Pinewood derby 3 lane races - Round Robin

[depcdivr]

Good Morning,

I have been put in charge of running our cub scout pack's Pinewood derby.  We will be using a 3 lane track and I want to run a round robin style race to determine the fastest cars.  

Is there a round robin generator program available that will allow me to specify the number of entrants(at this point unknown but may be around 40-50) and the number of racers running a time (3).  

I can only seem to find generators that put two entries together but not 3.  

I am looking for a program to do this because I will have to generate the races at the event since I will not have a final total of how many entrants until race time.  I would hate to have it set at 49 then only have 33 kids show up creating a bunch of non-sense races.

Help.  

BTW the race is on 2/24 so I need assistance ASAP.

[Ian Wakeling]

I don't know of any software that is going to help.  There are other problems as for many numbers of cars there will be no balanced round-robin schedule that exists.  The good numbers of cars to have would be 39,43,45,49 & 51 cars.  However, you may not want to go down this route at all, since the number of races will be high, you need 247 races for 39 cars and 425 races for 51 cars in order for everyone to race each other once.

Have a look at this message board thread also on pine cars, you may be better off dividing the entrants into 7 groups of 6 or 7 and then having 10 or 14 races within each group (race each other twice within a group).  This would be less than 100 races in total.  Then the 7 group winners all race each other once in finals.

[depcdivr]

After searching for a solution to this issue I had an idea.  If I was to use your program to schedule a round robin for 39 cars (or another multiple of 3).  Once that was complete I took the first three numbers as the first heat.  For instance, the generator scheduled teams (1 2) (3 37) and (38 39).  I would then make my heats (1 2 3) and (37 38 39).  Each round would contain all of the teams (cars) and it would be randomly generated.  

I understand that if I do a true round robin it would be a crazy amount of races.  What I am looking to do is have all of the cars race per round and then give a point to the 1st place finisher.  After like 10 or 20 rounds there would be a handful of cars that win more than others.  Once they are established we would do a true round robin with those cars to determine the 1st, 2nd and 3rd place cars.  

[Ian Wakeling]

I don't believe your suggestion of transforming the pairwise round-robin into triples will work, as you will soon find that some pairs of cars will race each more than once.

The only ideal schedules for your race format, which can be divided into rounds, are when the number of cars is of the form 6i+3 where I is a whole number.  Below I gives some examples that may be useful for your race day.  Note that as  everyone races each other exactly once in these schedules, that you are free to use as many or as few of the rounds as you like.

If you would like to think about the other multiples of 3 within your range and tell me how many rounds you would like for each then it might be possible to come up with suitable schedules for you.

9, 15, & 21 Cars see here

27 & 33 Cars (see message further down this page)

