12 Team Tournament (need reply by 7/6 am)

[MikeMack]

I've seen several examples of 12 team tournaments but I haven't found one that meets my criteria for my BeerLympics this Sat. (7/6) and foolish me thought this would be an easy setup - which after days of trying and even resulting in collaborating with Chat GPT have left me with no results...

Here are the tournament parameters:
- 12 teams
- I have an unlimited amount of games (cornhole, flip cup, Beerio Kart, JackBox Trivia, etc.) I can utilize so I'm flexible on this.
- There are 2 sets of rounds to be played with a break in between, a halftime
----- ex. if there are 11 unique games for the entire tournament then a set of 6 unique game would be played followed by a break and then another set of 5 different games would be played

Tournament Structure:
- Each team MUST play each game exactly once
- Every team to play each other team once but not more than 2x
----- Preferably each team would play each other team EXACTLY once
- We can add a bye for each team if needed to fulfill the requirements of the tournament structure
----- If a bye is added, then each team will have to have a bye

Is this structure even possible? If not, is it possible with 10 or 14 teams?

[Ian Wakeling]

There is a 10 team schedule here and a 12 team schedule here that should help.  These have the properties that you want, each team exactly once in each row and in each column, and all teams player each other exactly once.  I could find the 14 team version if you wish.

[MikeMack]

Thanks for your reply Ian!
I saw this post, but I have 6 games the first set, then a halftime, then 5 more games after.

I'm doing this because of the limited space. I have to run a set of 6 games and have every team play those 6 games first.
Then those games go away, I use the halftime to set up the 5 new games, and then every team plays those 5 games - all without playing another team again and having played every game exactly once.

The issue in your suggested schedule is that it includes all 11 games as a possibility for any given round.

Is what I'm asking for possible?

[Ian Wakeling]

Yes, this is possible by rearranging the 12 player schedule you can find in reply #1 here.  For example:

      G1    G2    G3    G4    G5    G6    G7    G8    G9   G10   G11   Bye
 R1 (F D) (J K) (A G) (E L) (C H) (I B)
 R2 (E J) (H F) (B K) (I C) (L G) (A D)
 R3 (L I) (G B) (J H) (K D) (E A) (C F)
 R4 (G C) (L A) (I D) (J B) (F K) (E H)
 R5 (H K) (I E) (L C) (F A) (D B) (G J)
 R6 (A B) (C D) (E F) (G H) (I J) (K L)
 R7                                     (D H) (K G) (C E) (I F) (J L) [A B]
 R8                                     (B L) (F J) (K I) (E G) (A H) [C D]
 R9                                     (C J) (D L) (H B) (K A) (G I) [E F]
R10                                     (A I) (B E) (L F) (D J) (C K) [G H]
R11                                     (K E) (A C) (G D) (H L) (B F) [I J]
R12                                     (F G) (H I) (J A) (B C) (D E) [K L]