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Which answer in this list is the correct answer to this question? (2017)

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Re: Which answer in this list is the correct answer to this question? (2017)

#61

Post by PeterStuer »

decasia wrote: post #49
thaumasiotes wrote: post #20

Earlier quoted context omitted.

Everyone in the comment thread seems to be focused on whether each proposition can be true. This is looking for your keys under the lamppost despite the fact that you dropped them in the dark. It's easy to determine whether a proposition can be true. But the question doesn't ask about that. It just asks "which of these is the correct answer to this question?" There are no stated criteria for being the correct answer,…

This seems like a crucial problem with the initial question. As with so many puzzles like this, it assumes that the reader will make similar (unargued, unstated) assumptions as the writer. But what justifies that methodological assumption? Nothing, as thaumasiotes is pointing out.

Any communication relies by necessity on a mutual implicit frame of reference, and while there most certainly are cases where question tread the line of unambiguous interpretability (I have suffered these many times, especially in education tests), I'd say in this case the demands are rather benign.

Re: Which answer in this list is the correct answer to this question? (2017)

#62

Post by northern-lights »

I didn't see a logical explanation that explains why an option is correct or not, so here's one:

Q Which answer in this list is the correct answer to this question?

1. All of the below. 2. None of the below. 3. All of the above. 4. One of the above. 5. None of the above. 6. None of the above.

I'll assume "is the answer" to be "True" and "is not the answer" to be "False" in my explanations to make it more readable.

Lets say 1 is True. This implies - 2, 3, 4, 5, 6 are also True. Now, if 2 is True, then it means 3, 4, 5, 6 are False. This contradicts what 1 says. So, 1 cannot be True.

Lets say 2 is True. This implies - 3, 4, 5, 6 are False. If 3 is False, it means both 1 and 2 cannot be True. Since, we've assumed 2 to be True, 1 can indeed be False, so this is consistent. If 4 is False, then it means either less than one or more than one out of 1, 2, 3 are True. Zero out of 1, 2, 3 cannot be True since it contradicts our assumption of 2 being True. So either two or three out of 1, 2, 3 have to be True. Since, we've already established than 1 is False, that leaves 3 to be True along with our assumption of 2 being True. But 3 cannot be True since it contradicts 2. So 2 cannot be True.

Lets say 3 is True. This implies 1, 2 are True. We've already established that 1, 2 are False. Moreover, 2 being True will contradict 3 being True. So 3 cannot be True.

Lets say 4 is True. This implies that exactly one of 1, 2, 3 is True. We've already established that they are False. So 4 cannot be True.

Lets say 5 is True. We now know that 1, 2, 3, 4 are not True. So, this is consistent. We'll come back to this.

Lets say 6 is True. This implies that 5 is False. If 5 is False, it means all of the above 5 - 1, 2 , 3, 4 are True which we've found not to be True. So 6 cannot be True.

That leaves only 5 to be answer to the question.

Re: Which answer in this list is the correct answer to this question? (2017)

#63

Post by torstenvl »

northern-lights wrote: post #62

I didn't see a logical explanation that explains why an option is correct or not, so here's one: Q Which answer in this list is the correct answer to this question? 1. All of the below. 2. None of the below. 3. All of the above. 4. One of the above. 5. None of the above. 6. None of the above. I'll assume "is the answer" to be "True" and "is not the answer" to be "False" in my explanations to make it more readable. Le…

> If 5 is False, it means all of the above 5 - 1, 2 , 3, 4 are True

That is incorrect. "Not All False" does not imply "All True."

Re: Which answer in this list is the correct answer to this question? (2017)

#64

Post by Asooka »

jcims wrote: post #54
thegeekpirate wrote: post #48

Earlier quoted context omitted.

