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I have a maths question I can't wrap my head around.

Assume you have a container of volume X. You need to fill it with 4 types of boxes A, B, C, D of different sizes. A is the smallest box, B is three times bigger than A, C is 30 bigger than B and D is twice as big as C.

So: B = 3A, C = 30B = 90A, D = 2C = 60B = 180A

The capacity of the container is 40D (i.e. the container can hold a maximum of 40 size D boxes at one time).

Question: How many unique combinations of boxes can you have to fill the container? What is the distribution of the number of boxes? (Calculate min, max, mean and 95th percentile)

Julia
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  • One would think that the shape of the boxes matters, e.g. what if the container is really narrow and really long? – Bram28 Oct 30 '17 at 19:38
  • In this case it doesn't matter. The container can hold a max of 40D or 80C or 2400B or 7200A or any combination of them. – Julia Oct 30 '17 at 19:43
  • You can get inspiration here: https://math.stackexchange.com/questions/15521/making-change-for-a-dollar-and-other-number-partitioning-problems – Bram28 Oct 30 '17 at 19:50

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