To figure out; to discover or find a solution; to deduce.(verb)
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Use "puzzle out" in a sentence
"The silver dragon suddenly dropped to all fours, clearly beset by some sort of agony, although Stoddard could not puzzle out what was happening."
"Leaving Lord Tuttlehope to puzzle out for himself what the languid Lady Deverell had to do with the matter, Will made his way to Miss Ashmore's side."
"As it was, though elevators and conveyor belts fell into disrepair, disuse, and finally into the oblivion of forgotten function, the essential machinery of the Ship continued its automatic service to its ignorant human freight, or waited, quiet and ready, for someone bright enough to puzzle out its key."