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what is the question? 5 and 6 are the only possible. But if 5 is true then 6 is false None of the above can be true only with "more than one of the above (but different than all, none or one)", but then we would not be talking about the correct answer. It is assumed than only an answer can be correct. I suppose than 6 then. Updated: you are right, 6 can't be true, is the 5
It has to be 5
It seems that 5 is a winner, as stated in the accepted answer. That's a pity, first I thought the goal of the question was to create an instance of Yablo's Paradox. Yablo's paradox is important because you cannot just argue that the paradox arises from an obviously incorrect definition, as people sometimes do for classical semantic paradoxes.
But is it an answer to the question? If the question were something completely different, "How green is interstellar space?", then we would still find 5 as the answer. But "None of the above" is a non-answer. And "What is the answer to this question?" is not well defined.
An expert system answer (Prolog, CLIPS) would be cool to see here.
Using the clpb library [0]: solution([A1,A2,A3,A4,A5,A6]) :- sat(A1 =:= A2*A3*A4*A5*A6), sat(A2 =:= ~(A3+A4+A5+A6)), sat(A3 =:= A1*A2), sat(A4 =:= A1+A2+A3), sat(A5 =:= ~(A1+A2+A3+A4)), sat(A6 =:= ~(A1+A2+A3+A4+A5)). [0] https://www.metalevel.at/prolog/puzzles
(declare-const a1 Bool)
(declare-const a2 Bool)
(declare-const a3 Bool)
(declare-const a4 Bool)
(declare-const a5 Bool)
(declare-const a6 Bool)
(assert (= a1 (and a2 (and a3 (and a4 (and a5 a6))))))
(assert (= a2 (not (or a3 (or a4 (or a5 a6))))))
(assert (= a3 (and a1 a2)))
(assert (= a4 (or a1 (or a2 a3))))
(assert (= a5 (not (or a1 (or a2 (or a3 a4))))))
(assert (= a6 (not (or a1 (or a2 (or a3 (or a4 a5)))))))
(assert (or a1 (or a2 (or a3 (or a4 (or a5 a6))))))
(check-sat)
(get-model)
(exit)
Additionally forcing a5 to be false by adding the following to the list of assertions:
(assert (not a5))
Edit: Finally, to make sure there's not some possible solution where a5 is true as well as another assertion you could alternatively add this assertion:
(assert (and a5 (or a1 (or a2 (or a3 (or a4 (or a6)))))))
Similar one I enjoyed in the Naive Bayes article from yesterday https://blog.floydhub.com/naive-bayes-for-machine-learning/ Multiple Choice: If you choose an answer to this question at random, what is the chance you will be correct? A) 25% B) 50% C) 60% D) 25%
The answer to that question is obviously 0% Now, what would be the answer to the same question with the answer options: A) 20% B) 40% C) 60% D) 20% E) 0%
0% and 100% are indefensible for any uninformed prior.
There are two answers giving the correct probability for uniform prior. One of the 25% is a wrong answer despite being indistinguishable. Such a thing can happen because of a typo or in any myriad of ways. It's not a paradox.
If it asked the question "knowing that probability of success for random single choice question out of 4 answers is 25%, what is the probability of selecting the correct answer at random from one of the below?" That formulation implies an informed prior.
That'd have the answer of prior% with 50% for uniform prior, but it's not duplicated, so the actual answer is 0% making it a paradox. If it were duplicated, (answers only 25% and 50% available) the either answer of 50% would hold.
But that was not the question asked in yours or former question.
LinkedIn's skill tests are hilariously poor. They ask unanswerable questions, and mistype the answers. The more familiar you are with the subject matter, the more uncertain you become.
I felt like there was a big difference in the quality of the questions and answers for each quiz. For the AWS one, for example, the phrasing used for most of the questions and answers made the correct answer basically obvious without actually knowing it to be correct.
D O G
x A D
_______
D O G
A D O
_______
A G O G
Earlier quoted context omitted.
The answer to that question is obviously 0% Now, what would be the answer to the same question with the answer options: A) 20% B) 40% C) 60% D) 20% E) 0%
Your answer above is incorrect in a very funny way. "At random" implies an uninformed prior, but the question presupposes there's a correct answer, as 0% is missing. 0% and 100% are indefensible for any uninformed prior. There are two answers giving the correct probability for uniform prior. One of the 25% is a wrong answer despite being indistinguishable. Such a thing can happen because of a typo or in any myriad of…
If none of the answers are correct, the chance of picking the correct answer is 0%.