puzzle over

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

: complicate, entangle

: to solve with difficulty or ingenuity

: 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

: forward beyond an edge or brink and often down

: across the brim

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

: so as to exceed or surpass

: excessive

: to an excessive degree