Etymology
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riddle (n.1)

"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.

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riddle (v.1)

"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.

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riddle (v.2)

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.

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riddle (n.2)

"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.

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burial (n.)

"act of burying," late 13c.; earlier "tomb" (c. 1200), false singular from Old English byrgels "tomb," from byrgan "to bury" + suffix -els; a compound also found in Old Saxon burgisli, suggesting a Proto-Germanic *burgisli-, from PIE root *bhergh- (1) "to hide, protect." The Germanic suffix *-isli- (also in riddle (n.1), Old English hydels "hiding place," fætels "bag") became obsolete and was felt as a plural of the Latin-derived suffix -al (2) forming nouns of action from verbs (survival, approval, removal, etc.). In the "act of burying a dead person" sense it is now regarded as bury + -al. Burial-ground is from 1803.

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*krei- 
Proto-Indo-European root meaning "to sieve," thus "discriminate, distinguish."

It forms all or part of: ascertain; certain; concern; concert; crime; criminal; crisis; critic; criterion; decree; diacritic; discern; disconcert; discreet; discriminate; endocrine; excrement; excrete; garble; hypocrisy; incertitude; recrement; recriminate; riddle (n.2) "coarse sieve;" secret; secretary.

It is the hypothetical source of/evidence for its existence is provided by: Greek krinein "to separate, decide, judge," krinesthai "to explain;" Latin cribrum "sieve," crimen "judgment, crime," cernere "to sift, distinguish, separate;" Old Irish criathar, Old Welsh cruitr "sieve;" Middle Irish crich "border, boundary;" Old English hriddel "sieve."
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*re- 

*rē-, Proto-Indo-European root meaning "to reason, count;" a variant of PIE root *ar-, also arə-, "to fit together." 

It forms all or part of: Alfred; arraign; arithmetic; Conrad; dread; Eldred; Ethelred; hatred; hundred; kindred; logarithm; Ralph; rate (n.) "estimated value or worth;" rathskeller; ratify; ratio; ration; read; reason; rede; rhyme; riddle (n.1) "word-game;" rite; ritual.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit radh- "to succeed, accomplish;" Greek arithmos "number, amount;" Latin reri "to consider, confirm, ratify," ritus "rite, religious custom;" Old Church Slavonic raditi "to take thought, attend to;" Old Irish im-radim "to deliberate, consider;" Old English rædan "to advise, counsel, persuade; read;" Old English, Old High German rim "number;" Old Irish rim "number," dorimu "I count."

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read (v.)

Middle English reden, ireden, "to counsel, advise," also "to read," from Old English rædan, gerædan (West Saxon), redan, geredan (Anglian) "to advise, counsel, persuade; discuss, deliberate; rule, guide; arrange, equip; forebode; to read (observe and apprehend the meaning of something written), utter aloud (words, letters, etc.); to explain; to learn through reading; to put in order."

This is reconstructed to be from Proto-Germanic *redan, source also of Old Norse raða, Old Frisian reda, Dutch raden, Old High German ratan, German raten "to advise, counsel, interpret, guess," from PIE root *re- "to reason, count."

Cognate words in most modern Germanic languages still mean "counsel, advise" (compare rede). Old English also had a related noun ræd, red "advice," and read is connected to riddle (n.1) via the notion of "interpret." Century Dictionary notes that the past participle should be written red, as it formerly was, and as in lead/led. Middle English past participle variants include eradde, irad, ired, iræd, irudde.  

The sense-transference to "interpret and understand the meaning of written symbols" is said to be unique to English and (perhaps under Old English influence) Old Norse raða. Most languages use a word rooted in the idea of "gather up" as their word for "read" (such as French lire, from Latin legere).

Sense of "make out the character of (a person)" is attested from 1610s. Musical sense of "perform (at first sight) from the notes" is by 1792. To read up "systematically study" is from 1842; read out (v.) "expel by proclamation" (Society of Friends) is from 1788. Read-only in computer jargon is recorded from 1961.

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enigma (n.)
1530s, "statement which conceals a hidden meaning or known thing under obscure words or forms," earlier enigmate (mid-15c.), from Latin aenigma "riddle," from Greek ainigma (plural ainigmata) "a dark saying, riddle," from ainissesthai "speak obscurely, speak in riddles," from ainos "tale, story; saying, proverb;" according to Liddell & Scott, a poetic and Ionic word, of unknown origin. General sense in English of "anything inexplicable to an observer" is from c. 1600.
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logogriph (n.)
type of word puzzle based on synonyms, etc., and often in the form of a verse, 1590s, from French logogriphe, from Greek logos "word" (see Logos) + gripos/griphos "riddle," a figurative use, literally "fishing basket, creel," probably from a pre-Greek word in a lost Mediterranean language. "The variation [p/ph] is typical for Pre-Greek words; such an origin for a fisherman's word is quite understandable" [Beekes].
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