Round Robin Tournament Scheduling

10 Rounds, X teams, X locations

esavs08 · 6 · 3874

esavs08

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on: July 31, 2015, 04:37:18 PM
Hi All,

I am trying to schedule a round robin style event.  There will only be 10 rounds, no matter how many teams (some teams will not play each other, that is fine).  The number of teams could be 12, 14, 16, 18, 20, 22, 24, 28, or 32 (the number varies every year; if an odd number, there is a ghost team).  I would like to have schedules for all scenarios.

Requirements:
- 10 rounds only, no exceptions
- No team plays a team twice*
- No team plays at a location twice*
- *minimum of 10 locations, max of 16 locations - the number of locations is dependent on the number of teams; if 18 or fewer teams, then some will play each other twice and play at a location twice, that is fine.
- Some teams won't play each other when the # of rounds to complete the true round robin exceeds 10, that is fine.

See the attachment for my blank "template", maybe this will help.

Any one have scheduling ideas?  Is there a way to modify Ian's spreadsheet generator to take in to account my requirements?

This makes sense in my head, I can clarify if need be.


Ian Wakeling

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Reply #1 on: August 01, 2015, 02:38:23 AM
If there are 20 or fewer teams, then you can make do with only 10 locations, but I do not see that teams have to play each other twice.  For example see the first 5 schedules below, where the columns could be the locations and the rows the rounds. For 22 teams, would the last schedule be suitable?  I am thinking that you just leave out the last round so everyone plays at exactly 10 out of the 11 locations.

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

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

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

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

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

22 teams
(B F) (D U) (R Q) (O H) (V N) (J L) (A T) (M S) (I K) (G P) (E C)
(J C) (O P) (M K) (B T) (G U) (I Q) (E F) (D N) (V S) (A H) (R L)
(R U) (A Q) (V T) (E S) (O L) (M H) (J N) (G C) (D F) (B K) (I P)
(A S) (V C) (J P) (G Q) (M F) (E U) (O K) (I T) (R H) (D L) (B N)
(D H) (R S) (A C) (M U) (J K) (O F) (V P) (E Q) (B L) (I N) (G T)
(I L) (B H) (D S) (J F) (A P) (V K) (R C) (O U) (G N) (E T) (M Q)
(V Q) (J T) (O N) (I C) (E H) (G S) (M L) (B P) (A U) (R F) (D K)
(O T) (M N) (E L) (D P) (I S) (B C) (G H) (R K) (J Q) (V U) (A F)
(E N) (G L) (I H) (A K) (D C) (R P) (B S) (V F) (M T) (O Q) (J U)
(G K) (I F) (B U) (V L) (R T) (A N) (D Q) (J H) (E P) (M C) (O S)
(M P) (E K) (G F) (R N) (B Q) (D T) (I U) (A L) (O C) (J S) (V H) [11th round - do not play]
« Last Edit: August 01, 2015, 02:44:56 AM by Ian »


esavs08

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Reply #2 on: August 03, 2015, 09:41:54 AM
This looks great!  Is my request possible for 24+ teams?

With a 10 round limit, teams will only get to 10 out of X locations, which is ok.

Thanks!


Ian Wakeling

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Reply #3 on: August 04, 2015, 02:14:38 AM
Yes this is possible.  The remaining square schedules are below.