Run it online here: https://onlinegdb.com/rkZhWVniH

Thanks for posting this, because I'm a Python n00b and I had no idea what this line was doing: itertools.product((True, False), repeat=6) The site made it easy for me to spend 30 seconds figuring it out. My interpretation is that that line generates what I'll call a truth table (not sure if that's what it formally is) then brute force searches for rows that satisfy all of the listed constraints. I'd also hazard that…

The product of two iterables is a list of pairs of each item in the first iterable and each item in the second iterable (same as set product in math):

[a, b] × [c, d] = [(a, b), (a, c), (b, c), (b, d)]

The number of elements of the product of two iterables is the product of the number of elements of each. You can similarly have a product of 3, 4, etc. iterables.

The repeat keyword argument to product specifies that we want not a product of several different iterables, but the product of an iterable with itself N times. So we pass a tuple of all possible boolean values (True, False) and ask that it be raised to the 6th power, giving us all possible 6-tuples of all possible boolean values.

Re: Which answer in this list is the correct answer to this question? (2017)

#65

Post by brlewis »

eino wrote: post #53

The question implies there is one correct answer. Do you agree it can be rephrased as "Which answers in this list are the correct answers to this question?", so as to make it more difficult, while keeping the same answer?

It could be rephrased that way without changing the answer, but I don't think it would be any harder that way. You can still start with question 1 and continue downward to logically deduce the answer.

Re: Which answer in this list is the correct answer to this question? (2017)

#66

Post by jayrhynas »

jetrink wrote: post #27

I've always thought of these as "Wayside School" problems, because I first encountered them in the children's book, Sideways Arithmetic From Wayside School by Louis Sachar. I highly recommend it for any child who is into puzzles. I really enjoyed how the book deconstructed the format of tests and quizzes that I was so familiar with at the time. My favorite section was the sideways math, where words are added or multi…

I think it's A=5 D=1 G=2 O=0

102 x 51 = 5202

Re: Which answer in this list is the correct answer to this question? (2017)

#68

Post by Asooka »

dtjohnnyb wrote: post #17

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%

That depends on whether we consider A and D the same answer or not. If we can assume that A does not imply D and vice-versa, then we can pick either A or D and be correct (but not both) - in essence our picking either answer collapses the question's wave-function to be one or the other.

Re: Which answer in this list is the correct answer to this question? (2017)

#69

Post by jdmichal »

jcims wrote: post #54
thegeekpirate wrote: post #48

Earlier quoted context omitted.

Run it online here: https://onlinegdb.com/rkZhWVniH

Thanks for posting this, because I'm a Python n00b and I had no idea what this line was doing: itertools.product((True, False), repeat=6) The site made it easy for me to spend 30 seconds figuring it out. My interpretation is that that line generates what I'll call a truth table (not sure if that's what it formally is) then brute force searches for rows that satisfy all of the listed constraints. I'd also hazard that…

I think you have the general idea down. But as you suspected it's not a truth table. It's all cross-product permutations (hence the name `product`) of six items from the set {True, False}. So that line is creating a iterator that looks like this:

    (True, True, True, True, True, True)
    (True, True, True, True, True, False)
    (True, True, True, True, False, True)
    (True, True, True, True, False, False)
    (True, True, True, False, True, True)
Though not necessarily in this order... I'm unfamiliar with the actual implementation. Since the values are bits, they could have achieved the same effect by incrementing a six-bit integer. Which is a nice proof that the number of permutations here is 2^6. (Generally it's s^n, where s is the set size and n is the count of elements.)

Re: Which answer in this list is the correct answer to this question? (2017)

#70

Post by arnvald »

lovasoa wrote: post #43

Here is a single python statement that solves the problem: print([ q for q in itertools.product((True, False), repeat=6) if q == ( all(q[1:]), # 1. All of the below. not any(q[2:]), # 2. None of the below. all(q[:2]), # 3. All of the above. any(q[:3]), # 4. One of the above. not any(q[:4]), # 5. None of the above. not any(q[:5]), # 6. None of the above. ) ]) https://gist.github.com/lovasoa/f2b4ed93e755bf4172583d28f20…

wouldn't any(q[:3]) (the 4th sentence) return true even if 2 or 3 of the above were correct? If I understand correctly, it should be true if exactly one of the above is correct, not at least one.

Although, I'm probably wrong, since the question says "which answer is correct", implying only one can be correct.

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