14 groups of 3

[Bandit]

Hi,

I am trying to generate a schedule for 42 dart players where all the players need to score as well but not while playing. This essentially means that 3 players are allocated per board. Two will play while 1 scores. All players need to play against each other.

I did see a post where there was a similar schedule for golf but consisted of 51 players. Can you assist?

Ideally, if possible, I would like something in an excel spreadsheet where one can just enter the number of players and it will generate the schedule.

Thanks.

[Ian Wakeling]

Do you intend that when players A B & C are allocated a board that :

A plays B while C scores, then
A plays C while B scores, then
B plays C while A scores.

If you want this, then unfortunately it can not be made to work for 42 players, however 39 and 45 players are possible.

Alternatively, if it doesn't really matter who scores whom, then you just consider it as arranging a standard 42 player round robin in rounds of 14 games.  I can make this I think.

[Bandit]

Hi Ian,

Thanks for the response.

The scenario you described is exactly what I'm looking for. I tried the normal round robin scheduler but it schedules 21 games. I though we can play this on 14 boards which leaves 14 players to score but when I get to the next round, 1 or more players are scheduled to play in two games.

Do you have anything that will only schedule 14 games per round?

[Ian Wakeling]

I can make the schedule below.   But I fear it might be a nightmare to administrate as people have to move around so much.  Also note that if you cut it up into rounds (days?) of three games then sometimes a player will play just once, while others play three times.  The best option may be to try and cut back to 39 players.

