This puzzle says: A man enters a room with two doors. One door is open, one is closed. He walks through neither. How?
The important detail is that the riddle only says the room has two doors. It does not say the man must leave through one of them.
One possible answer is that he leaves through a window.
If the room has a window or another opening, he can enter the room and later leave without walking through either of the two doors. The puzzle encourages you to assume that a door must be used simply because the doors are specifically mentioned.
Like many lateral-thinking riddles, the solution comes from questioning an assumption that was never actually stated in the question.