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

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

28 Teams
(16 22) (18 28) (10  4) (11  3) (15 19) ( 2 24) (17  8) (14 26) (25 12) (20  6) ( 1 13) ( 7  9) (23  5) (21 27)
( 2 12) (10 19) (21 26) (14  4) (18  9) (20 27) ( 1  5) (25 24) (16  8) (11 28) (23 22) (15  3) ( 7 13) (17  6)
( 1 28) (25 13) (20 24) (21  8) ( 7 22) (17 19) (10  9) ( 2  3) (23 27) (18 26) (15  4) (11 12) (14  6) (16  5)
(25 27) (11  8) (16  9) (10 24) (14  5) (18  6) (20 12) (15 28) (17  4) ( 1  3) (21 19) (23 13) ( 2 22) ( 7 26)
(14  3) ( 7  5) (11 27) (20 22) (25  8) (21 13) (23 19) (18  4) (15  9) (17 12) ( 2  6) ( 1 26) (16 24) (10 28)
(11 19) (16 27) (17 22) (25  6) (20 26) ( 1 12) (14 13) (23  9) (18  5) ( 7  4) (10  3) ( 2  8) (21 28) (15 24)
(23 26) (20  4) ( 1 19) ( 2  5) (16 12) (14 28) ( 7  3) (17 27) (21 22) (15  8) (11 24) (10  6) (25  9) (18 13)
( 7  6) (21  3) (23 12) (17 13) ( 1 24) (10 26) (15 22) (11  5) (14 19) ( 2 27) (16 28) (25  4) (18  8) (20  9)
(15 13) ( 2  9) (18  3) (23 28) (21  6) (25 22) (16  4) ( 7 19) (11 26) (10  5) (20  8) (17 24) ( 1 27) (14 12)
(17  9) (23  6) ( 7 28) (18 19) ( 2  4) (15  5) (21 24) ( 1  8) (20  3) (16 13) (25 26) (14 27) (10 12) (11 22)
(21  4) (15 12) (25  5) (16 26) (11 13) ( 7  8) (18 27) (10 22) ( 1  6) (23 24) (14  9) (20 28) (17  3) ( 2 19)
(20  5) (14 24) (15  6) ( 1  9) (17 28) (16  3) ( 2 26) (21 12) (10 13) (25 19) ( 7 27) (18 22) (11  4) (23  8)
(18 24) ( 1 22) (14  8) ( 7 12) (10 27) (23  4) (11  6) (20 13) ( 2 28) (21  9) (17  5) (16 19) (15 26) (25  3)
(10  8) (17 26) ( 2 13) (15 27) (23  3) (11  9) (25 28) (16  6) ( 7 24) (14 22) (18 12) (21  5) (20 19) ( 1  4)

30 Teams
(18  5) (20 16) (11 17) (19 28) (24  3) ( 7 25) ( 6 15) (14 10) (29 23) ( 4 12) ( 8  2) (22 30) (26 27) ( 1 13) ( 9 21)
( 9 13) ( 1 17) (20 25) ( 6 21) (14 30) ( 8 27) (19 16) (29 15) ( 7  2) (22 10) (11 28) (18 23) ( 4  3) (24 12) (26  5)
(19 23) (29 30) ( 4 15) (18 10) (22 27) (14  3) ( 9 12) (11 13) ( 8 25) (24  5) (26 21) (20 17) ( 7 28) ( 6  2) ( 1 16)
(11  3) ( 9 15) (18 30) (22 16) (19 13) (29 28) (26  2) (24 23) (20 10) ( 7 17) ( 6 27) ( 8 21) ( 1 12) (14  5) ( 4 25)
(29 12) ( 4 21) (22  5) (20 13) (18 15) (24 10) ( 8 17) ( 7 16) (26  3) (14 28) ( 1 25) (11 27) (19  2) ( 9 30) ( 6 23)
(22 25) (11 12) (14  2) (24 15) ( 7 21) (26 13) (29 27) (18  3) (19 30) ( 6 16) (20 23) ( 1  5) ( 9 10) ( 4 17) ( 8 28)
( 8 30) ( 6 10) (29 13) ( 9  2) (20  5) (18 16) (22 23) ( 4 28) (11 21) ( 1 27) (19 17) (26 15) (24 25) ( 7  3) (14 12)
(20  2) (22  3) ( 1 10) ( 7 12) (29 17) ( 4 23) (14 21) ( 6 30) (18 13) (11 25) ( 9  5) (24 28) ( 8 15) (26 16) (19 27)
(26 10) ( 7 27) (19 21) (29  5) (11 16) (20 12) ( 1  3) ( 9 25) ( 6 28) (18  2) (14 15) ( 4 13) (22 17) ( 8 23) (24 30)
( 1 28) (26 23) ( 9  3) ( 4 27) ( 6 25) (22 21) (24 13) ( 8 12) (14 16) (20 15) ( 7 30) (29  2) (11  5) (19 10) (18 17)
(24 21) (19 25) (26 28) (14 17) ( 1 23) ( 6  5) ( 4 30) (22  2) ( 9 27) ( 8 13) (18 12) ( 7 10) (29 16) (11 15) (20  3)
(14 27) (24  2) ( 8 16) (11 23) (26 12) ( 9 17) (18 25) (19  5) ( 1 15) (29 21) ( 4 10) ( 6  3) (20 30) (22 28) ( 7 13)
( 6 17) (14 13) ( 7 23) ( 8  3) ( 9 28) ( 1  2) (11 10) (20 27) ( 4  5) (26 30) (24 16) (19 12) (18 21) (29 25) (22 15)
( 4 16) (18 28) (24 27) ( 1 30) ( 8 10) (19 15) ( 7  5) (26 17) (22 12) ( 9 23) (29  3) (14 25) ( 6 13) (20 21) (11  2)
( 7 15) ( 8  5) ( 6 12) (26 25) ( 4  2) (11 30) (20 28) ( 1 21) (24 17) (19  3) (22 13) ( 9 16) (14 23) (18 27) (29 10)

