Max Number of Boxes in a Container - Deriving the Formula

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In summary, the conversation discusses the maximum number of rectangular boxes that can be put into an empty container and how to arrange them to optimize the number of boxes. There is a question about deriving a formula for this problem, but it is suggested that the best way to find the answer is through trial and error. The conversation also mentions that there are some classic puzzles related to packing objects into containers that can be challenging.
  • #1
realler
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just got a interesting question from my friend...

there is an empty container.
different sizes of rectangular boxes are to put into it

1.what is the maximum number of boxes can be put into it? and
2.how to arrange them to optimize the number of boxes?

Can anyone derive the formula on this questions ??


it seems to me that an infinite amount of boxes can be put in it.. coz the question didnt limit the size... so .. if the size of the boxes approahes 0... the there can be unlimited number of boxes.....
hmmm... what do u guys think?
 
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  • #2
That's and extremely difficult problem. Probably the most efficient way to answer the question is "actually do it and see"!
 
  • #3
There are actually some classic puzzles based on packing balls into boxes which can be surprisingly difficult.
 

What is the formula for calculating the maximum number of boxes that can fit in a container?

The formula for calculating the maximum number of boxes that can fit in a container is: (Container Length / Box Length) x (Container Width / Box Width) x (Container Height / Box Height).

What are the factors that affect the maximum number of boxes that can fit in a container?

The factors that affect the maximum number of boxes that can fit in a container are the dimensions of the container and the dimensions of the boxes being used.

Can the formula for calculating the maximum number of boxes in a container be applied to any type of container?

Yes, the formula can be applied to any type of container as long as the dimensions of the container and the boxes are known.

Is there a way to maximize the number of boxes that can fit in a container?

Yes, the number of boxes can be maximized by using boxes that have the smallest dimensions possible and arranging them in a way that minimizes empty space in the container.

What is the significance of knowing the maximum number of boxes that can fit in a container?

Knowing the maximum number of boxes that can fit in a container is important for efficient packaging and transportation, as it helps to minimize wasted space and reduce costs.

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