(13 26) (10 40) ( 4  8) ( 1  9) ( 6 30) (18 25) (29 42) ( 7 31) (23 34) (19 22) (15 33) (11 21) (28 39) (-----)
(19 24) (32 37) ( 9 27) (20 33) (16 30) ( 8 12) (17 41) ( 3  5) (14 39) (35 36) (21 25) (15 38) ( 2 34) (-----)
( 7 38) (37 40) (16 36) (11 20) (28 29) ( 4 22) (13 27) (23 35) (18 19) (10 26) ( 1 42) ( 6 12) (30 31) (-----)
( 8 22) (41 42) ( 7 11) (15 30) (14 33) (18 39) (24 25) ( 9 10) ( 3 40) ( 2 28) (17 21) (20 34) ( 5 32) (-----)
( 1 14) ( 5  6) (23 27) ( 3 26) (12 38) (19 39) (13 36) ( 9 37) (18 30) ( 2 29) ( 8 16) (33 35) ( 4 31) (-----)
(22 24) (17 35) (11 42) (21 36) ( 7 28) ( 1 34) (20 29) ( 3 37) (10 13) (32 40) ( 4 23) (15 41) ( 8 25) (-----)
( 9 40) (16 33) (11 12) (19 38) ( 2 14) (22 27) (15 24) ( 8 39) ( 6 17) ( 1 10) (26 31) ( 5 18) (30 36) (-----)
(21 28) ( 8 23) ( 4  7) (25 34) (10 29) (30 42) (17 31) (13 15) ( 5 37) (11 36) ( 3 35) (20 32) (22 41) (26 33)
( 1 39) (19 35) (16 42) ( 3 11) (18 36) (12 40) (24 30) ( 5 27) (26 32) (23 25) (15 31) ( 6  9) ( 2 38) (14 22)
( 4 28) (37 39) (21 42) (19 29) ( 7 34) ( 1  6) (35 38) ( 3  8) (10 33) ( 5 17) (27 31) (20 41) ( 2 13) (16 22)
(11 16) (21 39) ( 8 14) (13 23) (24 36) ( 9 12) (15 27) (32 41) (17 18) ( 4 30) ( 6 42) ( 5 26) (19 40) (25 31)
(21 33) (29 37) (38 40) (10 32) ( 1 22) (31 34) (30 39) (20 25) ( 2 26) (16 19) ( 8 24) ( 3  7) (28 41) (12 35)
( 1 13) (26 29) ( 4 14) ( 5 24) ( 9 33) ( 7 25) (11 32) (23 42) (31 41) (17 20) (27 38) (16 18) (15 36) ( 6 35)
(10 18) (19 30) ( 3 27) (23 37) (22 33) (40 42) ( 8 15) (28 38) ( 9 39) (12 34) (21 41) ( 2 17) (26 35) (14 32)
(12 31) (22 26) ( 7  9) ( 1 16) ( 6 36) (10 11) (27 29) (21 24) (25 41) (30 37) ( 5 28) ( 2  4) (13 14) (20 35)
( 7 16) (35 39) (11 22) ( 5 33) (23 40) (15 18) ( 9 30) (19 20) ( 8 32) (25 27) (13 42) (24 34) (10 38) ( 3 17)
( 4 19) ( 3 22) ( 1 41) ( 8 27) (18 28) (16 23) ( 6 26) (29 40) ( 9 20) ( 2 37) (15 21) (12 36) (14 31) (32 33)
(15 29) ( 1 27) (11 19) ( 9 42) ( 7 36) (32 35) ( 5 30) (24 39) (21 38) (10 12) ( 4 33) ( 2 25) (13 17) (18 34)
(28 37) (11 33) ( 3 41) (12 22) ( 6 20) (34 42) (16 39) (13 24) (14 40) ( 8 18) (10 31) ( 1 32) (23 36) ( 4 26)
( 7 17) (15 26) ( 2  6) ( 1 38) (25 35) ( 9 28) ( 5 20) (30 32) (14 41) (19 31) (27 33) (21 23) (12 29) ( 3 13)
(39 40) (10 24) ( 2 35) ( 4 37) (12 16) (34 41) ( 1  8) (11 17) ( 7 26) (22 36) (27 32) (28 42) (18 21) (19 25)
( 9 29) ( 3 28) ( 7 21) ( 4 34) (25 26) ( 6 40) (30 38) (31 37) (13 33) (10 27) (12 42) (15 20) ( 5 14) (22 23)
(34 40) (14 35) ( 6 29) (17 19) (10 36) ( 5 23) ( 1 28) (31 39) ( 2  8) (11 15) (25 38) (16 41) (24 32) (18 27)
(31 33) ( 7 19) (26 38) ( 3 14) ( 5 13) (22 29) ( 8 20) (18 37) ( 4 39) (11 23) (16 21) (12 30) ( 9 32) (25 42)
(34 36) (20 38) (17 24) ( 8 35) (11 37) (10 42) (23 41) ( 6 14) ( 4 12) ( 2 16) ( 1  7) (15 40) (27 28) (18 26)
( 1 12) (14 34) ( 5 40) (13 21) (37 42) (15 25) ( 9 22) (29 31) ( 3  4) (28 30) (10 19) (39 41) ( 2 32) ( 6 33)
(17 36) (26 40) (14 24) (20 21) ( 7 12) ( 3 29) (18 23) ( 6 27) ( 2 11) ( 5 38) ( 1 25) ( 8 10) ( 4 16) (35 37)
(18 32) (22 42) (17 40) ( 2 20) ( 6 23) (33 41) (19 21) ( 9 38) ( 8 31) (13 39) ( 7 10) (24 28) ( 3 30) (15 34)
( 1 35) (11 39) ( 5 31) (17 28) ( 4 38) (27 30) (19 36) (13 34) (14 16) (26 37) (25 40) (12 41) (18 29) ( 3 15)
(17 30) (12 20) ( 4 32) (33 36) ( 6 38) (18 22) (27 34) ( 5  9) (21 35) ( 3 10) ( 8 13) ( 2 24) ( 7 23) (31 42)
( 5  7) (13 25) ( 1  3) ( 6 19) ( 4 21) (14 20) (24 26) (23 28) (15 37) (11 41) (38 42) (22 40) ( 9 16) (29 39)
