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Few days ago I've been told about a riddle as can be seen in this episode of Scrubs:

Two coins add up to 30 cents and one of them is not a nickel.
So, what are they?
It's a riddle. You'll figure it out!

Like you can see in the episode, the two bad guys fail to solve the riddle because they intepret "one of them is not a nickel" as

Two coins, 30 cents, no nickels.

That interpretation seems to be a common one as apparent from this explanation of Dr. Math.

I have two big questions about this riddle and the phrase "one (of them) is not a ...":

  1. In none of the English dictionaries, I could find "everyone (of them)" as a meaning for "one (of them)". In my native languages (German and Russian), such a meaning of the expression "one (of them) ..." does not exist either. Rather, pointing out the one of the things is not X, would have the pragmatic consequence to the listener to assume that other of the things are X. So, for me it's a riddle why this riddle should be a riddle. Where can I find evidence or other examples for this usage of "one (of them) is not a ..."?
  2. In the explanation of Dr. Math mentioned above, it says

    One thing to consider is exactly how you could rephrase the question so that this confusion is avoided, and thereby rendering the problem trivial instead of puzzling. Adding two small words goes a long way: "Two US coins added together total fifty-five cents, but one [of them] is not a nickel. What are the two coins?".

Here I don't understand why the adding of "of them" should render the problem trivial. In the Scrubs episode and many other versions I've seen on the web, the riddle already contains "of them" and is still presented as a riddle.

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    The hearer is intended to mis-parse it as "not one of them is", i.e. there are no nickels. In reality, it means that "one of them is not" -- and the other one is. (In which case the math becomes easy instead of impossible.) This is actually a pretty grammatically insightful riddle; it seems to understand something about how we perceive the semantic structure despite the surface order. A deeper explanation of why we do that would probably be suited to linguistics.se. – Luke Sawczak Dec 2 '17 at 12:52
  • This riddle has sometimes been suggested as a one-line test of suitability for a programming career . . . – peterG Dec 2 '17 at 18:29
  • And that might explain why programmers and users often have so much trouble understanding each other. – Tᴚoɯɐuo Dec 3 '17 at 13:57
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I don't completely agree with the poster on Dr. Math. The language here is completely clear whether you say "of them" or not, but people make a mistake when encountering this because of the way they expect information to be presented.

When someone quickly says "one of them is not a nickel" without specifying which coin they are talking about, the listener may heuristically assume the statement applies to both coins. It's like a "without loss of generality" assumption in math. If you had said "the first one is not a nickel" then no one would go down that logical path.

The language itself is unambiguous and in a riddle this type of careful listening is necessary but in conversation you would say something that makes that possibility clear, like "they are not both nickels" or "at most one of them is a nickel." When you say "is not a nickel," people who assume you are trying to help rather than trick them assume that neither is a nickel. If anything, they will assume that you made a mistake as you were speaking.

  • The answer does not entirely respond to just the original question, but it does provide the rational to the answer of the riddle. – Corvus B Dec 10 '17 at 3:37
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    @CorvusB The OP has completely changed the question since I wrote this answer and is now asking pretty much only things that he did not get from his first round of answers. As a result, nothing here makes sense any more. Question should be deleted or something so we can start fresh. – farnsy Dec 10 '17 at 11:57
  • Hard to answer a moving target! :D – Corvus B Dec 10 '17 at 15:29

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