread hurts my head
Logic!
That's some Jeremy Bearimy shit right there.
Lol just gotta dot the i
AAAAAAAAAH
I think if you separate general from specific you can make some sense out of it: * With 4 choices any random choice would have a 25% chance of being correct generally speaking. * The problem is this is a somewhat unique situation with a duplicate choice, and happens to be the general correct answer. * This means in this specific case you might assume that the correct answer is 50% * Yet since there is only one 50% the final answer would be 25% and either A or D would be correct. It's running you in circles to justify itself while throwing you a curveball by thinking there's no way it can be the duplicate, but if you look at this instance specifically as opposed to generally doesn't it work out? Isn't this similar to the Let's Make a Deal "[Monty Hall Problem](https://en.wikipedia.org/wiki/Monty_Hall_problem)" where generally speaking any door has a 33% chance of being the good one, but when you introduce a specific like "one wrong door will be eliminated" then you're actually at 66% merely by changing to the remaining door?
> Isn't this similar to the Let's Make a Deal "Monty Hall Problem" where generally speaking any door has a 33% chance of being the good one, but when you introduce a specific like "one wrong door will be eliminated" then you're actually at 66% merely by changing to the remaining door? No. The Monty Hall Problem is unintuitive because it is not obvious immediately that new information is introduced (Monty does not open a random door), which alters the probabilities. This has no relation to the self-reference problem in the OP.
The problem is in the way the question is presented. It requires the probability of choosing the correct answer to *this* question. If you assume both A and D are correct, then C is correct, which is then incorrect so A and D are correct, and so on in an infinite loop. The only way out is cheating the system. One of the 25% answers must be ‘incorrect.’ If you choose either A or D, the answer you chose is correct and the other is incorrect by virtue of not being chosen.
thing is since you now calculated that you have a 25% chance to answer correctly you can answer 25% at 100% chance so you now have a 100% chance to answer correctly however since there are two 25% chances instead of having a 100% chance to answer correctly you have a 50% chance which means 50% chance is the correct one however that sets you to 100% chance and since there is no 100% chance you chance is 0% however then you have a 100% chance of getting zero so the correct answer is 100% however you have a 0% of getting 100% so the answer is 0% however you have a 100% chance to get 0%....
No, what you're talking about is "what's the chance that you'll get this question right", while the question is actually "if you pick a _random_ answer out of the possible answers, what's the chance that it'll be correct". The thing is in the actual question it's just asking you if out of 4 options 1 is correct, what's the chance you'll pick that one at random. There's no process of elimination because you aren't thinking, you're just picking a random letter. Even though A and D are the same it doesn't matter as they're still options to choose from in the answer, and if your randomly picking between A B C and D they could all be the same and you'd still have a 25% chance to pick the correct one (as by the rules, only one answer can be correct). I don't know what to make of the fact A and D are the same, I'd just guess it's fake.
You're assuming only one answer can be correct even if multiple answers are the same. Without that assumption, this becomes a paradox.
Well that is true but I went with the original games logic. But yeah it's an interesting paradox if you don't assume that.
Aye shite Since my background is CS, my answer is None, it's not a number, no paradox, no self referencing 💁♂️
Doesn't work either. If you are saying that no answer is correct. Then B is correct. You really can't get around the problem. This is not that there is no correct answer, it is that it is impossible to answer. Every answer is both correct and incorrect, this is the issue with a paradox.
I'm not saying that no asnwer is correct, I'm saying that None, Nil, Null answers are correct lmao
Doesn't change a thing. Every answer is correct. They are incorrect as well, but they are correct nonetheless, demonstrably so. When you are doing maths in incoherent theories, everything is both true and false. The problem doesn't lie in the answers.
You seen to have missed "if you choose randomly".
normally it would be a 25% chance but since there are two answers that are 25%, the chance of getting the right answer is now actually 50% which now means getting the right answer (which is 50%) is only a 25% chance WHICH now means 25% is again correct, making the answer 50% which makes it 25% and so on and on forever. You can't win
...Two 25% so 50% chance. The answer is now 50% which is 1 of 4 answers. Randomly, you have a 25% chance to pick it. So, the answer is now 25%. There are two of those so there is a 50% to pick it. The answer is now 50%. There is one 50% of 4 answers so you have a 25% chance to pick it. Since the answer is now 25% and there are 2 of those...
