Max Number of Boxes in a Container - Deriving the Formula

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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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That's and extremely difficult problem. Probably the most efficient way to answer the question is "actually do it and see"!
 
There are actually some classic puzzles based on packing balls into boxes which can be surprisingly difficult.
 

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