"spiked metal ring for holding a belt, etc.," c. 1300, bukel, from Old French bocle "boss (of a shield)," then "shield," then by further extension "buckle, metal ring," (12c., Modern French boucle), from Latin buccula "cheek strap of a helmet," in Late Latin "boss of a shield," diminutive of bucca "cheek" (see bouche).
Boucle in the middle ages had the double sense of a "shield's boss" and "a ring"; the last sense has alone survived, and it metaph. developed in the boucle de cheveux, ringlets. [Kitchin]
c. 1600, "state of being puzzled," from puzzle (v.); meaning "perplexing question, difficult problem" is from 1650s; that of "a toy contrived to test one's ingenuity" is from 1814. Puzzle-ring "number of small rings intertwined inseparably with one another that can be arranged as a single ring" is by 1877.