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

  • Context: Undergrad 
  • Thread starter Thread starter rusty009
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SUMMARY

The problem involves organizing 30 card players into 6 groups of 5, ensuring that no player plays with another player more than once. The maximum number of months these players can continue this arrangement is 6 months. This is achieved by rotating players among groups each month while adhering to the rule that no two players from the same original group can play together again. The solution relies on combinatorial principles and the concept of graph theory to ensure unique pairings.

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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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