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PUZZLE

Definition:

[noun] a particularly baffling problem that is said to have a correct solution; "he loved to solve chessmate puzzles"; "that's a real puzzler"
Synonyms: mystifier, teaser
[noun] a toy that tests your ingenuity
[verb] be a mystery or bewildering to; "This beats me!"; "Got me
Synonyms: perplex, vex, stick, get, mystify, baffle, beat, pose, bewilder, flummox, stupefy, nonplus, gravel, amaze, dumbfound
[verb] be uncertain about; think about without fully understanding or being able to decide; "We puzzled over her sudden departure"