puzzle over

:  to offer or represent to (someone) a problem difficult to solve or a situation difficult to resolve :  challenge mentally

:  to exert (oneself, one's mind, etc.) over such a problem or situation

:  complicate, entangle

:  the state of being puzzled :  perplexity

:  something that puzzles

:  a question, problem, or contrivance designed for testing ingenuity

:  across a barrier or intervening (see intervene 4) space

:  across the goal line in football

:  forward beyond an edge or brink and often down

: used as a function word to indicate motion or situation in a position higher than or above another

: used as a function word to indicate the possession of authority, power, or jurisdiction in regard to some thing or person

: used as a function word to indicate superiority, advantage, or preference

:  upper, higher

:  outer, covering

:  excessive

:  to leap over