scratch one's head

Idioms  

1. 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.

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Example Sentences

"If you look at the volume of Egyptian goods that are for sale, and you look at the volume of Egyptian cotton that's produced, it would lead one to scratch one's head," Lea said.

From Reuters

The stridency with which Scalia attacked them, especially in his later years, could only make one scratch one’s head.

From Slate

If you look in broad daylight you can't see to the end of the street, and there are side-streets, too, and one can do nothing but scratch one's head.

From Project Gutenberg