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

scratch your head

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

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
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.
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.
HERE'S a mathematical conundrum that's guaranteed to put a smile on your face while you scratch your head at the same time.
You'll laugh, sometimes scratch your head, but often say, "I never detected that insight before.
Here's an answer that may make you scratch your head.
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.