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Social square - 16 players, 5 rounds (Read 23691 times)
George Nigriny(Guest)
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Social square - 16 players, 5 rounds
12/24/05 at 09:06:43
 
George Nigriny wrote posing this question:

My challenge isn't matching teams or player v. player, but rotating players on teams over a given number of matches.  It seems pretty simple to me but I'm having an awful time working it out and avoiding conflicts.
 
Here are the specifics:
 
Sixeen players.  Four teams each day.  One round of golf each day for five days (five rounds of golf).  Each player needs to be teamed with each other player once and only once.  Sixteen players is the right number of players to work for five rounds.  For example.
 
Day 1 (round one)
Team 1: players a,b,c,d
Team 2: players e,f,g,h
Team 3: players i,j,k,l
Team 4: players m,n,o,p
 
And so on, so that each day the teams are different and each player plays with each other player once and only once over the course of five days (rounds).

 
A plan popped out after some chicken scrawling, head scratching and click clacking on the keyboard.

A social square

ABCD EFGH IJKL MNOP
AEIM BFJN CGKO DHLP
AFKP BELO CHIN DGJM
AGLN BHKM CEJP DFIO
AHJO BGIP CFLM DEKN
This leads to an interesting question.  Can the generalized problem be solved?
Schedule m x m players to play in m+1 rounds of m teams of m players each, so that every player is paired with every other player only once.

I found a algorithm that seems to work when m is a prime number, stay tuned...
 
Sunday, February 8 2004, 10:44 pm
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Strike_Ump
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Posts: 6
Re: Social square - 16 players, 5 rounds
Reply #1 - 04/01/11 at 13:06:51
 
George,  
 
if you are still around i would love to know the conclusions of your problem. There is no way I can figure it out myself  Smiley
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Richard A. DeVenezia
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Re: Social square - 16 players, 5 rounds
Reply #2 - 04/02/11 at 08:07:19
 
Hi Strike_Ump:
 
There is a link on the learn more page, but here it is directly.
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