Scratch your head - Idioms by The Free Dictionary
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.
scratch your head 1 think hard in order to find a solution to something. 2 feel or express bewilderment. informal
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.