TITLE: Unique Groups for Game Tournament
QUESTION [9 upvotes]: I am trying to put together a Munchkin game tournament where I am assuming I will have 16 people coming to my tournament. As part of that, I want to have as many games as possible where people are not playing against the same player twice. (So, every combination is unique.)
I can easily come up with these groups for three rounds of the tournament. Is it possible to do more? If so, can you point me in the right direction? Unfortunately, I think I am confusing my combinations and permutations and it's leaving me stumped.

REPLY [4 votes]: These kinds of problems can be difficult; see the discussion  Math Games: Social Golfer Problem about scheduling threesomes as well as foursomes playing concurrently, a topic called resolvable Steiner systems.  The case of 16 people in foursomes over 5 days is shown (both as a listing of 4-sets and as a strange diagram) in nearly the middle of that page/article.
Day 1: ABCD EFGH IJKL MNOP
Day 2: AEIM BFJN CGKO DHLP
Day 3: AFKP BELO CHIN DGJM
Day 4: AGLN BHKM CEJP DFIO
Day 5: AHJO BGIP CFLM DEKN