noun
at one's wit's end; at a complete loss
Describes a state of deep perplexity where one cannot think of any solution, often with a physical gesture of tilting the head in thought. A yojijukugo used in literary or emphatic contexts.
難問に思案投首の体で立ち尽くした。
He stood there at his wit's end over the difficult problem.
Standard yojijukugo spelling.
Variant spelling with 投げ首; less common but still used.
A yojijukugo combining 思案 (thought, consideration) and 投げ首 (throwing one's head, i.e., tilting the head in perplexity). The exact origin is uncertain, but it vividly depicts the posture of deep thought when stumped.