puzzle vs excogitate

puzzle is a noun but excogitate is not a noun.

Word	Noun	Adjective	Verb	Adverb
puzzle	Yes	No	Yes	No
excogitate	No	No	Yes	No

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

puzzle: be uncertain about; think about without fully understanding or being able to decide
excogitate: reflect deeply on a subject

puzzle (noun)	excogitate (noun)
a game that tests your ingenuity
a particularly baffling problem that is said to have a correct solution

puzzle (verb)	excogitate (verb)
be a mystery or bewildering to	reflect deeply on a subject
be uncertain about; think about without fully understanding or being able to decide	come up with (an idea, plan, explanation, theory, or principle) after a mental effort