Grouping Elements: Making m Groups of n Elements w/ t Uses

In summary, the conversation discusses how many groups of size m can be made from n elements, where each element is used the same number of times t. It also raises the question of whether this number is infinite if repetition is allowed. An example is given of 8 teams being grouped in triplets, with the requirement of each team playing the same number of times. The possibility of using different numbers in each triplet is also mentioned.
  • #1
kaleidoscope
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How many groups size m can you make from n elements (m<n) such that each element is used the same number of times t (t>0)?

For instance, if you have 8 teams and group them in triplets, how many triplets do you need so that each team plays the same number of times?
 
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  • #2
kaleidoscope said:
How many groups size m can you make from n elements (m<n) such that each element is used the same number of times t (t>0)?

Why wouldn't this be infinite? If repetition is allowed, you can make n groups, each containing m repetitions of the nth element. You can also make 2n groups (so 2 groups contain repetitions of the same element), or 3n, or 4n...

For instance, if you have 8 teams and group them in triplets, how many triplets do you need so that each team plays the same number of times?

Would (1,1,1),(2,2,2),(3,3,3)...(8,8,8) be valid? Of course you can switch the numbers around; each team just needs to play 3 times.
 

Related to Grouping Elements: Making m Groups of n Elements w/ t Uses

What is the purpose of grouping elements?

The purpose of grouping elements is to organize a set of elements into smaller subsets based on a specific criteria. This can help in analyzing and understanding the properties and patterns of the elements more easily.

What is the formula for making m groups of n elements with t uses?

The formula for making m groups of n elements with t uses is m = t/n. This means that the total number of groups (m) is equal to the total number of uses (t) divided by the number of elements in each group (n).

How do you determine the number of elements in each group?

The number of elements in each group is determined by dividing the total number of elements by the total number of groups. For example, if there are 100 elements and 5 groups, then there will be 20 elements in each group.

What is the advantage of grouping elements?

The advantage of grouping elements is that it allows for easier data analysis and understanding of the elements. By breaking down a large set of elements into smaller groups, patterns and relationships between the elements can be identified more easily.

Can elements belong to more than one group?

Yes, elements can belong to more than one group. This is known as overlapping groups and it allows for a more flexible and comprehensive grouping system.

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