Round Robin - Ten Events, Fourteen Teams

[wallace1]

Hi!

I'm setting up a round-robin-esque event where there are 10 separate events and 14 different teams. It is important that each team participates in each event. It does not matter if each team plays each other team or if there are byes.

Could someone help with the set-up for that? What if there are 15 teams?

Thank you!

[Ian Wakeling]

Hi,

Would this schedule work for you?

(---) (A F) (---) (---) (C L) (G D) (H B) (K I) (J E) (M N)
(M J) (---) (---) (G E) (---) (A C) (K N) (H L) (D B) (F I)
(L E) (---) (H I) (M D) (A N) (K B) (C F) (---) (---) (G J)
(---) (---) (C N) (A I) (M B) (F E) (---) (J D) (G H) (L K)
(F B) (C E) (K J) (---) (D I) (H N) (M G) (---) (A L) (---)
(C K) (M I) (L F) (---) (J H) (---) (D E) (G N) (---) (A B)
(---) (D H) (G B) (L N) (K E) (---) (J A) (F M) (C I) (---)
(H A) (K G) (M E) (J B) (---) (---) (L I) (---) (F N) (D C)
(D N) (L B) (---) (H C) (F G) (J I) (---) (A E) (K M) (---)
(G I) (J N) (D A) (F K) (---) (L M) (---) (C B) (---) (H E)

The 14 teams are the letters A to N, and rows could be rounds and the columns events.

15 (or in fact any odd number of teams) is difficult, as no balanced schedule like the one above can exist.

[ironlionzion13]

Hi Ian - just found this post after searching for weeks trying to schedule an event I'm throwing in a few weeks. I'm in a fairly similar situation to the OP of this thread. The event will have 9 different activities & I'd ideally like to have a round robin tournament where each team plays each other team one time & each team plays each activity one time. If teams need to play an activity or team more than once or have a bye round, etc, so be it (I'd prefer it to work out perfectly where no games/teams are repeated or skipped but have a feeling that won't be possible).

Like I said, there will be 9 activities but I won't know the actual number of teams until the day of the event (people are terrible at RSVPing...). Is there a formula or site where I can plug in the number of teams & have it spit out a round by round schedule optimized to my desired set up?

Thanks so much - definitely bit off more than I could chew putting this event on!

[tpierick]

Hey I'm trying to find something very similar to this. Did you have any luck? I can't figure it out for the life of me. 14 teams playing each other once and each game once without repeating games or opponents. Thanks

[wallace1]

Ian- Thank you very much. This looks great. The event is already exceeding our expected capacity. Is it easy to expand this schedule to if there were still 10 events but with 16 and 18 teams?

tpierick - I ran through the schedule as Ian posted it, it will work perfectly for 14 teams for 10 events, without teams playing each other more than once and with each team participating in each event.

[Ian Wakeling]

@wallace1 -  I have put schedules below for 16, 18 and 20 teams.

10 events 16 teams

(I N) (G J) (A C) (E O) (D L) (---) (K B) (---) (H F) (P M)
(H D) (---) (B F) (P L) (O M) (G C) (---) (K I) (A N) (E J)
(A L) (K N) (---) (---) (H C) (P I) (G M) (B J) (D E) (O F)
(O C) (H L) (I J) (G K) (---) (B M) (E F) (P N) (---) (A D)
(K F) (D M) (---) (---) (G P) (A J) (O N) (E H) (I C) (B L)
(---) (I B) (H M) (D N) (A E) (K L) (P C) (G F) (O J) (---)
(---) (E C) (G N) (I M) (K J) (D F) (H A) (O L) (B P) (---)
(B G) (P F) (D O) (H J) (---) (E N) (I L) (A M) (---) (K C)
(E M) (O A) (P K) (B C) (I F) (---) (D J) (---) (G L) (H N)
(P J) (---) (E L) (A F) (B N) (O H) (---) (D C) (K M) (I G)

10 events 18 teams

(O H) (F M) (N I) (G D) (---) (C R) (P Q) (E J) (B A) (L K)
(N K) (C Q) (---) (E A) (O R) (J H) (B D) (P M) (L F) (G I)
(E Q) (L R) (F A) (C K) (P G) (B M) (N H) (---) (O I) (J D)
(G M) (---) (O D) (L H) (J A) (F N) (E R) (C I) (P K) (B Q)
(F D) (G H) (C B) (J I) (E M) (L Q) (O K) (N R) (---) (P A)
(P R) (B O) (E K) (F Q) (L I) (---) (J M) (G A) (N D) (C H)
(B I) (E D) (J R) (N P) (F H) (G K) (L A) (O Q) (C M) (---)
(---) (N A) (P H) (O M) (B K) (E I) (G C) (L D) (J Q) (F R)
(J L) (P I) (G Q) (B R) (C D) (O A) (---) (F K) (E H) (N M)
(C A) (J K) (L M) (---) (N Q) (P D) (F I) (B H) (G R) (O E)

