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The Collaborative International Dictionary
Enigmatology

Enigmatography \E*nig`ma*tog"ra*phy\, Enigmatology \E*nig`ma*tol"o*gy\, n. [Gr. ?, ?, an enigma + -graphy, -logy.] The art of making or of solving enigmas.

Wiktionary
enigmatology

n. the study of puzzles