Round Robin Tournament Scheduling

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Title: 26 teams playing 13 different games
Post by: hamouche on December 08, 2021, 07:26:14 AM

Hi guys, 
I am preparing a tournament in which 26 teams play 13 different games. Can someone help me with the scheduling. I can't find any mathematical model that fits this model and going with the trial and error  algorithm is too time consuming.

So not all teams will play against each others (logically) but all teams should play all games and I do not want to have a pattern ( for example for team B to always play after team A at a certain game)

Thank you:)

Title: Re: 26 teams playing 13 different games
Post by: Ian Wakeling on December 09, 2021, 03:24:25 AM

I think you mean a tournament with 13 rounds something like this:

(L E) (A R) (H Y) (N P) (T K) (Q D) (I W) (Z X) (O V) (B G) (M U) (C F) (J S)
(A S) (O P) (Q R) (T W) (Z Y) (B V) (H E) (C D) (M K) (L U) (J X) (I G) (N F)
(T D) (Z G) (M F) (Q U) (B S) (J W) (O X) (L P) (C E) (N Y) (I R) (A K) (H V)
(I Y) (H D) (T X) (A V) (O U) (Z F) (N K) (M S) (Q G) (C W) (B E) (J P) (L R)
(B W) (L Y) (I K) (J R) (N V) (H X) (C P) (T U) (A D) (Q F) (O G) (Z S) (M E)
(O F) (M W) (B P) (Z E) (C R) (L K) (Q S) (I V) (J Y) (A X) (N D) (H U) (T G)
(H R) (Q V) (Z D) (O K) (M X) (C G) (T Y) (J F) (B U) (I E) (L S) (N W) (A P)
(N X) (T F) (O S) (H G) (Q E) (M P) (A U) (B R) (Z W) (J K) (C Y) (L V) (I D)
(J U) (N S) (A E) (I F) (H W) (O R) (L G) (Q Y) (T P) (M V) (Z K) (B D) (C X)
(Q P) (B K) (C V) (M Y) (J D) (I U) (Z R) (N G) (L X) (H S) (A F) (T E) (O W)
(Z V) (C U) (J G) (B X) (L F) (N E) (M D) (A W) (I S) (T R) (H P) (O Y) (Q K)
(C K) (I X) (N U) (L D) (A G) (T S) (J V) (O E) (H F) (Z P) (Q W) (M R) (B Y)
(M G) (J E) (L W) (C S) (I P) (A Y) (B F) (H K) (N R) (O D) (T V) (Q X) (Z U)

where the rows could be rounds and the columns the 13 games.  It may look random, but it has been made from two orthogonal Latin squares (https://en.wikipedia.org/wiki/Mutually_orthogonal_Latin_squares), meaning that all games will be between 2 distinct groups of teams.  These are:
(A B C H I J L M N O Q T Z) and (D E F G K P R S U V W X Y)
If you don't tell the teams about this pattern, then I guess they are unlikely to notice it.