scratch your head

scratch (one's) head

To be puzzled, doubtful, or uncertain; to have trouble understanding something. 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