



 
Don, It is hard to find the "best" schedule for 11 players over 6 rounds. I have a program to do that and it is running, but it could take a long time as there are about $2000^5$ possibilities to check. As a first step, the program finds a schedule that is "close to" balanced. The best one it found is copied below.
The way to read it is that the players are the 11 positions in the sequence and the numbers indicate the groups. One Day 1 the groups are 1, 2, 3, 4; 5, 6, 7, 8; 9, 10, 11. On Day 2 group zero is 1, 2, 5, 8, and so on. There are a couple of flaws. For one, player 1 is always in group zero. For another, some players are together 4 times. In a perfect world (which probably does not exist), no pair of players would be together more than two times. On the other hand, in a perfect world some pairs of players would play together only once, and I think that that this schedule has every pair of players together once (though I did not check carefully). If an improvement is found, I will send a followup answer. A feasible alternative is to try generating a few million schedules at random and then sending the "best" one of those. Victoria Don Responded
Hi Don, Rather than number the players from 1 to 11 I named them with letters, A, B, C, ... up to K. I then redid Victoria's table with the players names at the head of each column. Each day there are three groups, group zero which is a foursome, group one which is a foursome and group two which is a threesome. To see which group a player is with on any day look down the column. For example player C is in group zero on day 1, group one on day 2, group zero on day 3, group one on day 4, and the threesomes on days 5 and 6.
Does this help? Don wrote again
Don, It isn't so easy to make a few small changes and not spoil the balance completely. The way my program currently works is based on the false assumption that the groups are the same size. Since, in that case, the groups could be renumbered, it is ok to always put player 1 in group number 1, and of player 2 is not also in group 1, then s/he can go in group 2. I've made a try at changing the schedule. But really I am just eyeballing it. You can probably do at least as well as me.
Victoria  


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