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It involves logical/mathematical puzzle(s), so no wishy washy different interpretations like in riddles.

The puzzle in question tells a story involving a puzzle, but some details about the puzzle in the story are incomplete or missing. The solvers in story (assumed to be super capable of making logical conclusions) either know the whole puzzle or more of it than we do, and we usually are told whether that solver(s) managed to solve it. If a solver in the story doesn't have enough information, they sometimes ask a question or just asks for more information.

An example would be: My friend asked me how old my 3 children were. I said to him: "The sum of their ages is my house number and the product of their ages is 72." He told me that he didn't have enough information to work it out, so I told him that the oldest one really likes chocolate chip cookies. He was able to solve it then. How old are my children? (This one is also known as a census puzzle, I think.)

Another example: Once when I visited the Island of Knights and Knaves, I saw a group of 3 residents. I asked: "Is at least one of you a knight?" One of them answered and then I knew the answer to my question. (In case some of you don't know, "The Island of Knights and Knaves" is a type of puzzle where every resident is either a knight or a knave. A knight can only tell the truth while a knave can only tell lies.)

These two examples only have one solver (my friend in the first and me in the second), but there can be multiple solvers who received different amount of information, and we can even have incomplete information about their ability to solve it (e.g. two solvers who initially didn't have enough information each asked a different question and we only know that either both or neither managed to solve it after getting an answer).

In Slovene, this type of puzzle is called metauganka (uganka = puzzle). However, the term metapuzzle in English refers to something else. I've done some searching on the internet, including here, but didn't get an answer.

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    $\begingroup$ I'd probably just call them "Deduction Puzzles", but maybe someone knows a more specific name. $\endgroup$ Jun 10 at 13:25
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    $\begingroup$ I don't know if this puzzle category has a name either. Maybe you could use meta-reasoning puzzle, or epistemic reasoning puzzle? $\endgroup$ Jun 10 at 14:02
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    $\begingroup$ On PSE we use the tag meta-knowledge for these. Doesn't exactly roll off the tongue though. $\endgroup$
    – Bass
    Jun 10 at 21:31
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    $\begingroup$ Smullyan referred to them as "metapuzzles". $\endgroup$ Nov 10 at 11:56
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They are sometimes called epistemic puzzles or in more simple terms knowledge puzzles, as they involve reasoning about knowledge and reasoning about reasoning about knowledge, and so on. Note that the first link is to a blog by a professional logician, so it is probably as good as you are going to get in terms of a recognized name for such puzzles.

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I would call them "metaknowledge" puzzles, as the audience is given knowledge about the in-universe solvers' knowledge.

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