puzzle

v. mystify, baffle; confound, confuse; perplex, bewilder

n. enigma, riddle; problem; game composed of differently shaped pieces which fit together to form a picture, jigsaw

A puzzle is a problem or enigma that challenges ingenuity. In a basic puzzle you piece together objects in a logical way in order to come up with the desired shape, picture or solution. Puzzles are often contrived as a form of entertainment, but they can also stem from serious mathematical or logistical problems — in such cases, their successful resolution can be a significant contribution to mathematical  research.
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Noun
1. a particularly baffling problem that is said to have a correct solution; "he loved to solve chessmate puzzles"; "that's a real puzzler"
(synonym) puzzler, mystifier, teaser
(hypernym) problem
2. a toy that tests your ingenuity
(hypernym) plaything, toy
(hyponym) Chinese puzzle
Verb
1. be a mystery or bewildering to; "This beats me!"; "Got me--I don't know the answer!"; "a vexing problem"; "This question really stuck me"
(synonym) perplex, vex, stick, get, mystify, baffle, beat, pose, bewilder, flummox, stupefy, nonplus, gravel, amaze, dumbfound
(hypernym) confuse, throw, fox, befuddle, fuddle, bedevil, confound, discombobulate
(hyponym) stump, mix up
(see-also) puzzle over
(derivation) puzzler, mystifier, teaser
2. be uncertain about; think about without fully understanding or being able to decide; "We puzzled over her sudden departure"
(hypernym) chew over, think over, meditate, ponder, excogitate, contemplate, muse, reflect, mull, mull over, ruminate, speculate
(derivation) puzzler, mystifier, teaser

n. puzzle, jigsaw, puzzle consisting of differently shaped pieces which fit together to form a picture; enigma, riddle, problem

n. puzzle, jigsaw puzzle, game composed of differently shaped pieces which fit together to form a picture