Put down an unanswerable question (4)
I believe the answer is:
koan
'question' is the definition.
(I know that koan is a type of problem)
'put down an unanswerable' is the wordplay.
I cannot quite see how this works, but
'an' could be 'a' and 'a' is found in the answer.
The remaining letters 'kon' is a valid word which might be clued in a way I don't understand.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for koan that I've seen before include "There's no reason for it" , "Zen paradox; OK, no (anag.)" , "Zen riddle" .)