10 Team Round Robin Tournament - 3 Tunnels/Fields/Courts

[Jmcmahon82]

Hi everyone!
Looking to make a 10 Team Round Robin Tournament. No eliminations. All teams play each other 1 time.

There are 3 "fields" available (batting cage tunnels).

All teams need to play each other once.
We don't want any team to have back to back byes.

That's about it for requirements.

An Excel form would be great, but clearly not necessary.

[Ian Wakeling]

I think the following schedule will work for your tournament :

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

There are 15 rounds and every team has 6 byes. None of the byes are back-to-back as you can see from the binary table below which has a 1 if a team plays in a round and a zero if they have a bye:

     A B C D E F G H I J
R001 1 1 1 1 0 0 1 1 0 0
R002 0 0 0 1 1 1 0 1 1 1
R003 1 1 1 0 1 0 1 0 0 1
R004 1 0 1 1 0 1 0 1 1 0
R005 0 1 1 0 1 0 1 0 1 1
R006 1 1 0 1 0 1 0 1 0 1
R007 0 0 1 1 1 1 1 0 1 0
R008 1 1 0 0 1 0 0 1 1 1
R009 0 1 1 1 0 1 1 0 0 1
R010 1 1 0 0 1 1 0 1 1 0
R011 1 0 1 1 0 0 1 1 0 1
R012 1 1 0 0 1 1 1 0 1 0
R013 0 0 1 1 1 0 0 1 1 1
R014 1 1 0 1 0 1 1 0 1 0
R015 0 0 1 0 1 1 1 1 0 1

[Jmcmahon82]

This was perfect! Nice!

Would you be able to do an 8,9,11,12 team scenario just like this one?

PM me an email address/contact info and I'd happily compensate for the time!

[Ian Wakeling]

Here are options for 11 and 12 teams, I will look at 8 and 9 later.

With 11 teams there is a short first round with just one game, so it is impossible to avoid back-to-back byes for all teams in rounds 1 & 2, but you could give teams different start times to avoid the issue.

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

     A B C D E F G H I J K
R001 0 0 1 1 0 0 0 0 0 0 0
R002 0 1 0 0 1 1 1 0 0 1 1
R003 1 0 1 1 1 0 0 1 1 0 0
R004 0 1 0 0 1 1 1 0 0 1 1
R005 1 0 1 1 0 0 0 1 1 0 1
R006 1 1 0 0 1 1 1 0 0 1 0
R007 0 0 1 1 0 0 0 1 1 1 1
R008 1 1 0 0 1 1 1 0 1 0 0
R009 1 0 1 1 0 0 0 1 0 1 1
R010 0 1 0 0 1 1 1 1 1 0 0
R011 1 1 1 1 0 0 0 0 0 1 1
R012 0 0 1 0 1 1 1 1 1 0 0
R013 1 1 0 1 0 1 0 0 0 1 1
R014 0 0 1 0 1 0 1 1 1 1 0
R015 1 1 0 1 0 1 0 0 1 0 1
R016 0 1 1 0 1 0 1 1 0 1 0
R017 1 0 0 1 0 1 1 0 1 0 1
R018 1 1 1 0 1 0 0 1 0 1 0
R019 0 0 0 1 0 1 1 1 1 0 1


With 12 teams there are 22 rounds and teams have as many byes as games, I think some level of back-to-back byes is unavoidable - I count 7 of them below (they happen for teams A,B,D,E,F,H and J).

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

     A B C D E F G H I J K L
R001 0 1 0 1 1 1 0 1 0 1 0 0
R002 1 0 1 0 0 0 1 0 1 0 1 1
R003 0 1 0 1 1 1 0 1 0 1 0 0
R004 1 0 1 0 0 0 1 0 1 0 1 1
R005 0 1 0 1 1 1 0 1 0 1 0 0
R006 0 0 1 1 0 0 1 0 1 0 1 1
R007 1 1 0 0 1 1 0 1 0 1 0 0
R008 0 0 1 1 0 0 1 0 1 0 1 1
R009 1 1 0 0 1 1 1 0 1 0 0 0
R010 0 0 1 1 0 0 0 1 0 1 1 1
R011 1 1 0 0 1 1 1 0 1 0 0 0
R012 0 0 1 1 0 0 0 1 0 1 1 1
R013 1 1 0 0 1 1 1 0 1 0 0 0
R014 0 0 1 0 0 1 0 1 0 1 1 1
R015 1 0 0 1 1 0 1 1 1 0 0 0
R016 0 1 1 0 0 1 0 0 0 1 1 1
R017 1 0 0 1 0 0 1 1 1 1 0 0
R018 0 1 1 0 1 1 0 0 0 0 1 1
R019 1 0 0 1 0 0 1 1 1 1 0 0
R020 0 1 1 0 1 1 0 0 0 0 1 1
R021 1 0 0 1 0 0 1 1 1 1 0 0
R022 1 1 1 0 1 0 0 0 0 0 1 1

[Ian Wakeling]

Here are 8 and 9 as promised.  Hope that helps.


8 teams:

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

     A B C D E F G H
R001 0 0 0 0 0 1 0 1
R002 1 1 1 1 1 0 1 0
R003 1 0 0 1 1 1 1 1
R004 1 1 1 1 1 1 0 0
R005 0 1 1 0 1 1 1 1
R006 1 1 1 1 0 0 1 1
R007 0 1 0 1 1 1 1 1
R008 1 1 1 1 1 0 0 1
R009 1 1 1 0 1 1 1 0
R010 1 0 1 1 0 1 1 1

9 teams:

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

     A B C D E F G H I
R001 1 0 0 1 1 1 0 1 1
R002 0 1 1 1 1 0 1 0 1
R003 1 1 1 0 0 1 1 1 0
R004 1 0 0 1 1 1 0 1 1
R005 0 1 1 1 1 0 1 0 1
R006 1 0 1 1 0 1 1 1 0
R007 1 1 0 0 1 1 1 0 1
R008 0 1 1 1 0 1 0 1 1
R009 1 1 0 1 1 0 1 1 0
R010 0 1 1 0 1 1 1 0 1
R011 1 0 1 1 1 0 1 1 0
R012 1 1 1 0 0 1 0 1 1