scratch your head

scratch (one's) head

To show that one is puzzled, doubtful, or uncertain; to show that one has trouble understanding something. Literally scratching one's head can indicate the same thing. His decision to pull the plug on the lucrative program has everyone scratching their heads.
See also: head, scratch
Farlex Dictionary of Idioms.

scratch your head

1 think hard in order to find a solution to something. 2 feel or express bewilderment. informal
See also: head, scratch
Farlex Partner Idioms Dictionary

scratch your ˈhead (over something)

think hard in order to find an answer to something: We’re all scratching our heads for a solution to this problem.
See also: head, scratch
Farlex Partner Idioms Dictionary
See also:
  • (one) could use (something)
  • give (one) (one's) head
  • give head
  • give somebody their head
  • give someone their head
  • (one) could stand (something)
  • deep water
  • drive (one) out of office
  • force (one) out of office
  • force out of office
References in periodicals archive
What follows is a brain-twisting game of cat and mouse that seems ergonomically designed to make you scratch your head.
OUR KIND OF TRAITOR Cert [...]
"This is the notion that when you're having a conversation with somebody and you don't care where your hands are, and the other person scratches their head, you scratch your head," said Sasha Ondobaka of the Donders Institute for Brain, Cognition and Behaviour at Radboud University Nijmegen in the Netherlands.
We're not like chameleons copying everything everybody does
HERE'S a mathematical conundrum that's guaranteed to put a smile on your face while you scratch your head at the same time.
How to find your age from your appetite; THE SATURDAY SILLY TEASER
You'll laugh, sometimes scratch your head, but often say, "I never detected that insight before."
Commentary on the Torah. (Briefly Noted)
To make messages jump from cell to cell--when your brain signals your hand to scratch your head, for example--your brain creates chemicals called neurotransmitters.
Meet your incredible brain: check out command central for everything you do. (Heads Up Real News About Drugs And Your Body)
It wasn't meant as a compliment, but it could be taken as such; you could applaud this book as a geek-show, the kind that makes you blink, scratch your head, and look at the world with different eyes for a moment.
Invisible Republic: Bob Dylan's Basement Tapes
So, now you know and there's no need to scratch your head or elsewhere if someone mentions Dhobie Itch.
Kaye Adams