From Longman Dictionary of Contemporary Englishpuzzle something ↔ out phrasal verbSOLVE/FIND THE ANSWERto solve a confusing or difficult problem by thinking about it carefully He lay looking at the ceiling, trying to puzzle things out. → puzzle→ See Verb table
Examples from the Corpus
puzzle out• Eight-twenty the cards and puzzles go out...• He lay in bed, for some time, and stared up at the ceiling trying to puzzle it out.• A puzzle solved itself out here. 