The phrase "to puzzle over" means to think deeply and carefully about something, often trying to figure out a problem or make sense of something that is confusing. Full definition
I had many brokers puzzle over why I would not buy their deals, even though they were cheap relative to their ratings. (alephblog.com)
It is absolutely * not * the same puzzle over and over, as others have said. (metacritic.com)
I actually prefer detective / mystery games with clever puzzles over the basic object search, as long as they are clever and not too easy or way too difficult. (lovemyfire.com)