scratch one's head

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
References in periodicals archive ?
Putting them on more than the Prime Minister's salary of PS142,500 makes one scratch one's head a little bit.
Of course, when you're being attacked for being provocative, for preventing a smooth ride, for annoying these gentlemen to the north, of course it can make one scratch one's head and wonder if one is doing the right thing.