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Let's say I have 500 boxes and 500 hundred non-identical items.

I would like to have sets of 40, chosen among those 500 hundred items and my objective is to keep the number of same items in any 2 boxes at a minimum.

1. What would be that minimum number of common items?

2. If it's not easy to calculate, could someone suggest an algorithm. I can write little php, so I may try to get it calculated.

Thanks in advance.

p.s. I'm asking it here, hoping that someone smarter than me could come up with a quick way to calculate it. Of course, I'm not expecting anyone to spend much time on it to solve it for me, but it would nice to know if there are no short-cuts to calculate it.

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# Minimum number of common elements in sets

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