



 
Each player plays with only 3 others each day. With an "incomplete design" like this it is very easy to avoid any two players playing together twice.On the first day they can play
On the second day slide the second row up 1, the third row up 2, and the last row up 3:
Do this again on each succeeding day. You can do this for up to seven days before anybody plays with the same person. This works because 28/4 = 7 is prime and greater than or equal to 5. If you wanted everybody to play with everybody else you would need at least 9 days so that a player could play the other (281) = 27 three at a time. Finding designs that let each pair play together exactly once is mach harder and cannot always be done. Good Hunting!  


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. 