To determine a path through the 5 rooms with 16 doors, you would need specific information about the layout and connections between the rooms and doors. However, a general approach would be to create a systematic plan to enter each room and exit through different doors, ensuring that each door is used only once. You could employ a backtracking method to explore all possible routes, ensuring you cover all doors while avoiding repetition. Without a specific layout, a definitive path cannot be provided.
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