Can you always pack smaller rectangles into a single unique bigger rectangle (known in advance) without overlapping if
- Every smaller piece fits inside the bigger rectangle individually.
- The total volume of all the smaller pieces is less than or equal to the bigger rectangle.
I don't want the exact packing, instead I just want to know if I can safely assume that there must exist a solution if the above conditions are met.
Context: I need to extend this to three dimensions and need a simple and fast heuristic to tell me if a possible solution can theoretically exist or not.