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. © 2015 Farlex, Inc, all rights reserved.

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 © Farlex 2017

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 © Farlex 2017
See also:
References in periodicals archive ?
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You'll laugh, sometimes scratch your head, but often say, "I never detected that insight before."
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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.
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So, now you know and there's no need to scratch your head or elsewhere if someone mentions Dhobie Itch.
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