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This is about the objective interpretations/assessment/quantification of riddles. Let us define a riddle as a type of puzzle relying on the usage of only language and context.

Using precise English as a formal (non-opinion based) tool, and examples and sources like dictionaries, grammar sources (ELU.SE maybe), and perhaps literature (e.g. The Hobbit), or even possibly sources from this SE, explain how to construct and what defines a "solid" Riddle?

I might expect that the answer might contain something like: a "solid" Riddle should have one and only one interpretation which coherently addresses each line/clue contained in the Riddle.

Related:
Question about writing rhyming riddles.
Tips for solving riddles.

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    $\begingroup$ Rely on language, make good use of the fact others can't see "quotation marks" $\endgroup$ – warspyking Nov 20 '14 at 10:02
  • $\begingroup$ I'm not really sure what you mean when you say "Using precise English as a formal (non-opinion based) tool". Care to expand on that? $\endgroup$ – A E Nov 20 '14 at 17:08
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    $\begingroup$ youtube.com/watch?v=4PFWtZIqcKc $\endgroup$ – A E Nov 20 '14 at 17:26
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    $\begingroup$ @AE That's the kind of thing this question intends to have explored. Like maybe, what conditions could define and bring about "solidity" in a satisfactory way. English is ambiguous, and even the available answer from frodo demonstrates that when several ambiguous clues are given, we need to choose interpretations of each one and where there is an intersection between them all we have a riddle answer. Also note that math is dependent on interpretation too - and relies on some kind of agreement (like language) - and it could be argued is also inherently ambiguous. $\endgroup$ – d'alar'cop Nov 20 '14 at 17:26
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    $\begingroup$ @AE hilarious - so British :p anyway, yes, well one clue taken on its own, I agree does not give enough to go by.... that's why often there are at least 5 or more... one must show a little common sense too :p $\endgroup$ – d'alar'cop Nov 20 '14 at 17:28
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As you say in the question: there should be exactly one interpretation which fits each clue given. However hard the riddle a supermajority of fluent English (or whatever your target language may be) speakers must, when presented with the solution, consider it the only correct one.

In practise, this is going to mean finding the unique qualities of whatever your solution is, then using those as clues.

e.g. Elephant. It's a huge, grey, living creature. It has extremely thick limbs, a trunk and large ears. None of these in isolation is unique, but together they only describe an elephant. Of course, this is not yet a riddle. You will then need to obfuscate the clues (by metaphor, vague description, literary allusion) throwing out any which cannot be disguised sufficiently. Hopefully at that point you will still have enough clues to uniquely define your solution.

So for the elephant example, large limbs is too straightforward. Perhaps we could compare them to other large, vertical cylinders. Like pillars, or trees. We could refer to the trunk by function (hose, snorkel) or by alternative meaning of 'trunk' (trees, luggage). Both give us options for trees, so let's go with that. "I walk on trees, I drink through a tree". Elephants are heavy, but they are also light grey, so we could have "heavier than a boulder, lighter than a raven's feather". And so on...

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    $\begingroup$ nice. maybe you could flesh out your Elephant example with all metaphors you were talking about :) $\endgroup$ – d'alar'cop Nov 20 '14 at 10:13
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    $\begingroup$ Sadly, I lack talent in that area. I'll do something with it though. $\endgroup$ – frodoskywalker Nov 20 '14 at 10:14
  • $\begingroup$ What lack of talent? Nice. But how about an argument that a solution to the metaphor version would be unique? (that's important) ;) $\endgroup$ – d'alar'cop Nov 20 '14 at 10:52
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    $\begingroup$ @Sp3000 that's true, legs/trees needs improvement. However, I don't think it's a problem if a single clue can lead someone down the wrong path (or even a pair), so long as they can't make it fit all of the clues. $\endgroup$ – frodoskywalker Nov 20 '14 at 11:29
  • $\begingroup$ Trees! Trees everywhere... $\endgroup$ – Mr Pie Jul 27 '18 at 11:17
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What for me is the most important property in a "solid" riddle - "the twist". These are small confusing details in a riddle. Let me give you an example (one of my favourite riddles in Neil Gaiman's "The books of magic"):

When there is a fire in me, then I am still cold; When I own your true love’s face then you will not see me; To all things I give no more than I am given; In time I may have all things, and yet I can keep nothing.

