head-scratching1
/ˈhɛdˌskratʃɪŋ/noun
The action of scratching one's head, especially in puzzlement or thought; an instance of this. Hence: perplexity; deep thought. Compare to scratch one's head.
Origin
Mid 19th century; earliest use found in Blackwood's Magazine. From head + scratching.
head-scratching2
/ˈhɛdˌskratʃɪŋ/adjective
1Of a question, situation, etc.: such as might cause one to scratch one's head in puzzlement, thought, etc.; specifically baffling, perplexing.
2That scratches one's head, especially in puzzlement.
Origin
Early 19th century; earliest use found in Western Monthly Review. From head + scratching.