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- Well, I haven't seen much too close to my solution posted elsewhere, so I'm going to post the answer rephrased in a manner that I hope will get everyone changing their perspective, even if it doesn't match mine 100%.

The key issue to me is that by design, a question with a multiple choice answer must have different answers for each choice. Any deviation from that design is erroneous. For example, let's say the answers are:

A = 60%, B=60%, C=60%, and D=60%.

I chose those numbers because 60% is usually the first possibility eliminated in the original problem, as it is not a multiple of 25%.

I also want to stress that I think it is reasonable to presume that any answer in the multiple choice list**might**be the correct answer, especially since we are probably guessing because we can't solve the problem, and can't eliminate any of the answers other than by guessing.

So with the above situation of all of the choices being 60%, what are the odds of getting the answer correct? The answer, of course, is 25%.

Huh? Yes, because 75% of the choices we were given are erroneous. So by choosing 60%, we still have only a 25% chance of getting the answer correct.

And this logic holds for any quantity of repetition, and the original example with 25% for both A and D is the same way. Not only that, if the original example had the 50% figure duplicated, or the 60% figure duplicated, it would still be a 25% chance of us getting the answer correct, because WE ARE GUESSING. THAT IS THE KEY POINT.

Thank you for your attention.Nov 1, 2011 - +Bernard Matthews That would work if the question did not directly reference the answer set, which is known. The question asks us what is the "chance" that we would pick the correct answer "to THIS question at random," not that we are guessing and not that it's any multiple choice question but the one being answered. Since the answer set is known, we are not guessing, but we can still pick an answer at random. Because the question requires knowledge of the answer set, and the answer set is known, the question becomes unanswerable by it's self-reference through the answer set.

Further, I submit, given your hypothetical answer set, that most would see how paradoxical the question and answer set is. The answers given are not those mathematically possible, even if picked at random for any other question than "THIS" one, one might assume to answer outside of the set that the chance, with your answer set, of answering this question correctly is "0%," but that answer is not given, in a known answer set, therefore, the question is still unanswerable.

I also submit, that given an answer set of: A) 25%, B) 50%, C) 75%, or D) 100%, the question is still unanswerable, even if one of the answers seems mathematically correct "25%." By the nature of the circular reference of question to known answer set, the question itself creates the paradox that does not allow an answer.Nov 3, 2011 - I loathe you.Nov 4, 2011
- AD(after death)

but i would pick a(alpha)Nov 9, 2011 - Cool non of this answer are right.

If you choose B as right answer the possibility is 25%, to answer right.

If you choose A&D as right answer the possibility is 50%, to answer right.

and C is bullshit.Nov 10, 2011 - Simon Lombard, very interesting analysis. But I disagree.

By generalizing the question from the one given, you make one critical assumption--that one of the answers is in fact correct for the generalized question.

So we run your analysis and then have to bring the generalized back to the reality--and find there is no such answer, so your analysis doesn't lead to a solution in this case. Either we presume the answer is one of the listed ones or we presume it is not. Both presumptions lead to an answer of zero. Which is not an answer among thems listed. Contradiction... :)Dec 11, 2013

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