puzzle

[1]	baffle , bewilder , confuse , confound , mystify , flummox , perplex , nonplus , stymie , stump
[2]	puzzle over , study , ponder (over) , mull over , contemplate , meditate on/upon/over , consider , muse over/on , reflect on/over , think about/over/on
[3]	puzzle out , perplex , vex , solve , decipher , stick , get , crack (the code) , unravel , mystify , baffle , work out , figure out , beat , pose , think through , sort out , bewilder , flummox , unlock , stupefy , nonplus , gravel , amaze , dumbfound

[1]	puzzler , mystifier , teaser
[2]	enigma , problem , question , paradox , poser , mystery , riddle , conundrum , (Colloq) brain-teaser