"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., redels, 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 in early Modern English. The meaning "anything which puzzles or perplexes" is from late 14c.
"perforate (something) all over with many holes," 1817 (implied in riddled), earlier "sift, pass (grain) through a riddle" (early 13c.), from Middle English ridelle "coarse sieve," from late Old English hriddel "sieve," which is altered by dissimilation from Old English hridder "sieve" (see riddle (n.2)). The notion is of making something (later someone) resemble a riddle.
1570s, "to pose as a riddle, speak in riddles," from riddle (n.1). Earlier it meant "to puzzle" (over something), early 15c. Transitive sense of "to interpret or solve a riddle" is from 1580s (as in riddle me this). Related: Riddled; riddler; riddling.
"coarse sieve" for grain, sand, etc., mid-14c., ridel, 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"). The parallel form ridder long survived.