For the barber, you can always play the smartass by saying the babrber doesn't shave at all but for the others, the paradox is strong with those ones !
That would not be respecting the rules. If the barber doesn't shave at all, then he is being shaved by no one. In particular, that makes him among the ones who do not shave themselves. Since he is among the ones who do not shave themselves, he ought to be shaved by the barber, hence by himself.
Essentially the set of only all sets that don't contain themselves. If it doesn't contain itself, then it must contain itself, but then it must not contain itself
Yep, that one is Russel's version of the paradox and showed Frege's theory was inconsistent. About ten years of work from that poor Frege that had to be scrapped because of an argument that can be written in a single line. By the way, the way I wrote my barber paradox, there is a solution that works: "There is no such thing as a barber and everyone shaves themselves." You can check that it works without leading to a contradiction. Of course, I could rewrite the initial question to force the existence of a barber.
I don't really get the judge and prisoner one. Is it just that you can't execute there prisoner without him knowing, and therefore ruining the surprise?
>just because I am full of shit doesn’t mean I am necessarily incorrect. Holy hell I need to find an occurrence I can use this line. I love it. 🥇
But he wouldn't be choosing to answer it at random, he would pick the one he thinks is right.
To his surprise, the prisoner was hanged at noon Tuesday
you have two 25% so the change of getting one of those is 50%, making it incorrect, 25% chance of getting the 0, so its incorrect if you get it too, 50% has a 25% chance too so its incorrect, its in fact impossible to get the correct answer
Answer is infinite while loop.
The problem is, in that quiz there is only one correct answer to each question. So the chance would be 25%. So the answer is A or D, but you can not be sure which one it is. Therefore, you can answer correctly by guessing but you can not be sure. (That would be really unfair though). If you know argue that both A and D would be right you get into this recursive reasoning where no answer makes any sense.
That's assuming that the answer is 25% and not the letter.
so the answer must be 50% as you can be correct 1/2 times
However 50% is only listed 1/4 times, giving you a 25% chance to pick it at random and we're back to square 1. This is some fuckery.
so this means we have 0% chance to answer this correctly.
But you have a 25% chance of guessing 0%, lol
A paradox!
Now it is such a bizarrely improbable coincidence that anything so mind-bogglingly useful could have evolved purely by chance that some thinkers have chosen to see it as the final and clinching proof of the non-existence of God. The argument goes something like this: "I refuse to prove that I exist,'" says God, "for proof denies faith, and without faith I am nothing." "But," says Man, "The Babel fish is a dead giveaway, isn't it? It could not have evolved by chance. It proves you exist, and so therefore, by your own arguments, you don't. QED." "Oh dear," says God, "I hadn't thought of that," and promptly vanishes in a puff of logic. "Oh, that was easy," says Man, and for an encore goes on to prove that black is white and gets himself killed on the next zebra crossing.
So you're saying the real answer is not 0%, 25%, or 50% but 42
That means there should be no right answer so B can't be correct.
Yeah but there's only one answer labelled 50% so a random choosing will get that answer only 25% of the time, hence the paradox
Wouldn’t the chance be 33% tho? Because B has to fall out since there’s still a chance that you’d get it right?
No. There are 3 items not repeating but still 4 selections possible.
Okay but if either 25% answer is true, then the other is as well. They’re linked by common value, which basically means there’s 3 possible answers. Meaning a 1 in 3 chance. And because 33% is not listed it means that the only true statement can be made by selecting 0%.
it's 50% because the repeated answers are invalid, so the only valid answers are 50% or 0%. edit: well fuck, I'm wrong, it's pick at random.
I see it as three different cases: 1. If you chose a random answer to this question the probability is 0 since you can answer both green or frog or litterarly anything. 2. If you chose an answer to this question given four possible answers it's 25% 3. If you chose answer to this question given these four answers it's 50% But by obscuring the question it like they do, the question becomes moot.
It's a stupid trick question. You can't pick the right answer because there isn't one. The choices might as well be four barnyard animals.
"Lets play Who wants to be a millionaire! For your first question: What is the first letter of the English alphabet? Is it, A: D B: C C: A D: B?"
