scratch (one's) 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 one's head

Express puzzlement or perplexity, think hard, as in They scratched their heads over this vexing question, but no one knew the answer. Although literally scratching one's head may simply betoken the fact that it itches, it also may indicate mental mystification or bewilderment. The term's figurative use dates from the first half of the 1900s.
See also: head, scratch
The American Heritage® Dictionary of Idioms by Christine Ammer. Copyright © 2003, 1997 by The Christine Ammer 1992 Trust. Published by Houghton Mifflin Harcourt Publishing Company. 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
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