Probably simple combinatorics problem

Fudge

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Jul 9, 2017
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I have really no idea what I'm doing in the realm of combinatorics, so this problem has pretty thoroughly stumped me. I'd probably have more to say, but I do not have a paper in pencil right now (long story) so doing this kinda work, mmmmmmmmeeeeeeeeeeehhhhhh. Also, sorry if I've put this in the wrong category, this is a gray branch after all

Anyway, the problem is a weird variation of the Kirkland Schoolgirl Problem, really the reverse of it, actually.

If I have n objects, and I group them in every possible arrangement of x, where n>x, how many interactions would I have to make to ensure atleast one interaction is present in every possible group, and how would I arrange said interactions


Or,


I have a large group of 25 school children, some of these children are friends with one another, what is the optimal way (The fewest friendships having to be formed before hand) for every single group of 6 students to have at least one friendship among them.

Oh, if you're curious, a friend of mine is making an unorthodox fighting game, where the school children are fighters, and the friendships are little voice blurb interactions.

Thank you a lot in advanced.
 
Why don't you start with PUTTING one interaction in each group and then seeing what you have left?
 
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