Solve the Maximum Months for 30 Card Players in 6 Groups of 5 | Maths Help

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To solve the problem of 30 card players forming 6 groups of 5 each month without repeating pairings, the maximum number of months they can play is limited by the combinations of players. Each player can only play with 4 others per month, leading to a need for a systematic rotation to avoid repeats. The suggested method involves redistributing players each month while ensuring that no two players from the same original group play together again. This approach can theoretically continue indefinitely if executed correctly, as long as the grouping and distribution are managed properly. The key is to maintain a structure that prevents any prior pairings from reoccurring.
rusty009
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Hi,

someone just asked me this on MSN and it's bugging me, here's the question

30 card players want to play in 6 groups of 5 every month, such that no player ever plays with another player again in a subsequent month.



What is the maximum number of months that the players could play under these rules? Why?

I'm not sure where to start and solve it really, first thoughts tell me permutations but can't really see how to do it, I've been out of this game for too long ! Any help would be appreciated, thanks in advance.
 
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Randomly pick 6 groups of 5, and let them play on one table each. The next month each player from one group distribute themselves to the other tables such that no two persons from one group is on the same table. Now let them play, and repeat the process next month. This can go on indefinitely.
 
I think the interpretation is that no two players which have previously played will play again.
 

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