Minimum number of common elements in sets

In summary, the conversation discusses the question of how to distribute 500 non-identical items into sets of 40, while minimizing the number of common items in any two sets. The poster is asking for an algorithm to calculate this minimum number, and clarifies that there is an unlimited quantity of each item. They provide an example of preparing gift boxes for children, with 500 boxes and 500 different gifts.
  • #1
kamarala
2
0
Hello,

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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  • #2
So some of the 500 items are identical, but not all of them? How many of each identical set are there?
 
  • #3
nonvestigial said:
So some of the 500 items are identical, but not all of them? How many of each identical set are there?

Hmm, I think I was not clear enough, my bad.

I have unlimited quantity of each item. I would like to fill in the boxes with 40 items and I would like to keep the number of common items in any box to a minimum.

Like, I have 500 different gifts (with unlimited quantity) to choose from and I would like to prepare gift boxes for children and I will put 40 gifts in each of them. I want to keep the boxes that any 2 children gets as different as possible.

I hope I could make it clear.

Edit: And there are a total of 500 boxes / children.
 
Last edited:

What is the definition of minimum number of common elements in sets?

The minimum number of common elements in sets refers to the smallest number of elements that are present in all given sets.

How is the minimum number of common elements in sets calculated?

The minimum number of common elements in sets is calculated by finding the intersection of the sets, which is the set of all elements that are present in all given sets. The size of this intersection set is the minimum number of common elements.

Why is the minimum number of common elements in sets important?

The minimum number of common elements in sets is important because it represents the smallest set of elements that can be used to describe the given sets. It can also help identify relationships and patterns between sets.

Can the minimum number of common elements in sets be zero?

Yes, the minimum number of common elements in sets can be zero if there are no elements that are present in all given sets. This means that the sets do not have any common elements.

How can the minimum number of common elements in sets be used in real-world applications?

The minimum number of common elements in sets can be used in various fields such as statistics, data analysis, and computer science to identify similarities and differences between sets. It can also be used in pattern recognition and data mining to make predictions and classifications.

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