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Looking for single word definition for a question or riddle that seemingly has no answer. Designed to confuse. Not paradox or conundrum. I.e "What is the sounds of on hand clapping?"

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3  
This is called a (Zen) koan. –  Mitch Sep 7 '13 at 23:54
    
"One hand" or "on hand"? –  GEdgar Sep 9 '13 at 21:15

5 Answers 5

That would be a Zen (short) story ;-) . See:

http://www.101zenstories.com/index.php?story=21

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For which the loan-word Kōan is often used, though not all kōans are riddles. –  Jon Hanna Sep 17 '13 at 14:55
    
Has "koan" entered the English lexicon? I see it on Dictionary.com but have never read or heard it in common usage. –  SammyB Sep 18 '13 at 14:46

A paradox?

a seemingly absurd or contradictory statement or proposition which when investigated may prove to be well founded or true: the uncertainty principle leads to all sorts of paradoxes, like the particles being in two places at once

A conundrum?

a confusing and difficult problem or question: one of the most difficult conundrums for the experts

An enigma?

a person or thing that is mysterious or difficult to understand: Madeleine was still an enigma to him

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you could call it a catch-22 defined in the dictionary as

  1. a frustrating situation in which one is trapped by contradictory regulations or conditions.
  2. any illogical or paradoxical problem or situation; dilemma.
  3. a condition, regulation, etc., preventing the resolution of a problem or situation; catch.
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  • Intractable
  • Gordian Knot
  • Dilemma
  • Inconsistency
  • Round Square
  • Mutally Exclusive
  • Unrecognizable Pattern
  • Wild Goose Chase
  • Inconsistent Model
  • Nonsense
  • Time Waster
  • Logical Illogic
  • Circular Logic
  • Axiom
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I recognize that this does not actually answer the question, but… I think there is a modern tendency to insist on having a word for something, at any cost. I suggest that you allow the possibility of having to use more than one word.

For the definitive feature of the expression, I would use “paradox” or “incoherent” (or possibly “internally inconsistent”)… or just “meaningless”.

I think here I would use “incoherent question” — given your desire for conciseness. With the luxury of using enough words: “a question built around an internally inconsistent concept”.

(The term “meaningless” includes things that are quite without meaning, which is not useful here.)

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