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

45 Cars (22 rounds of 15 races each)
(1 2 24) (3 4 17) (25 39 26) (5 6 18) (27 40 28) (7 8 19) (29 41 30) (9 10 20) (31 42 32) (11 12 21) (33 43 34) (13 14 22) (35 44 36) (15 16 23) (37 45 38)
(1 3 25) (2 4 39) (24 17 26) (9 11 18) (31 40 33) (10 12 19) (32 41 34) (14 16 20) (36 42 38) (13 15 21) (35 43 37) (6 8 22) (28 44 30) (5 7 23) (27 45 29)
(1 4 26) (2 17 25) (24 3 39) (14 15 18) (36 40 37) (13 16 19) (35 41 38) (5 8 20) (27 42 30) (6 7 21) (28 43 29) (10 11 22) (32 44 33) (9 12 23) (31 45 34)
(1 5 27) (9 13 17) (31 39 35) (2 6 40) (24 18 28) (11 15 19) (33 41 37) (4 8 42) (26 20 30) (10 14 21) (32 43 36) (12 16 22) (34 44 38) (3 7 45) (25 23 29)
(1 6 28) (11 16 17) (33 39 38) (2 18 27) (24 5 40) (9 14 19) (31 41 36) (12 15 20) (34 42 37) (4 7 43) (26 21 29) (3 8 44) (25 22 30) (10 13 23) (32 45 35)
(1 7 29) (12 14 17) (34 39 36) (10 16 18) (32 40 38) (2 8 41) (24 19 30) (11 13 20) (33 42 35) (4 21 28) (26 6 43) (9 15 22) (31 44 37) (3 23 27) (25 5 45)
(1 8 30) (10 15 17) (32 39 37) (12 13 18) (34 40 35) (2 19 29) (24 7 41) (4 20 27) (26 5 42) (9 16 21) (31 43 38) (3 22 28) (25 6 44) (11 14 23) (33 45 36)
(1 9 31) (5 13 39) (27 17 35) (3 11 40) (25 18 33) (6 14 41) (28 19 36) (2 10 42) (24 20 32) (8 16 43) (30 21 38) (7 15 44) (29 22 37) (4 12 45) (26 23 34)
(1 10 32) (8 15 39) (30 17 37) (7 16 40) (29 18 38) (3 12 41) (25 19 34) (2 20 31) (24 9 42) (5 14 43) (27 21 36) (4 11 44) (26 22 33) (6 13 45) (28 23 35)
(1 11 33) (6 16 39) (28 17 38) (3 18 31) (25 9 40) (5 15 41) (27 19 37) (7 13 42) (29 20 35) (2 12 43) (24 21 34) (4 22 32) (26 10 44) (8 14 45) (30 23 36)
(1 12 34) (7 14 39) (29 17 36) (8 13 40) (30 18 35) (3 19 32) (25 10 41) (6 15 42) (28 20 37) (2 21 33) (24 11 43) (5 16 44) (27 22 38) (4 23 31) (26 9 45)
(1 13 35) (5 17 31) (27 9 39) (8 18 34) (30 12 40) (4 16 41) (26 19 38) (7 20 33) (29 11 42) (3 15 43) (25 21 37) (2 14 44) (24 22 36) (6 23 32) (28 10 45)
(1 14 36) (7 17 34) (29 12 39) (4 15 40) (26 18 37) (6 19 31) (28 9 41) (3 16 42) (25 20 38) (5 21 32) (27 10 43) (2 22 35) (24 13 44) (8 23 33) (30 11 45)
(1 15 37) (8 17 32) (30 10 39) (4 18 36) (26 14 40) (5 19 33) (27 11 41) (6 20 34) (28 12 42) (3 21 35) (25 13 43) (7 22 31) (29 9 44) (2 16 45) (24 23 38)
(1 16 38) (6 17 33) (28 11 39) (7 18 32) (29 10 40) (4 19 35) (26 13 41) (3 20 36) (25 14 42) (8 21 31) (30 9 43) (5 22 34) (27 12 44) (2 23 37) (24 15 45)
(1 17 39) (2 3 26) (24 4 25) (5 9 35) (27 13 31) (6 11 38) (28 16 33) (7 12 36) (29 14 34) (8 10 37) (30 15 32) (18 20 22) (40 21 45) (19 43 44) (41 42 23)
(1 18 40) (2 5 28) (24 6 27) (3 9 33) (25 11 31) (4 14 37) (26 15 36) (7 10 38) (29 16 32) (8 12 35) (30 13 34) (17 20 21) (39 44 23) (19 42 45) (41 43 22)
(1 19 41) (2 7 30) (24 8 29) (3 10 34) (25 12 32) (4 13 38) (26 16 35) (5 11 37) (27 15 33) (6 9 36) (28 14 31) (17 42 43) (39 22 45) (18 21 23) (40 20 44)
(1 20 42) (2 9 32) (24 10 31) (3 14 38) (25 16 36) (4 5 30) (26 8 27) (6 12 37) (28 15 34) (7 11 35) (29 13 33) (17 44 45) (39 18 41) (40 43 23) (19 21 22)
(1 21 43) (2 11 34) (24 12 33) (3 13 37) (25 15 35) (4 6 29) (26 7 28) (5 10 36) (27 14 32) (8 9 38) (30 16 31) (17 22 23) (39 40 19) (18 42 44) (41 20 45)
(1 22 44) (2 13 36) (24 14 35) (3 6 30) (25 8 28) (4 10 33) (26 11 32) (5 12 38) (27 16 34) (7 9 37) (29 15 31) (17 40 41) (39 42 21) (18 43 45) (19 20 23)
(1 23 45) (2 15 38) (24 16 37) (3 5 29) (25 7 27) (4 9 34) (26 12 31) (6 10 35) (28 13 32) (8 11 36) (30 14 33) (17 18 19) (39 20 43) (40 42 22) (41 21 44)

