How can I figure out what size shipping box I need based on multiple different smaller boxes?

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Is there a math formula I can use to provide a guideline of what length x width x height box I would need to buy based on smaller individual boxes that I want to put inside this larger box?

For example, if I have the following box dimensions; what large box size would I need to buy to fit these packages inside it?

  • Box # 1: 15 x 10 x 5
  • Box # 2: 10 x 8 x 3
  • Box # 3: 5 x 3 x 2
  • Box # 4: 11 x 9 x 8
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In general, this problem is very hard. See for example this paper. For the particular example you quote, an informal approach using common sense and trial-and-error is as good as any.