I wrote an article on the [Social Golfer Problem](http://www.maa.org/editorial/mathgames/mathgames_08_14_07.html), 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](https://math.stackexchange.com/questions/43995/unique-groups-for-game-tournament)

I compiled best-known solutions for pairs, triplets, and quadruplets at the [Social Golfer Problem Demonstration](http://demonstrations.wolfram.com/SocialGolferProblem/). 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?