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Unanswerable puzzle?

 
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Given the following choices, what's the probability of randomly choosing one and being correct?

What is the probability of randomly picking the correct answer to this question?
1. 25%
2. 0%
3. 25%
4. 50%

[Question edited for brevity]
 
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At this site, we usually respond with: what do YOU think, and we'll let you know what we think  
 
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That puzzle belongs in MD! It has four answers, all of them wrong
 
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That's not true Campbell. If all answers were wrong, then answer 2 would be correct. Instead, the problem is undecidable, or rather, the question is unanswerable.

The issue is that the question is self-referential. It falls square in the same domain as Russell's Paradox. I think Gödel would say that you can't at the same time pose or understand the question, and give a correct answer to it in the same terms used by the question.
 
Junilu Lacar
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Stephan van Hulst wrote:The issue is that the question is self-referential. It falls square in the same domain as Russell's Paradox. I think Gödel would say that you can't at the same time pose or understand the question, and give a correct answer to it in the same terms used by the question.


Hammer meets nail right on the head.
 
Junilu Lacar
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Stephan van Hulst wrote:If all answers were wrong, then answer 2 would be correct.


This is the paradox because if answer 2 is correct then clearly not all the answers are wrong. It's the Schrodinger's cat answer.
 
Piet Souris
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The question is meaningless. What is the answer to the question: is 25% correct or not? But the fun is of course that if 0% is correct (??) then we have 25% chance of getting it right. So with 50% chance we get it right. But choosing 50% has only 25% chance, ad infinitum.

Wasn't it Hilbert cs who tried to tame self-references?
 
Stephan van Hulst
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Pretty much any mathematician worth their salt was at it at that time, seeing as that set theory was being recognized as bedrock upon which all mathematics is built.

A first solution came from Ernst Zermelo. A definitive answer came from Kurt Gödel.
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