10 events 20 teams

(S G) (Q C) (R P) (A N) (F I) (D H) (E J) (T O) (M L) (B K)
(T K) (B N) (S I) (D C) (M H) (E P) (A L) (R J) (F O) (Q G)
(B J) (T P) (F C) (R L) (A G) (S N) (M I) (Q K) (E H) (D O)
(Q H) (D L) (M O) (T J) (S K) (B C) (F P) (E G) (R N) (A I)
(D I) (A J) (E K) (B H) (R O) (F L) (Q N) (M C) (T G) (S P)
(R C) (E O) (A H) (F K) (Q J) (T I) (D G) (S L) (B P) (M N)
(M P) (F G) (Q L) (E I) (T C) (A K) (B O) (D N) (S J) (R H)
(F N) (M K) (D J) (S O) (B L) (R G) (T H) (A P) (Q I) (E C)
(A O) (R I) (B G) (Q P) (E N) (M J) (S C) (F H) (D K) (T L)
(E L) (S H) (T N) (M G) (D P) (Q O) (R K) (B I) (A C) (F J)

@tpierick - I am not sure what you are asking for, so you may need to clarify.  If you have 13 events and 13 rounds, then it is possible to have all 14 teams play each other exactly once.  Does that work? For example:

(B H) (---) (K N) (---) (G I) (F D) (E C) (A L) (---) (---) (---) (---) (J M)
(---) (---) (B D) (K C) (---) (---) (I L) (J G) (N E) (M A) (---) (---) (H F)
(C N) (---) (---) (I D) (A J) (K E) (---) (M H) (F G) (L B) (---) (---) (---)
(---) (---) (---) (---) (H D) (L N) (G B) (---) (C M) (---) (J E) (I F) (K A)
(K G) (C J) (---) (B A) (---) (---) (D M) (E F) (---) (---) (L H) (---) (I N)
(---) (A H) (---) (---) (N F) (---) (---) (K D) (---) (E I) (M G) (J L) (C B)
(---) (D E) (J H) (N G) (L C) (M B) (F A) (---) (---) (---) (K I) (---) (---)
(I M) (---) (E L) (J F) (---) (A G) (---) (---) (---) (H N) (D C) (K B) (---)
(L F) (B I) (---) (H E) (K M) (---) (N J) (---) (---) (G D) (---) (A C) (---)
(E A) (M N) (G C) (---) (---) (---) (---) (---) (H I) (K J) (F B) (---) (L D)
(---) (G L) (---) (---) (---) (I J) (K H) (N B) (D A) (F C) (---) (E M) (---)
(---) (K F) (A I) (M L) (---) (C H) (---) (---) (B J) (---) (---) (D N) (G E)
(D J) (---) (F M) (---) (B E) (---) (---) (C I) (K L) (---) (N A) (H G) (---)

@ironlionzion13 - Like tpierick, I think you may be looking for a full round robin where each team plays each other exactly once.  This constrains the problem to situations where there is an even number of teams - call this number 2n - and also there must be 2n-1 activities and rounds.  So the only nice solution to the problem as you state it, is to have 10 teams and 9 activites, for example:

(B F) (J C) (G E) (---) (D H) (A I) (---) (---) (---)
(E D) (---) (---) (J A) (---) (---) (C B) (G I) (F H)
(---) (---) (---) (I F) (---) (E B) (J G) (C H) (D A)
(---) (---) (---) (D B) (C A) (H G) (F E) (---) (J I)
(J H) (I E) (B A) (G C) (---) (---) (---) (F D) (---)
(I C) (H B) (J D) (---) (G F) (---) (---) (A E) (---)
(A G) (---) (F C) (E H) (---) (---) (I D) (J B) (---)
(---) (D G) (---) (---) (B I) (J F) (H A) (---) (E C)
(---) (A F) (H I) (---) (J E) (C D) (---) (---) (B G)

[wallace1]

Ian- Thank you so much! This is a tremendous help, and I appreciate your prompt assistance.

[ironlionzion13]

That program is a lifesaver Ian. Can't thank you enough!