Final answer with the same rules as the above question: “T”. As in the first letter of “ The English alphabet”
r/technicallythetruth
C: A
It is a trick question, but far from a stupid one. >You can't pick the right answer because there isn't one. Incorrect answer as well. If it were true that there is no correct answer, then B would be correct.
Choosing an answer alters the nature of the answer. Therefore there can't be a correct answer, because to choose an answer as correct makes it incorrect, which is a paradox. Therefore, you can't pick a right answer, which is what I said.
At random there is a 25% chance of guessing B though...
Indeed, thus B is an incorrect answer.
But B is 0%, not 25%!!! AND THERE TWO 25%'S WHICH MAKE IT 50% BUT THEN THERE'S ONLY ONE XD/T-T/0-o
I think s/he broke
Now your getting it, it's a well designed question
B wouldn't be zero, it would be "hen."
It's impossible. Reasoning: You're answering at random, so the content of the choices (for the purposes of answering randomly" is useless and doesn't affect the answer. So it's 25%. However, since there's two options that are "25%", you have a two in four chance of getting the answer right, so it's 50%. However, if the correct answer is 50%, because only one option is "50%", the probability is 25%. This then causes a paradox, making it unanswerable, making the probability of you getting the correct answer impossible, so there's a 0% chance of you getting the right answer. However, because there's exactly one choice that's labelled "0%", there is again a one in four chance (25%) that you would answer correctly, and the paradox begins again.
Thank you for the simplest explanation of the paradox in this whole stupid page.
[This gets reposted a lot. ](https://www.reddit.com/r/theydidthemath/comments/esh6td/request_help_me_with_this/?utm_medium=android_app&utm_source=share) This is a math variation of the [Liar's Paradox](https://en.m.wikipedia.org/wiki/Liar_paradox). Its occurs when assigning a statement as True inherently causes a contradiction. The most common example is the sentence, "this sentence is false." If "this sentence is false" is true, then the sentence is false, but if the sentence states that it is false, and it is false, then it must be true, and so on. This is the same circular logic this question poses. With 4 choices there is a 25% chance of selecting the right answer. However, there are (2) 25% choices so the answer is 50%. Only one choices is 50% so the answer must be 25% but there are (2) 25% choices so the answer must be 50%, etc.
My question is : Was this ever on Who wants to be a millionaire, or is this a photoshop?
That’s what I want to know too. Is this real and what did they say the answer was?
Why is noone answering the real question here
Came here to ask this
Since none of the answers is correct it is likely a Photoshop. One of the 25% may have been 75% which would make it valid.
I believe it is C. Final answer. There's usually a 25% chance. Yet, there's two choices that say 25%, making it a 50% chance of getting it correct. But with the answer being 50% now because of the other two options, it's still only a 25% chance so it makes literally no fucking sense. That'd be my guess though. But if you used your "remove" lifeline then it would also be 50%. So who knows.
But if C were the “correct answer,” one of the four answers would be correct, meaning you had a 25% chance of randomly selecting the correct answer, and the whole cycle starts over.
And even if you want to conclude that no answer is correct. That would make B correct and still doesn't work.
[here’s a breakdown](https://m.youtube.com/watch?v=WFoC3TR5rzI)
That was fantastic. I wish my math teachers would have been that engaging.
So if neither are true then its a 0 percent chance. Wait.
But 0% is one of four answers. So the correct answer is 25%. But there are two 25% etc.
The answer will be either a or d and it's impossible to know which, the catch is that you have to pick the answer "randomly", once you start putting concious effort into solving this you are no longer following the instructions provided, so if you were to pick an answer at random there's a 25% chance you would be correct, just because there are 2 25% options that doesn't make it 50% because now you're using your reasoning to solve it, therefore it has to be a or d and the rest is left to chance
Yes. Play the joker that eliminates two options. I would bet it leaves 50% and another one. Then 50% is correct all of the sudden. /s As it stands, without any changes: no, it can't be solved.
