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Definition of puzzle:

1. Bewilderment; perplexity; something to try ingenuity.
2. To confuse; to bewilder; to be perplexed.

Synonyms:

induce, regulate, secret, fix, mystification, vex, tangle, receive, go, frustration, mother, beat out, frustrate, bilk, distress, exhaust, tormenter, draw, scramble, lay, hold fast, clue, wash up, closed book, pay back, query, capture, have, drive, alarm, nettle, throw, dizzy, pay off, irritate, get at, noughts and crosses, personate, quiver, bemuse, shake up, get to, paradox, amaze, incur, shell, present, discombobulate, dumbfound, unsettle, tucker, stickler, outwit, tormentor, let, clear, hangman, pound, muddle, complicate, stick around, bewilderment, outfox, crossword, thump, circumvent, teaser, spoil, quandary, oracle, begin, thrum, bring, wedge, confuse, besot, bind, obtain, nonplus, feelings, position, cling, lodge, work over, acquire, vexer, beget, posture, jumble, produce, question, sire, jigsaw, bond, aim, beat up, bother, bunk, devil, thing, set about, cross, concern, quizmaster, tick, set out, get down, beat, sit, suffer, cleave, stun, find, ticktack, drum, pulsate, start out, trounce, take, raise up, experience, stick to, stimulate, puzzlement, tucker out, stay, thwart, place, bewilder, crush, annoy, bugger off, convey, father, cohere, unknown quantity, brain teaser, sustain, arrest, sting, puzzler, astound, grow, charades, fetch, vanquish, ticktock, buzz off, addle, perplexity, tease, quiz, put, perplex, generate, chafe, fuddle, entanglement, rile, model, disturb, flap, overreach, come, stick by, scram, tear apart, flummox, stick, agitate, cause, adhere, issue, befuddle, gravel, answer, dilemma, annoyer, foil, solution, catch, nark, worry, deposit, become, mix up, mystify, confound, astonish, baffle, pose, get under one's skin, commove, start, arrive, set, engender, stir up, contract, impersonate, mystifier, stay put, develop, stupefy, stand by, get, commence, frighten, bring forth, weigh on, scotch, rag, head-scratcher, outsmart, make, ambiguity.

• complexity (part of speech: noun)
  • convolution, 
  • abstruseness, 
  • mystery, 
  • difficulty, 
  • intricacy, 
  • obscurity, 
  • cabalism, 
  • complexity, 
  • subtlety
• uncertainty (part of speech: noun)
  • changeability, 
  • unsureness, 
  • deniability, 
  • questionability, 
  • disputability, 
  • incertitude, 
  • vagueness, 
  • tentativeness, 
  • moot point, 
  • uncertainty, 
  • ambivalence, 
  • confusion, 
  • controversy
• secret (part of speech: noun)
  • cryptogram, 
  • problem, 
  • brainteaser, 
  • enigma, 
  • labyrinth, 
  • code, 
  • riddle, 
  • conundrum, 
  • poser, 
  • maze, 
  • mystery, 
  • cipher