Puzzle over
Definition 1 of 1
Pro Tip 1/3Deep Thought
Indicates spending a long time thinking about something complex or confusing. 
He puzzled over the mysterious poem, trying to unlock its meaning.
Pro Tip 2/3Problem Solving
Used when trying to find a solution to a difficult problem or situation. 
They puzzled over how to fix the engine with the limited tools they had.
Pro Tip 3/3Mental Engagement
Requires active engagement of the mind, not just casual thinking. 
The scientist spent nights puzzling over the data, seeking a breakthrough.