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 dragonaut March 27th, 2013 12:46 PM

Conceptual real world math problem. Balls in Bags

No idea what math category this falls under but I've found myself up against a real world conceptual math problem involving one of my projects at work.

Hopefully someone can help me with this one.

Here's the concept:
There are a certain number of bags of different sizes, and a certain number of balls of different sizes. A bag of size 2 can hold a ball of size 2, or two balls of size 1, for example. If I'm given the size of each bag, and the size of each ball, I need a formula that will tell me if there is at least one arrangement that will fit all the balls into the bags.
If there is no formula is there at least a procedure that is guaranteed to produce the right arrangement? For example: Start with the largest bag and fill it with balls, starting with largest ball, then take the next largest bag.... etc.

How can this be done?

Much appreciated!

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