( 4  9) (27 42) ( 2 10) (17 33) (20 23) (32 36) (24 31) (12 21) ( 5  8) ( 7 18) (29 35) ( 3 34) (38 41) (13 30)
(36 38) ( 7 42) (22 28) (13 40) ( 2  5) (17 26) ( 9 11) (16 37) ( 6 24) (12 39) ( 1 15) (14 29) ( 3 25) (19 32)
( 8 36) (11 27) (23 29) ( 9 41) (34 37) ( 3 19) (10 28) ( 2 31) (21 30) ( 4 20) (35 40) (24 33) (13 18) ( 1 17)
( 7 15) (28 35) (17 22) ( 5 11) (16 25) (12 14) (29 38) (13 32) (20 31) ( 9 34) (26 42) (27 41) ( 2 19) ( 6 39)
( 1 20) (16 24) (32 38) (31 40) (25 29) (10 22) ( 3 18) ( 4 42) ( 2 36) (27 37) ( 8 21) (33 39) (23 30) ( 9 13)
(36 39) (11 26) ( 5 35) ( 1 40) (34 38) ( 4 13) (21 32) (12 19) (17 42) (28 31) ( 2 41) (24 27) ( 7 14) ( 6 15)
( 3 20) ( 9 23) (26 39) (28 34) ( 2 21) ( 8 33) (14 19) ( 1 18) (10 16) (30 40) (11 31) (25 37) (17 29) (22 38)
(23 32) (15 22) (16 35) ( 6 13) ( 1 26) ( 4 27) (14 17) (20 36) (18 42) ( 2  9) (10 34) ( 7 29) (12 24) ( 5 41)
(30 33) (25 32) (13 38) ( 8 19) (10 14) ( 3 31) (20 39) (16 28) (35 42) (21 40) (26 27) (11 29) (12 37) ( 1 24)
( 7 22) ( 2 23) (14 37) ( 9 26) (15 17) ( 6 34) (18 40) ( 3 21) ( 5 25) ( 1 29) (32 39) (27 36) (30 41) ( 4 24)
(28 33) ( 5 12) ( 4 18) (20 37) (27 40) (19 42) ( 8 29) (10 30) ( 6 16) (13 35) (25 39) (11 24) ( 9 31) (17 38)
(34 39) ( 6 21) ( 5 22) ( 3 38) (14 26) (17 32) ( 2 33) ( 7 20) (36 41) ( 1 11) (13 16) (15 23) ( 9 19) (18 24)
(33 40) (22 25) (17 37) ( 4 35) ( 7  8) (12 28) (10 15) (20 27) ( 5 36) (31 32) (14 30) ( 2 42) (16 29) ( 6 41)
( 1  5) ( 8 42) (11 13) (15 35) ( 7 33) (16 20) (12 26) ( 3 39) ( 9 24) ( 6 18) (23 38) (22 30) (21 37) (19 34)
(28 40) (17 27) (29 32) (24 37) (11 30) (23 31) (22 34) ( 6 25) (38 39) (10 41) ( 2  7) ( 1  4) (14 36) ( 3 12)
( 4 15) (11 28) (35 41) (14 42) (12 13) (22 39) (18 20) (16 40) ( 5 19) ( 9 17) (33 38) ( 6  8) (10 23) (21 26)
( 4 29) (13 37) (18 31) (10 25) ( 2 30) ( 7 27) (24 41) (15 16) ( 1 33) (20 28) (22 32) ( 3  6) (17 34) (26 36)
(12 32) ( 7 35) ( 4 17) (21 27) (16 38) (39 42) (29 41) ( 9 14) ( 8 28) (11 40) ( 6 31) (13 19) ( 5 34) (23 24)
( 9 36) (14 15) (16 26) ( 1 19) (21 34) (25 30) (20 22) ( 6 11) ( 3 33) ( 5 10) ( 7 37) (17 23) (18 35) ( 2 39)
(28 32) ( 8 34) (37 38) (26 30) (12 27) (14 25) ( 1  2) (15 39) (24 42) (13 31) (29 36) (20 40) ( 4 41) (23 33)
( 2 22) ( 4 40) ( 6 10) ( 9 21) (36 42) ( 5 15) (24 35) (25 28) (19 37) ( 3 16) ( 7 39) (11 18) ( 8 17) (29 34)
(25 33) (20 30) ( 7 41) ( 2 12) (13 28) ( 1 31) (11 38) ( 8 37) (14 21) ( 3 42) (15 32) (10 39) (23 26) (27 35)
(24 38) (14 23) ( 1 36) ( 8 40) (26 34) (12 25) (16 31) ( 5 29) (10 17) ( 3  9) (18 41) ( 4  6) (22 37) (19 28)
(23 39) (30 35) ( 2 40) (21 29) (36 37) ( 9 15) ( 3 32) (11 34) ( 7 13) ( 6 28) (20 24) (12 33) (19 27) ( 5 42)
( 4 10) (28 36) (33 42) (19 41) (17 25) (11 35) ( 8 26) (16 34) ( 1 37) (14 38) ( 3 23) (22 31) (12 18) ( 7 32)
( 9 35) (15 19) ( 4 11) (13 41) ( 2 27) ( 5 39) (26 28) ( 6 22) ( 7 24) (29 33) (30 34) (21 31) (10 20) (36 40)
(31 38) ( 3 24) ( 5 21) ( 2 18) (11 14) ( 8 41) (19 23) (25 36) (13 22) (16 17) (33 37) (32 42) (12 15) ( 1 30)
( 6 37) ( 9 18) ( 8 38) (27 39) (33 34) (14 28) (16 32) ( 7 30) (40 41) (10 21) ( 4 36) (31 35) (24 29) (20 26)
( 2  3) ( 8 11) (15 42) (14 18) ( 6  7) (26 41) (19 33) ( 4  5) (12 17) (22 35) (32 34) ( 9 25) ( 1 23) (13 20)
( 8 30) (31 36) ( 1 21) (13 29) (18 38) (12 23) (17 39) (11 25) (10 37) ( 6 32) (16 27) (34 35) (24 40) (15 28)
(20 42) (19 26) ( 7 40) ( 8  9) (21 22) ( 4 25) ( 2 15) (37 41) (18 33) (10 35) ( 5 16) ( 3 36) (14 27) (29 30)