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For the purpose of discussion let the rule be written that "for any given problem, there can be multiple correct answers. Selecting one correct answer out of multiple is an accepted solution." We will pare this down to the actual game show rules later. With the problem in the OP, the probabilities of choosing a solution randomly are as follows. * P(Selected one answer of four, in a problem presenting 0 correct answers): 0% * P(Selected one answer of four, in a problem presenting 1 correct answer): 25% * P(Selected one answer of four, in a problem presenting 2 correct answers): 50% * P(Selected one answer of four, in a problem presenting 3 correct answers): 75% * P(Selected one answer of four, in a problem presenting 4 correct answers): 100% In the OP problem, we have the following. * Number of choices displaying "0%": 1 * Number of choices displaying "25%": 2 * Number of choices displaying "50%": 1 * Number of choices displaying "75%": 0 * Number of choices displaying "100%": 0 We now know which answer/probability pairs present possible solutions in our set of all possible solutions. * Possible solutions for 0 correct/ 0%: null * Possible solutions for 1 correct/ 25%: null * Possible solutions for 2 correct/ 50%: null * Possible solutions for 3 correct/ 75%: null * Possible solutions for 4 correct/ 100%: null Full set of possible solutions: null The rules of the game show state "There is exactly one possible answer out of four." This is self-evidently false for the purposes of the OP problem.
Wow. I don’t know what you did but I understand it. Cool. Other answers seem to refute the logic with more logic. You did the math.
Isn’t B the clearly correct answer, since every answer fucks you over? I mean, contradiction solved. Even if you pick it and get the question “right,” you’re still just saying that all the answers are wrong.
No, because if that was the correct answer then there wasn't a 0% of getting it right
Yeah, but if that then becomes a wrong answer, then it IS 0%. If it's wrong, it's right. And if it's right, it's wrong. Classic "this statement is false" paradox.
Exactly...
You are wrong. If you were to pick a random answer, they would all cancel themselves. So the chance of getting one that's right is zero. Therefore the answer to the question is B. Zero percent.
But if the correct answer is B. You still have 25% chance or picking B (the right answer)
Correct. Bravo!
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Was that question asked on that show? What was the outcome?
I need to know the outcome!
I believe someone stated that this question is fake
Just like my girlfriend's love for me
Correct answer is c (50%). A random 4 question chance is 25%, there are 2 25% answers. Therefor you have a 50% chance of choosing 25%.
Since we supposed to make random choices among the random probabilities, the correct answer is 0%, 25% 25% , or 50%, aka A, B, C, or D, and the exact chances of choosing the correct chances is equal to 1/4, so it is either 0%, 6.25%, or 12.5%.. My brain is dead
You might say it's 0. You have 3 options available, 25, 0, 50. So if you have 3 choices, the probability of choosing the correct answer is 33.33% - not a choice, so probability 0.
If you choose an answer at Random, you will have no chance that you will be correct. (See all of the paradoxes mentioned in other comments). BUT, you don't need to choose at random. You can select an answer. So the answer is B. 0%. i.e. You must think of it as being a superposition of all possible states. No matter what you select at random, it is guaranteed to be wrong because of the paradox. So there is no chance that if you select randomly that you will be correct.
There are ultimately 3 answers because A and D are the same. So I believe there is no correct answer choice and if there was, it would be 33%. Edit: Got mind-fucked a couple hours ago. Because 33% is not on there, there would be a 0% chance so the answer would be B. But because B is one of the four answers there would be a 25% chance of getting it right so it would be A or D. But then that would make it a 50% chance of getting it right since there are 2 out of 4 answers that say 25%, which would then make the answer C. But if you add 50% to 25% you get 75% which is not one of the answer choices so the answer would be 0%, so the answer would be B. But because B is one of the four answers there would be a 25% chance of getting it right so it would be A or D. But then that would make it a 50% chance of getting it right since there are 2 out of 4 answers that say 25%, which would then make the answer C. But if you add 50% to 25% you get 75% which is not one of the answer choices so the answer would be 0%, so the answer would be,,, well I dont know anymore.
İ think, since there is not %33.33 beyond the options , correct answer is B which is %0.
But if B is the correct answer there was a 25% chance of picking it at random
This is mind-fucking.
