mystery applies to what cannot be fully understood by reason or less strictly to whatever resists or defies explanation.
the mystery of the stone monoliths
problem applies to a question or difficulty calling for a solution or causing concern.
problems created by high technology
enigma applies to utterance or behavior that is very difficult to interpret.
his suicide remains an enigma
riddle suggests an enigma or problem involving paradox or apparent contradiction.
the riddle of the reclusive pop star
puzzle applies to an enigma or problem that challenges ingenuity for its solution.
the thief's motives were a puzzle for the police
Word History
Etymology
Noun (1)
Middle English redels, ridel, from Old English rǣdelse opinion, conjecture, riddle; akin to Old English rǣdan to interpret — more at read
Noun (2)
Middle English ridel, going back to Old English hriddel (attested once), alteration (by dissimilation or suffix substitution) of hridder, hrīder, going back to Germanic *hrīdra- (whence also Old Saxon hrīdra "sieve," Old High German rītera), going back to Indo-European *krei̯(h1)̯-dhro- or *krei̯(h1)̯-tro- (whence Latin crībrum "sieve," Old Irish críathar, Old Welsh cruitr "winnowing fan"), from *krei̯(h1)- "sift, separate" + *-dhro-, *-tro-, suffixes of instrument — more at certain entry 1