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**Calligar****Member**- Registered: 2011-09-24
- Posts: 272

A while ago, I was talking to someone on Omegle. For those who aren't familiar, Omegle is a website where you can video or text chat anonymously (unless you reveal who you are) with a random person online. One of the things they gave me was what they called an "Impossible Question", but supposedly actually has an answer. If I recall correctly, the question goes something like this...

I pick a random number from 1 to 100. Of the four numbers I list, which one did I pick?

A. 71

B. 81

C. 83

D. 90

I never was told what the answer was, but I'm curious what other people would choose (for those who even choose an answer).

There are always other variables. -[unknown]

But Nature flies from the infinite, for the infinite is unending or imperfect, and Nature ever seeks an end. -Aristotle

Everything makes sense, one only needs to figure out how. -[unknown]

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**Relentless****Member**- Registered: 2015-12-15
- Posts: 624

As a question of pure probability, they are all equally likely; the list has just been narrowed from 100 numbers to 4, giving you a 25% chance of guessing right instead of 1%.

There was a question I have heard of the same structure that led to a paradox, and so actually is impossible. It goes like this:

Q. If you choose an answer to this question at random, what is the probability that you will guess correctly?

A. 25%

B. 50%

C. 25%

D. 0%

*Last edited by Relentless (2016-01-09 13:42:27)*

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**mathaholic****Member**- From: Earth
- Registered: 2012-11-29
- Posts: 3,251

That seems random

Relentless is right. You have a 25% chance of getting the right answer, due to the fact that you have four choices.

Mathaholic | 10th most active poster | Maker of the 350,000th post | Person | rrr's classmate

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**Grantingriver****Member**- Registered: 2016-02-01
- Posts: 122

This question is not impossble!! You only have to be more creative to solve this type of problems. For example, your question did not include any information about the bases of the numbers in the list, so if you choose to take the base to be tridecimal or tetradecimal then 71 will be equivelant to 92 and 99 in the decimal base respectively, and this renders the problem to a trivial one since all the numbers in that list using these bases are more then 100 except "71" also this answer can not be rejected since the base of the numbers in the list is not restricted in the question. Therefore the answer is "71"!!!

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**mathaholic****Member**- From: Earth
- Registered: 2012-11-29
- Posts: 3,251

I see, Grantingriver. So it's kind of like a trick question or something...

Mathaholic | 10th most active poster | Maker of the 350,000th post | Person | rrr's classmate

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,039

Grantingriver wrote:

This question is not impossble!! You only have to be more creative to solve this type of problems. For example, your question did not include any information about the bases of the numbers in the list, so if you choose to take the base to be tridecimal or tetradecimal then 71 will be equivelant to 92 and 99 in the decimal base respectively, and this renders the problem to a trivial one since all the numbers in that list using these bases are more then 100 except "71" also this answer can not be rejected since the base of the numbers in the list is not restricted in the question. Therefore the answer is "71"!!!

What if I take the answer C to be in base 8 and the rest in base 20, though? I think the answer might be C!

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**Grantingriver****Member**- Registered: 2016-02-01
- Posts: 122

In logic there is a concept called "the universe of discourse" .For example, if someone talks about something he doesn't have to provide all the details, those details can be infered from the cotext. If another person bring irrelevant ideas to the topic which should be rolled out by those implicit details they would claim that he diverges from the universe of discourse and consider him as a "sophist", so if the argument which I have provided gets out the universe of discourse of the problem then someone can claim that I have produced a fallacy. However, if we suppose that the implicit details imply that the bases of the numbers in the list are decimal then the problem will be "impossible", but the person who asked the question claimed that it has a solution, this clue actually is a detail which included in the universe of discourse of the problem. In other ways it says that the numbers in the list are not in decimal base because ,if they are, the problem would be "impossible". Therefore we are in the universe of discourse and did not commit a fallacy. Now there are two possible solutions:

1) To change the base of each number in the list as we would like (your proposed solution)

2) To change all the numbers in the list to the same base.

If we choose the first way, we can do that for any number in the list, so that will send us back to the first square, but if we choose the second way, there will be just one number which satisfies the conditions (which is "71"), so we could reach a solution to the problem.

Q.E.D

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**Calligar****Member**- Registered: 2011-09-24
- Posts: 272

Grantingriver, that is interesting! I really do wonder if you are correct about that (the answer being A.), as that would lead to an actual answer. I mean, it's online and lots of people troll. But, that question did always stick with me because it felt **too** easy to say, yeah, I agree it's impossible because all answers are 25%. What can you do where it has an answer? Even if it were a troll, there must be some way to draw an answer out of it. I can't so easily dismiss the question in my head, because **why** would they ask me such a question that seems too easily dismissed as impossible, and even call it impossible as if to tempt me that if I agree, I'm just one more person who doesn't bother to give it any additional thought. Also, having a lot of personal experience working with different number bases, I'm inclined to agree with his reasoning. Right now, I'm thinking that if that has an answer, I'd have to agree and say it is A. 71.

There are always other variables. -[unknown]

But Nature flies from the infinite, for the infinite is unending or imperfect, and Nature ever seeks an end. -Aristotle

Everything makes sense, one only needs to figure out how. -[unknown]

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**thickhead****Member**- Registered: 2016-04-16
- Posts: 1,086

The question is not impossible but the answer is impossible.

**{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha{Gods rejoice at those places where ladies are respected.}**

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