infer vs puzzle out

infer and puzzle out both are verbs.

Word	Noun	Adjective	Verb	Adverb
infer	No	No	Yes	No
puzzle out	No	No	Yes	No

As verbs, puzzle out is a hypernym of infer; that is, puzzle out is a word with a broader meaning than infer:

infer: guess correctly; solve by guessing
puzzle out: find the solution to (a problem or question) or understand the meaning of

Other hypernyms of infer include figure out, lick, solve, work, work out.

infer (verb)	puzzle out (verb)
reason by deduction; establish by deduction	find the solution to (a problem or question) or understand the meaning of
believe to be the case
guess correctly; solve by guessing
conclude by reasoning; in logic
draw from specific cases for more general cases