scratch one's head

scratch + one's + head

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scratch one's head (third-person singular simple present scratches one's head, present participle scratching one's head, simple past and past participle scratched one's head)

1. (idiomatic) To puzzle, ponder, or wonder about something.

   Faced with a box full of hundreds of small parts and forty pages worth of assembly instructions, he could do little more than stand there and scratch his head.

   • 2010 December 28, Owen Phillips, “Sunderland 0 - 2 Blackpool”, in BBC‎:

     But Sunderland will be left scratching their heads at the result after creating enough chances to have won two games in a refreshingly open and frantic first period.