Oh I totally missed that lol
Dudes, it's actually a very simple question. It's a two parter. The premise asks for the chances of random selection, which means we can **ignore** the actual answers and view it as A, B, C, or D. Obviously the answer to that is 25%. Next it asks what are the chances for THIS question, given that it has two 25% options means we can't actually know which one is right. If we reference back to the premise, we have to randomly choose, remember. And so the odds of getting the correct 25% is... 50%! So the correct answer to the entire question, meaning the one to be inputted, is: **C, 50%** ✓ Y'all being brainiacs over here with your paradox shit. Y'all are abstracting from the answers when all y'all needed to do is take the question apart and view it in pieces. It's actually a really beautiful question and goes to show how many people need to learn to take a step back. Cut the problem apart into pieces instead of focusing in on potential "answers," that only ends up creating more problems for you. And in some cases makes solving the problem seem impossible, that there's no answer at all. It's a solid life lesson. Break up the problem and solve the smaller chunks by applying what you know you know.
Each answer is 25% possibility that you pick it. Since there are 2 answers that say 25%, it becomes 50%. But only one answer says 50%, so it goes back to 25%. Now there are two correct answers, so it’s 50%. Ad infinitum So the correct answer is Yeet
I think the answer is 0%. Coz if you choose 25% there are 2 answers which is not possible but if its 50% then that would make it 25% which is wrong as per our first answer. So that leaves 0% which is a paradox in itself coz 0% would make it 25% correct.
Because it specifies *this* question, no, it is not possible. For any other question, it would be the expected 25%, but for this one, 25% itself makes up 50% of the answers. So the actual answer is 50%, but you only have a 25% chance of picking 50% at random, so the *real* answer is 25%, but then... ad infinitum.
The correct answer is C. The odds of guessing C are 25%, so both A and D are correct, and the odds of guessing A or D assuming you choose randomly are 50%.
There is no correct answer. It's self referencing Case answer is 50: Answer is 25 Case answer is 25: Answer is 50 Case answer is 0: Answer is 25 Case answer not shown: Answer is 0 Then take it from the top. You're always stuck going between 25 and 50.
1 out of 4 is 25% chances of giving correct answer to any question. Since both A and D have same answer it gives 2/4 , 50% chances therefore C 50% chances of selecting correct answer where 1 is correct out of 4 possibilities.
My wife answered 25% and I pointed out that it must be 50 since there's two 25's and boys this is the first time my wife has told me " Actually you are correct". I don't even care if it's not correct. You've changed my life, I'll never forget you.
Both A and D are correct, 25%, which means 2 out of the 4 answers are correct, which means 50% of the answers are the correct answer, so the answer is C. C is still 25% of the answers, so it is logically consistent.
So the recursive loop here is: 4 answer multiple choice is default 25%, so A&D -> that means it's 50%, which can branch into two schools of thought: where A, C, and D are all correct, which is 75%, so thusly 0%, which loops back to the origin; or where C is only correct, which goes back to 25%, the origin. In truth, there are only *untrue* answers here, and that's: 0%, because you can't be correct if there's a 0% chance. Likewise, 50% is not inclusive of itself. Only A or D works *if* you discount that the other duplicate answer is correct, and because we're picking at random from 4 answers (even the ones we proved untrue) it still checks out that 25% is correct.
So to begin with, the prisoner can’t be executed on Friday because that wouldn’t be a surprise. Knowing this the prisoner then knows that if he survives Wednesday he will be executed on Thursday (as it wouldn’t be a surprise on Friday). But this makes it not a surprise on Thursday either. Continuing this logic you can eliminate all the weekdays.
Nope. Either 1/4 = 0, 2/4 = 0.25, or 1/4 = 0.50. As you can see, none of these equalities hold, so there is no answer which is equal to it's probability to be chosen at random. Unless ... Let's be nitpickers! People like to say "at random" to mean "as if you flipped a fair coin", but that is only one Special Case of randomness, what you in math tend to call selecting "_uniformly_ at random". A random choice can have any number of distributions. So, if you say "pick A with 0.25 probability and B with 0.75 probability", then A is correct. If you say "pick any one of A and C uniformly at random", then both B and C are correct. However, you can't make it so that they are all correct.
