I wrote an article on the Social Golfer Problem, which has questions like:
Each day, 16 people play Munchkin in foursomes simultaneously. How many days can they play with no two people playing with each other twice? tournament
I compiled best-known solutions for pairs, triplets, and quadruplets at the Social Golfer Problem Demonstration. To compile this data, I had to read through a few hundred books and papers. Very often, an answer would be given in new-to-me difficult notation, or it would reference a previous paper, or it would just be "obvious".
Now that I am considered an "expert", I've been asked about quintets and sextets, and for larger number of groups. I don't recall seeing solutions for any of the below problems in the papers I perused, but it's possible I missed them.
- 30 play in groups of 3 each day. No two play together more than once. How many days?
- 33 play in groups of 3 each day. No two play together more than once. How many days?
- 36 play in groups of 3 each day. No two play together more than once. How many days?
- 40 play in groups of 4 each day. No two play together more than once. How many days?
- 44 play in groups of 4 each day. No two play together more than once. How many days?
- 48 play in groups of 4 each day. No two play together more than once. How many days?
- 52 play in groups of 4 each day. No two play together more than once. How many days?
- 25 play in groups of 5 each day. No two play together more than once. How many days?
- 30 play in groups of 5 each day. No two play together more than once. How many days?
- 35 play in groups of 5 each day. No two play together more than once. How many days?
- 40 play in groups of 5 each day. No two play together more than once. How many days?
- 45 play in groups of 5 each day. No two play together more than once. How many days?
- 50 play in groups of 5 each day. No two play together more than once. How many days?
- 55 play in groups of 5 each day. No two play together more than once. How many days?
- 60 play in groups of 5 each day. No two play together more than once. How many days?
- 36 play in groups of 6 each day. No two play together more than once. How many days?
- 42 play in groups of 6 each day. No two play together more than once. How many days?
- 48 play in groups of 6 each day. No two play together more than once. How many days?
- 54 play in groups of 6 each day. No two play together more than once. How many days?
- 60 play in groups of 6 each day. No two play together more than once. How many days?
- 66 play in groups of 6 each day. No two play together more than once. How many days?
- 72 play in groups of 6 each day. No two play together more than once. How many days?
Does anyone have any solutions to any of these?
A new (Dec 2020) paper on this topic uses symmetry to approach the problem, and publishes solutions for groups up to 50 participants: Breakout Group Allocation Schedules and the Social Golfer Problem with Adjacent Group Sizes