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Conference rusure::math

Title:Mathematics at DEC
Moderator:RUSURE::EDP
Created:Mon Feb 03 1986
Last Modified:Fri Jun 06 1997
Last Successful Update:Fri Jun 06 1997
Number of topics:2083
Total number of notes:14613

1114.0. "Tournament problem!" by USMFG::AWHITNEY () Thu Aug 24 1989 12:25

    Can it be done??????
    
    	Design a tournament schedule for 28 or 32 players for 
    a 20 week duration with the following conditions..
    
    Players change partners and opponents each week so
    
    	a. No two players are partners more than once in the
    	   tournament.
    	b. No two players are opponents more than once in the
    	   tournament. 
    
    I sure could use some help.....
    
    Regards, Al
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1114.14GL::GILBERTOwnership ObligatesThu Aug 24 1989 14:435
    We had a previous problem like this (though I think it may have
    been smaller), which was solved with (methinks) FoxGlove, an AI
    language derived from LISP.
    
    I'll search for it.
1114.220 * 2 > 32DWOVAX::YOUNGWe're no worse than anyone else. :-( Sun Aug 27 1989 22:0322
    The problem as stated can NOT be done:
    
    	With 32 players there are 31 potential opponents for each player.
    	Each week a player will use up 2 more of their potential
    	opponents.
    
    	Therefore after 15 weeks there will be only one potential opponent 
    	left, not enough for another week of play.
    
    	20 weeks is clearly impossible under these rules.
    
    The maximum number of weeks for these rules is :
    
    		[  (Number of players - 1) / 2 ]
    
    For 32 players this is 15 weeks (for 28 players it is 13 weeks).
    
    It is pretty easy to solve this for 8 weeks.  12 weeks with a little
    more trouble.  15 weeks I am not so sure how to solve, but it should be
    possible.
    
    --  BArry
1114.3Is there a solution?ELIS::BUREMAFri Jun 14 1991 05:449
    Re: .1 and also my note 1304
    
    Did anyone ever find the solution to this problem? I have developed
    some algorithms for this problem, but they have runtimes of O(N!), so
    they are only usable for small N. This same problem is also addressed
    in the algorithms conference but the algorithms posted there are still
    O(N!)... 8-(
    
    Wildrik