puzzle
n. a particularly baffling problem that is said to have a correct solution: He loved to solve chessmate puzzles. v. be uncertain about; think about without fully understanding or being able to decide: We puzzled over her sudden departure.
debate
n. 1. the formal presentation of and opposition to a stated proposition (usually followed by a vote.) 2. a discussion in which reasons are advanced for and against some proposition or proposal v. argue with one another: We debated the question of abortion.