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puzzle 
  vb 
1 baffle, beat  (slang) bewilder, confound, confuse, flummox, mystify, nonplus, perplex, stump 
2 ask oneself, brood, cudgel  or  rack one's brains, mull over, muse, ponder, study, think about, think hard, wonder 
3  (usually with)   out clear up, crack, crack the code, decipher, figure out, find the key, get it, get the answer, resolve, see, solve, sort out, suss (out)  (slang) think through, unravel, work out 
  n 
4 brain-teaser  (informal) conundrum, enigma, labyrinth, maze, mystery, paradox, poser, problem, question, question mark, riddle, teaser 
5 bafflement, bewilderment, confusion, difficulty, dilemma, perplexity, quandary, uncertainty