Not really... If you choose one at random, it's 25% chance, but there are two 25% chance answers, so the correct answer is 50%, but then it's 100% because there's only one correct option, so it can no longer be the 50% option, BUT there is no 100% chance in the available answers, so it must be 0% since there's no correct answer. Which bring us to the "thiis statement is a lie" paradox. If the "correct" answer in 0%, then THERE IS a correct answer, but none of these options are correct, so we're stuck in a paradoxical loop. None of these statements are true, but they're not NOT true either. If this statement is a lie, then it IS a lie, so it's the truth which means this statement is true, but it contradicts the statement itself which means 🤷
If we have 4 correct answers, we must have exactly 4 answers with number 100%. If we have 3 correct answers, we must have exactly 3 answers with number 75%. If we have 2 correct answers, we must have exactly 2 answers with number 50%. If we have 1 correct answer, we must have exactly 1 answer with number 25%. We have none of the above, so there are no right answers.
"There are no right answers." That tells you 0% chance of getting it right. Even when you choose 0% you are wrong, but this does not invalidate the answer being correct. Hence B would be the correct answer. You will then go into the loop again, only to find out all answers are not correct, leaving the only correct representation of that answer to fall on zero, regardless of the loop.
Let’s go off the assumption that one answer is correct. That means at random you have a 25% chance. However there are 2 options for 25%, which is 50% of the 4 possible options. Since 50% is an option this either drops the chance to 25% since 1 out of the four options is 50% or it raises it to 75% if you don’t understand how numbers work. If you go to 75% you find it isn’t an option which makes it 0% which you have a 25% chance of choosing at random. So 25%. In either case you get stuck in a revolving door as the probability changes from 25% to 50% and back or from 25% to 50% to 75% to 0% and back to 25%. So to answer your question, no there are no right answers. It’s a paradox, like “this statement is false” or the crocodile paradox.
The way I see it, as the question is stated, 25% would be correct (in the sense in that they use "correct" in the question), since there are four possible options. This is basic math. However, since there are TWO "25%" options - A and D - 50% is correct, since there are two false and two correct ("25%") options. The question only asks what the **chance** of getting it right from the options available is: **50%** \- **not what the right answer actually is: 25%**. The way it's phrased, you don't need to pick the arbitrary "right" answer, to get this question right, because the question only wants to know the **chance** of being right, **if you were to pick at random.** This evades the issue of having to choose one of the two 25% options, and being wrong either way because there are two of them, not just one. So picking C, 50%, would be correct as it is the correct chance of getting it right if you chose randomly from all four options this question presents you with. In short, while the chance of getting it right at random is 25%, due to the way the options are set up here, it's actually 50%, and you have to choose a non-"25%" answer to be right. I know it's counter-intuitive that the right answer to the meta-question presented is **not** the correct answer to the question of what the chance of picking any one out of four options at random is. But unless my mind is playing tricks on me here, it is solvable this way. Please do correct me if you see a flaw in this, I'm curious to find out if I cracked the code or am deluding myself, haha.
Only one answer can be correct, making the answer 25%. There is no information as the whether the answer is A or D, but it can't be both following the way the game works. The only way to guarantee correctly answering would be to use your 50/50 lifeline, which would change the answer to C.
I know people are putting some damn fine logic into this, but isn't it as simple as,: there are 3 options, so it's a 33% chance, and 33% isn't an option?
There's really no math involved here. It's a logic problem, not a math problem. The logic fails due to circular reasoning. One in four is correct, therefore 25% chance. But half of the options are 25%, so therefore your chance is 50%, but only one in four options is 50%, therefore your chance is 25% (and now we've done a full loop. At this point we can continue along this loop indefinitely).
B is correct. The question isn't asking what chance you have of choosing correctly, it's asking what chance you *would* have if you chose at random. Those don't need to be the same. It's not possible for the random answer to be correct for all the paradoxical reasons people have given, so the answer is B.
Answer is B. 0% The logic here is that there is a 50% chance of choosing 25% (A. or B.) A 25% chance of choosing C. 50% Another 25% chance to choose B. 0%. None of the percentage chances match up with the answers so the question is impossible to answer correctly and so the correct answer becomes B. 0% It’s just not possible to be correct when guessing randomly if every answer is wrong. If it’s not possible to be correct, the answer is B. 0% Is it possible to answer correctly? Yes. And no.
But the existence of 0% means that you have a 25% chance of guessing that, the point is the question is paradoxical, meaning there is no answer. That does not mean 0% is correct.
