Brain-teaser and coarse sieve (6)
I believe the answer is:
riddle
'brain-teaser and coarse sieve' is the definition.
(I've seen this before)
This is all the clue.
(Other definitions for riddle that I've seen before include "The large sieve is a puzzle" , "unsolved problem" , "Cryptic statement" , "Make many openings" , "Sieve or conundrum" .)