[Bandit]

Ian,

Thanks for the help. Can you provide the 45 player schedule (3 per board).

[Ian Wakeling]

The 45 player schedule is in the attached file (zipped Excel).  This may also be your best option for 42 players if players 37, 38 & 45 were assigned to be the three 'ghost' players.  So there would be 14 boards of 3 in round 1, and then in all subsequent rounds there would be 12 boards of three players, and 3 boards of two players.  Of course there would be nobody to score the game at the two player boards as the third player is a ghost, so you could bring all six of these players together at a single board.

[Bandit]

Hi Ian,

Perfect. Thanks very much for your assistance.

[Bandit]

Hi Ian,

I again need assistance please.

I need to organise a round robin darts tournament for 16 players with the scenario as described above... 3 per board, 2 play while the 3rd scores.

I have a schedule for 18 players but if I allocate them as "ghost" players, there is a round where 1 player does not play at all. Is there a way around this?

Thanks.

[Ian Wakeling]

I think the schedule below might work.  Note that 6 pairs of player meet twice as I have identified with the asterisks.

  (12  8  2)  ( 1 13 16) ( 6 11  3)  (4  7 14)  (9  5) (10 15)
  (10  9  3)  ( 2 14 16) ( 4 12  1)  (5  8 15)  (7  6) (11 13)
  (11  7  1)  ( 3 15 16) ( 5 10  2)  (6  9 13)  (8  4) (12 14)
  (13  8  3)* (10  4 11) (15  6 14)  (9 12 16)  (1  2) ( 5  7)
  (14  9  1)* (11  5 12) (13  4 15)  (7 10 16)  (2  3) ( 6  8)
  (15  7  2)* (12  6 10) (14  5 13)  (8 11 16)  (3  1) ( 4  9)
  (10  3 14)* (11  9  2) ( 1  6  5)  (7  8 13)  (4 16) (15 12)
  (11  1 15)* (12  7  3) ( 2  4  6)  (8  9 14)  (5 16) (13 10)
  (12  2 13)* (10  8  1) ( 3  5  4)  (9  7 15)  (6 16) (14 11)

* the first two players in a triple like this meet elsewhere in the schedule.  For example 8 and 13 also meet in round 7.

[Bandit]

Hi,

Thanks for the prompt response.

Is there any way that we can eliminate the players meeting a second time, even if it means allocating 4 to a board in the last rounds?

Also, will it work if we allocate 4 to a board right from the start?

[Ian Wakeling]

I think the only way would be to do as you suggest and always assign 4 players to a board.  You will need the schedule that you can find here.