This is a perfect example, because the riddle contains three twists. In the first sentence, the twist is the second part of the sentence ("then I am still cold"). Generally, there is a simple test for twists - the question "How the hell is this possible?". If you find yourself asking this question at some point, then you've just encountered a twist.

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    $\begingroup$ As lovely as the sentiment of your answer is. I was under the impression the OP wanted a non-opinion based answer. $\endgroup$ – Oblongamous Nov 20 '14 at 13:00
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    $\begingroup$ All answers are opinion-based, aren't they? Unless we make references to scientific studies (and I see no references until now). Moreover, I have the impression, we are here to define what a "solid" riddle is, which implies suggestions. This was just a suggestion, I don't really expect everyone to agree. $\endgroup$ – zlobi.wan.kenobi Nov 20 '14 at 13:07
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    $\begingroup$ It is a hard concept to label, one that I'm failing to see a definitive answer to. A possible conclusion could be a set of lines that describe one entity and one alone. whether it use personification, letter placement or words altenate meaning. We see to many times a riddle which the write has a lovely written riddle but has 2-4 different answers which fit all clues logically/metaphorically. This is what needs to be avoided $\endgroup$ – Oblongamous Nov 20 '14 at 14:06
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    $\begingroup$ The property you suggest is a good one and already proposed from @frodoskywalker . Optimally a good riddle will have just one answer. Which is actually extreme hard to achieve, because a concept/entity can be very subjective. $\endgroup$ – zlobi.wan.kenobi Nov 20 '14 at 14:45
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    $\begingroup$ I would rather suggest starting from the purpose of a riddle. In my opinion, this is not the answer. It is rather to light up the creativity of the reader. What do you think? What is your purpose when solving riddles? Is it because you like to have an answer or because you like the process of solving or anything else? (Btw. this one is not a rhetorical question to guide you to the right answer. I really want to know what is your motivation for solving riddles. And maybe there we can find the answer we are searching for). $\endgroup$ – zlobi.wan.kenobi Nov 21 '14 at 7:17
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There are more things in heaven and earth, d'alar'cop, than are dreamed of in your philosophy.

Uniqueness is tough. One of the chief devices used in riddling is metaphor. This guarantees non-uniqueness, in a sense, because the whole point of a metaphor is that two or more different things share certain properties. Because figurative language is another given in riddles, the interpretation of the metaphor is broadened further.

The idea is to use as many different figurative or metaphoric descriptions as are necessary to ensure that the intersection of their interpretations is a single word or phrase.

How do you achieve this, or better, how do you know when you have achieved this? In practical terms you can't. To be sure, you would have to map all of the words in the riddle's target language to all the possible interpretations of the riddle's statement and verify that the cardinality of the result is one.

If you look carefully at nearly any of the classic riddles, are they 100% solid? Are they a 100% fit? No. They may be good, they may be satisfying but are they rigorous (I assume this is what you mean by "solid")? Probably not.

Language is notoriously imprecise. Word meanings drift. "Solidity" is very difficult to achieve. I, myself, have tried to end-run the problem by constructing riddles that describe both the form and the content of the answer. I give some more or less metaphorical descriptions of the subject as in the classical riddles but I also give one or more clues such as you would find in cryptic crosswords. You can attack them from whichever end appeals to you most and use the other to verify your answer. Cryptic clues are a pretty good path to uniqueness.

I have had a number of artistic failures but with this method but I believe I have done fairly well in regard to being "solid". I cannot claim originality, by the way, a number of riddles of this type can be found in Jane Austen. Probably elsewhere as well but that's where I got the idea.

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