My brother wants to solve this math thingy for a potential game that he's making. Basically he wants to group 15 people into 3 groups of 5 people each. He wants this to happen 7 times where any given person is only in a group with another person twice and no more.

For example, each of these letters represent a person.

a, b, c, d, e, f, g, h, i, j, k, l, m, n, o.

1st round:
1st group: abcde
2nd group: fghij
3rd group: klmno

2nd round:
1st group: ?????
2nd group: ?????
3rd group: ?????

...

7th round:
1st group: ?????
2nd group: ?????
3rd group: ?????

I was thinking of running a C++ program to solve this, but my coding skills are pretty weak and I'm having a hard time thinking about how this would go together. Perhaps some math genius in the probability section could help me solve this.

I tried looking at smaller groups that are easier to solve to try and recognize some patterns, but part of me is wondering if this is just trial and error. As far as I know this might not even be possible.

This should be in SMP

Perhaps it should. Didn't see that spot in other topics as I don't frequent that part of the forum. I thought since it has something to do with combinations that it would fit in probability.

I guess it could since you could turn such questions into a bet.

Sounds like a matchmaker algorithm, used to create games of randomized opponents in a pvp setting. Will be harder the fewer the participants are, which is true for pvp lobbies of new or unpopular games.