at one's wits end
at one's wit's end or at wits end {adj. phr.}
Having no ideas as to how to meet a difficulty or solve a problem; feeling puzzled after having used up all of your ideas or resources; not knowing what to do; puzzled.
He had approached every friend and acquaintance for help in vain, and now he was at his wit's end.
The designer was at his wit's end: he had tried out wings of many different kinds but none would fly.
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Source: A Dictionary of American Idioms