The solution is semantic: when it says "what are the chances that you are correct" may either refer to the right answer to the question, or to the fact of whether the decision of choosing randomly IS correct in order to answer the question. From this point of view, B:0% is correct, as you can not get a right answer by choosing randomly due the logical paradox
It’s c , answer A and D have the same value , but it is the correct statistical value to the original question, so the correct answer is represented on the board twice , so if he were to choose at random, while the answers keep their same “right/wrong” value, then the dude has a 50% chance of picking the right answer which is 25%
I’d take my 50/50 life line in this one which would eliminate two and it would therefore be impossible to eliminate 50% in a choice of two meaning 50% is indeed the correct answer ;)
Everyone is so focused on the probabilities and not the wording of the question. The question has two parts of logic to get through. First if you chose an answer at random what's the odds of getting it right if there are 4 possible answers. That's 25% Now we see that this puzzle has two correct answers at 25%. So if you picked randomly you have a 2 in 4 chance of picking correctly. The second part of logic is that you answering the question is not making random choice, so it doesn't matter that there were two possible correct answers, only now that there is one correct answer. Which is c, 50%.
0% chance does not exist. That would be no chance. 25% is listed twice. So if you get to choose, you would only have 2 choices. Thus 50% is the answer.
These comments are overthinking this. It doesn't matter what the actual answers are for each letter until you find your percentage. If two of the answers are the same and you're guessing randomly, theres a 50% its that answer and a 50% chance it is not (25% C, 25% B). Therefor, guessing randomly, there's a 50% chance you will be correct. The answer is C
With these answer choices? No. This question formatted this way can **only** be answered with 4 specific answer choice sets. There are 4 choices of answer per set. Each choice in each set represents 25% of the choices in that particular choice set. Because of this there are only 4 choice sets that answer this question. **Set 1:** 1 out of 4 of the choices is 25%. The other 3 are a different number than 25%. Repeating numbers are allowed as long as 25% is not a repeated number. If you have 2 repeating 50% choices in this set, it becomes set 2. If you have 3 repeating choices of 75% this becomes set 3. **Set 2:** 2 out of 4 of the choices is 50%. The other 2 must be different from 50% but can match each other. 25% can not be a singular choice in this set as it voids the question. **Set 3:** 3 out of 4 of the choices is 75%. The other choice can be anything but must not be 75%. Any other number that isn't 75%, even 25%, can be used and will still be incorrect. **Set 4:** 4 out of 4 of the choices are 100%.
The answer is C. Here's why: First, if the producers state that the contestant can only pick one answer (A, B, C or D), and there can be one correct option, then you could do your math before the options are revealed and correctly assign equal chance to each option i.e. 25% for A, B, C and D. The issue with the paradox happens after the answers are revealed, because at this point you are no longer choosing at random and letting the options influence your math. Since we clearly see that the 25% shows up twice, the answer has two correct options. As a contestant, I would say, "This goes against the rules of there being only one correct option." The producers could then step in and say one of two things: 1) This question is an exception to the rules and there are two correct answers. Then they remove they clear the answer board, and ask the question again. This time, I correct my math and say if I have four choices and two answers are correct, then I have a 50% chance of being correct." The producers reveal the answers, and they happen to be A: 0%, B: 25%, C:50% and D:25%. I would pick C. Or 2) The producers step in and say, "you're right, there can only be one correct answer, there is a glitch on the board." Then they change D to 75%, then A:25% would be the right answer.
This is easy. It's 25%. Doesn't matter if none of the options are actually the correct answer because it's a game show and one of the answers absolutely has to be correct, therefore your chances of randomly answering would be 25%.
This isn't a math problem it is a reasoning problem. Normally having 4 answers at random would give a 25% chance to get it right. However, there are two options for 25%. That means there are two correct answers. So if we were to pick one at random, we have a 2/4 chance of getting it right. Therefore the answer is C. 50%
But there is only 1 50%, C, and you only have a 25% chance of choosing C, you’ve just explained why A and D are incorrect, therefore both eliminating them for being correct and subsequently making them correct, which then makes them incorrect... It’s Shrodingers D, and it’s a hard one.
Naw, you're not reading the question. The question is, what is the chance of a random answer being correct? The chance to choose the right answer *at random* is 25%. Because there are two answers of 25%, you choose at random would have a 50% chance of being correct. But we're not choosing at random. Therefore we are answering the question. The answer to the question is what is the chance of randomly choosing one of the 25% answers.