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Grouping Elements

  1. Dec 5, 2009 #1
    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?
  2. jcsd
  3. Dec 6, 2009 #2


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    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...

    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.
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