"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.
"perforate with many holes," 1817 (implied in riddled), earlier "sift" (early 13c.), from Middle English ridelle "coarse sieve," from late Old English hriddel "sieve," altered by dissimilation from Old English hridder "sieve" (see riddle (n.2)).
"coarse sieve," mid-14c., alteration of late Old English hriddel, a dissimilation of hridder, from Proto-Germanic *hrida- (source also of German Reiter), from PIE root *krei- "to sieve" (source also of Latin cribrum "sieve, riddle," Greek krinein "to separate, distinguish, decide").