32 Teams
( 6 14) (20 23) (27 31) (30 24) ( 8 12) (18  7) (21  5) (28 32) (19  2) ( 9 11) (29 10) (16  3) (15  1) (13 22) (26  4) (17 25)
(18 25) (28 10) (19 22) (29 32) (17  7) ( 6 12) ( 9  4) (20 24) (27  3) (21  1) (30 23) (13  2) (26 11) (16 31) (15  5) ( 8 14)
(17 22) (29  1) (13 25) (28  5) (18  2) ( 8  3) (26 24) (30  4) (16 12) (15 10) (20 11) (19  7) ( 9 23) (27 14) (21 32) ( 6 31)
(20 12) ( 6 24) ( 9  3) ( 8 23) (30 14) (28 25) (19  1) (18 10) (21 22) (27  4) (17 32) (26 31) (13  5) (15  2) (16 11) (29  7)
(19 23) (21 14) (18 11) (15 12) (13 24) (27 32) (20  2) ( 9  7) ( 6  5) (28 31) (26 25) (17  4) (30 22) ( 8  1) (29  3) (16 10)
(26  5) (16  2) (30 32) (27 22) ( 9  1) (15 11) (17 14) (13 31) (29 23) ( 8  7) (19  3) (20 10) (18 12) (28 24) ( 6 25) (21  4)
( 9 32) (27  7) (20  5) (16 25) (26 10) (21 23) (18 31) (19 14) (28 11) ( 6  2) (13 12) (30  1) (17  3) (29  4) ( 8 22) (15 24)
(13 11) (15 31) (17 23) (21  3) (19  4) (16  5) (30  7) (26  2) ( 8 32) (29 14) ( 9 22) (18 24) (20 25) ( 6 10) (28 12) (27  1)
(29  2) (17  5) (15  7) (18  1) (28 22) (30 31) (16 23) ( 8 11) (26 14) (13 32) ( 6  4) (21 25) (27 24) ( 9 12) (19 10) (20  3)
(30  3) ( 8  4) (26 12) ( 6 11) (20 31) (29 22) (13 10) (17  1) (15 25) (16 24) (18  5) ( 9 14) (19 32) (21  7) (27 23) (28  2)
(28  7) (18 32) (21  2) (17 10) (29 25) (20 14) (27 11) ( 6 23) ( 9 31) (19  5) ( 8 24) (15 22) (16  4) (26  3) (13  1) (30 12)
(15  4) (13  3) (29 24) (19 31) (21 11) (26  1) ( 8 25) (16 22) (30 10) (17 12) (27  2) (28 23) ( 6  7) (20 32) (18 14) ( 9  5)
(27 10) ( 9 25) ( 6  1) (26  7) (16 32) (19 24) (28  3) (21 12) (18  4) (20 22) (15 14) ( 8  5) (29 31) (17 11) (30  2) (13 23)
(21 24) (19 12) (28  4) (13 14) (15 23) ( 9 10) ( 6 22) (27 25) (20  1) (18  3) (16  7) (29 11) ( 8  2) (30  5) (17 31) (26 32)
( 8 31) (30 11) (16 14) (20  4) ( 6  3) (17  2) (15 32) (29  5) (13  7) (26 23) (28  1) (27 12) (21 10) (19 25) ( 9 24) (18 22)
(16  1) (26 22) ( 8 10) ( 9  2) (27  5) (13  4) (29 12) (15  3) (17 24) (30 25) (21 31) ( 6 32) (28 14) (18 23) (20  7) (19 11)


esavs08

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Reply #4 on: August 04, 2015, 11:22:59 AM
In order to play only 10 rounds for the 24-32 team squares, is it safe to just cut each off after the first 10 lines (rounds)?

Also, for 12-18 teams, is it possible to change the number of locations (columns) to match the number of matches being played rather than have 10 set locations for each, rounds (rows) remain at 10; e.g 16 teams, 8 matches, 8 locations, 10 rounds; 12 teams, 6 matches, 6 locations, 10 rounds; etc. Thanks!
« Last Edit: August 04, 2015, 12:25:52 PM by esavs08 »


Ian Wakeling

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Reply #5 on: August 05, 2015, 07:13:03 AM
Yes, you can cut after the first 10 lines.

For 12, 14, or 16 teams then use the schedules here.  Again cut off after 10 lines.  For 18 teams you can play this for rounds 1 to 9:

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


and then you will have to make a 10th round using team pairings that have not yet occurred, which I think should be easy to do.