A riddle or tricky question, especially one posed as a game or test of wit.
Possibly from 'car' (meaning 'turn' or 'twist' in some dialects) plus 'witchet' (a dialectal or archaic form related to 'witch' or tricky behavior). Very rare and archaic.
This wonderfully weird word shows up in historical texts as a challenge or riddle game—it's the kind of obscure term that reminds us English once had colorful names for everyday things like 'brain-teasers' that have mostly disappeared from modern speech.
Complete word intelligence in one call. Free tier — 50 lookups/day.