Tennis scheduling problem

Six friends share a winter indoor tennis contract that allows any four of them to play each Saturday morning for 30 weeks

NUM_WEEKS=30
GROUP_SIZE=6
NUM_PLAYERS_ON_COURT=4

Make a fair schedule such that

1. Every combination of 4 players is represented evenly
2. Everyone plays the same number of times
3. No one sits out on consecutive weeks.

Notes

1. The first condition can be met by enumerating all combinations of 4 people (6C4 = 15) and repeating them twice. If the number of weeks is not a multiple of 15, some combinations will occur 1 more time than the rest, but that cannot be helped.

2. The second condition is also tricky if N is not a multiple of 15. But it can be achieved for any multiple of 3 weeks (to be precise, it can be achieved when NUM_WEEKS * NUM_PLAYERS_ON_COURT is a multipe of GROUP_SIZE).

3. The only non brute force solution I know is a heuristic that mostly works, involving brute force for a few remaining cases. I ended up doing it partly manually and the final implementation is in hardcoded.py.

4. The interesting thing is condition #3 is easy to meet if we sacrifice the first condition that every combination be evenly represented. For example, We can have a simple round robin schedule where 1,2 sit out on week one, 3,4 on week two, 5,6 on week three, 1,2 again on week 4,....