S: (n) problem (a question raised for consideration or solution) "our homework consisted of ten problems to solve"
S: (n) puzzle, puzzler, mystifier, teaser (a particularly baffling problem that is said to have a correct solution) "he loved to solve chessmate puzzles"; "that's a real puzzler"
S: (n) case (a problem requiring investigation) "Perry Mason solved the case of the missing heir"
S: (v) riddle (set a difficult problem or riddle) "riddle me a riddle"
S: (v) riddle, screen (separate with a riddle, as grain from chaff)
S: (v) permeate, pervade, penetrate, interpenetrate, diffuse, imbue, riddle (spread or diffuse through) "An atmosphere of distrust has permeated this administration"; "music penetrated the entire building"; "His campaign was riddled with accusations and personal attacks"