Possibly you can clarify what you mean by an example, or by explaining the context more fully.
Tx for a keen answer! Sorry, my English is not brilliant, aspecially in the field of Math .
So, it is mainly educationally task. I have 36 ppl, which I have to divide into 6 full teams, (so, 6 ppl in an every team every round, team cannot be bigger or smaller then 6, every participant must have its new unique team next round). The task can be desribed to train skill of every individual involved in process, to make a teamwork with the completely "unknown" ppl. So, how times i can create an unique 6x6 team ( with no repeating team members) set?
My final purpose is to invent a kind of a scheme which team members will use to regroup into new teams. I also need this number of unique sets to plan, how many problems a teams will solve per one round.
To illustrate my problem, here is a solution ( made"by hand") for case of 9 ppl and 3x3 team ( teams are described in columns) :
1. round
a1 | b1 | c1 |
a2 | b2 | c2 |
a3 | b3 | c3 |
2. round | | |
a1 | a2 | a3 |
b1 | b2 | b3 |
c1 | c2 | c3 |
3. round | | |
a1 | b1 | c1 |
b2 | a2 | a3 |
c3 | c2 | b3 |
So I have 3 rounds to make 3x3 unique teams.
But I think you are asking about the number of ways to partition a set of 36 people into 6 teams of 6 each, where the order of the people in each team does not matter, and the order of the teams also does not matter. Is that right?
That's probably true, if I understood your sentence correctly.
Perhaps the sixes are not really teams, but groups sitting at a table playing some game as individuals, and you want to find the largest number of rounds you can play in which no two people ever play against one another (sit at the same table) more than once? That would make this a sort of tournament scheduling problem. You don't want ALL ways to partition, but a maximal set of partitionings under this condition.
This seems to be a good analogic exemple to me
Can you also tell us why you are asking,
Me and my friends have a unformal club, where we do play kind of Jeopardy game for teams. We have 6 stable teams, 6 ppl in each team. In January our club will have a 5-year anniversary, so just to make a challenge funnier, we have decided this time to make a mixed teams match every round.
and how you have tried to solve it?
Asked help to mathematicians in this forum Besides of satisfaction of my selfish needs, i assumed, it could be also an interesting case for solving.
We need to know what kind of help you need, particularly if this is an assignment for a class, but even if it is just a challenge you set for yourself, and want to learn from it (rather than just have someone do it for you).
But if I am interpreting it correctly, I think it is a rather difficult kind of problem.