In Zen Buddhism, there are any number of puzzles which are essentially nonsense questions. Masters ask their students these questions in an attempt to give the students a puzzle sufficiently interesting and difficult that the student's mind will worry at it like a dog with a juicy bone, quietly turn itself off in the meantime/state-of-being-stumped, and in that moment, when their mind is off, they will achieve (however briefly) Enlightenment.
The puzzles are called "koan", and the canonical example is "If a tree falls in a forest with no one to hear it, does it make a sound?". Evidence of 'understanding' a koan is realizing that the question it asks is predicated on something which is nonsense, and doing the appropriate end-run around the problem, á là the solution to the Gordian knot.