Nohemi

In a foursome, each player plays with three others.

Thus for one player to play for six days [s]he would need eighteen other players for a total of 19.

Five days exactly uses up the fifteen possible opponents. Thus you have found the best possible solution.

Good Hunting!
RD

Nohemi,

After 5 days every pair has played together exactly once. After 6 days there will be 24 pairs who have played twice while the rest have played once. A balanced schedule does not exist. You can't do any better than repeating any one of the previous 5 days, or using a random sixth day. If you either of these, your schedule will be best possible.

--Victoria