unusual scheduling?

[sezuh]

Hi Ian,
thanks ever so much for your suggestions in my other tread,I need your wonderful  help again, if I may?
do you have any ideas if those problem below can be solved or if they are covered in "The CRC Handbook of Combinatorial Designs" book?
1)foursome pairings for a total of 40 players, Each trio players, plays with all 39 possible partners exactly once,and every two players plays with all 39 possible partners exactly 19 times with 247 rounds?
2)foursome pairings for a total of 52 players, Each trio players plays with all 51 possible partners exactly once,and every two players plays with all 51 possible partners exactly 25 times with 425 rounds?
3)fivesome pairings for a total of 50 players, Each trio players plays with all 49 possible partners exactly once,and every two players plays with all 49 possible partners exactly 16 times with 196 rounds? I know it sounds crazy but do you think this is possible
to solve? If you can provideor suggestion for one round, I can manage to finish it hopefully??
I'll be very greatful if you could shed light to any one of those problem.
Thanks in advance for your help or suggestions.

[sezuh]

Hi Ian,
do you think those problem  are possible to solve?
I would very much appreciate your suggestions or help.
Thanks

[Ian Wakeling]

Sezuh,

If I have understood correctly, you are looking for a 'resolvable 3-design' where all possible triples of players occur exactly once - for example with 40 players and 247 rounds of foursomes, there are 2470 foursomes with 4 ways of taking a triple of players from each foursome, so 2470*4 which is the same as 40 choose 3.  The program that I used for the previous 50 player problem does not consider triples of players, so I can't offer any help there - all I can suggest is that you look for mathematical literature on these types of resolvable design.  The HCD book tells me that the unresolved foursome designs exist, so even if you followed this up you would not have an assignment of foursomes to rounds.

Ian.

[Ian Wakeling]

Sezuh,

I just found this article by Keith Mellinger, I think you should find it interesting.

Ian.

[sezuh]

Hi ian ,
thanks for the link its very interesting reading,i'll try some of the method in my day off see what I can do ?
In the mean time do you have in your computer system a solution for this?
fivesome pairings for a total of 25 players, every two players plays with all 24 possible partners exactly 8 times with 48 rounds?
thanks  ever so much for all the suggestions and help,very much appreciated.
Sezuh

[Ian Wakeling]

I am not sure how this differs from 8 copies of the affine geometry (which you could get from La Jolla or elsewhere).  

Ian.