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puzzle out (something)
To determine, clarify, or realize something through careful thought or consideration. They're still puzzling out how to get the system back online without losing any data. It took me a while, but I think I was able to puzzle out the solution to this riddle.
puzzle something out
to figure something out. It took me a while to puzzle it out. I can't puzzle out the meaning of this argument.
Clarify or solve something, as in It took him a while to puzzle out the significance of the statement. [Late 1700s]
To come to a conclusion or find an answer, especially as the result of a careful thought process: I puzzled out the identity of the murderer before finishing the novel. The answer escaped me at first, but I finally puzzled the problem out.