Green’s Dictionary of Slang

a hoaxing, puzzling question.

1785		Grose Classical Dict. of the Vulgar Tongue.
1864, 1867, 1870		Hotten Sl. Dict.
1873		Sl. Dict. (5th edn) 109: Carriwitchet, a hoaxing, puzzling question, not admitting of a satisfactory answer, as ‘How far is it from the first of July to London Bridge?’.
1909		J. Ware Passing Eng. of the Victorian Era.