head-scratcher
/ˈhɛdˌskratʃə/noun
1A person who scratches his or her head, especially in puzzlement or thought; (hence) a perplexed or thoughtful person. Compare to scratch one's head.
2 Informal (originally US ). A perplexing problem or question; something which causes bafflement or puzzlement.
3An implement for scratching the head. Now chiefly historical.
Origin
Early 17th century; earliest use found in Barten Holyday (1593–1661), Church of England clergyman and poet. From head + scratcher.
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