"A word game or joke, comprising a question or statement couched in deliberately puzzling terms, propounded for solving by the hearer/reader using clues embedded within that wording" [Oxford Dictionary of English Folklore], early 13c., from Old English rædels "riddle; counsel; conjecture; imagination; discussion," common Germanic (Old Frisian riedsal "riddle," Old Saxon radisli, Middle Dutch raetsel, Dutch raadsel, Old High German radisle, German Rätsel "riddle").
The first element is from Proto-Germanic *redaz-, from PIE *re-dh-, from root *re- "to reason, count." The ending is Old English noun suffix -els, the -s of which later was mistaken for a plural affix and stripped off. Meaning "anything which puzzles or perplexes" is from late 14c.