51 Cars (25 rounds of 17 races each)
(1 2 27) (3 7 26) (28 51 32) (6 11 50) (31 25 36) (8 9 38) (33 13 34) (22 21 48) (47 23 46) (4 12 20) (29 45 37) (5 15 43) (30 18 40) (14 16 49) (39 24 41) (17 10 44) (42 19 35)
(1 3 28) (2 7 51) (27 26 32) (4 8 22) (29 47 33) (9 10 39) (34 14 35) (23 17 49) (48 24 42) (5 13 21) (30 46 38) (6 16 44) (31 19 41) (15 12 50) (40 25 37) (18 11 45) (43 20 36)
(1 4 29) (3 8 47) (28 22 33) (5 9 23) (30 48 34) (10 11 40) (35 15 36) (24 18 50) (49 25 43) (2 12 45) (27 20 37) (6 14 17) (31 42 39) (16 13 51) (41 26 38) (19 7 46) (44 21 32)
(1 5 30) (4 9 48) (29 23 34) (6 10 24) (31 49 35) (11 7 41) (36 16 32) (25 19 51) (50 26 44) (3 13 46) (28 21 38) (2 15 18) (27 43 40) (12 14 47) (37 22 39) (20 8 42) (45 17 33)
(1 6 31) (5 10 49) (30 24 35) (2 11 25) (27 50 36) (7 8 37) (32 12 33) (26 20 47) (51 22 45) (4 14 42) (29 17 39) (3 16 19) (28 44 41) (13 15 48) (38 23 40) (21 9 43) (46 18 34)
(1 7 32) (2 26 28) (27 3 51) (8 12 6) (33 31 37) (11 16 30) (36 5 41) (13 14 43) (38 18 39) (9 17 25) (34 50 42) (10 20 48) (35 23 45) (19 21 29) (44 4 46) (22 15 49) (47 24 40)
(1 8 33) (3 22 29) (28 4 47) (7 12 31) (32 6 37) (9 13 2) (34 27 38) (14 15 44) (39 19 40) (10 18 26) (35 51 43) (11 21 49) (36 24 46) (20 17 30) (45 5 42) (23 16 50) (48 25 41)
(1 9 34) (4 23 30) (29 5 48) (8 13 27) (33 2 38) (10 14 3) (35 28 39) (15 16 45) (40 20 41) (7 17 50) (32 25 42) (11 19 22) (36 47 44) (21 18 31) (46 6 43) (24 12 51) (49 26 37)
(1 10 35) (5 24 31) (30 6 49) (9 14 28) (34 3 39) (11 15 4) (36 29 40) (16 12 46) (41 21 37) (8 18 51) (33 26 43) (7 20 23) (32 48 45) (17 19 27) (42 2 44) (25 13 47) (50 22 38)
(1 11 36) (6 25 27) (31 2 50) (10 15 29) (35 4 40) (7 16 5) (32 30 41) (12 13 42) (37 17 38) (9 19 47) (34 22 44) (8 21 24) (33 49 46) (18 20 28) (43 3 45) (26 14 48) (51 23 39)
(1 12 37) (7 6 33) (32 8 31) (13 17 11) (38 36 42) (16 21 35) (41 10 46) (18 19 48) (43 23 44) (2 20 29) (27 4 45) (14 22 5) (39 30 47) (15 25 28) (40 3 50) (24 26 34) (49 9 51)
(1 13 38) (8 2 34) (33 9 27) (12 17 36) (37 11 42) (14 18 7) (39 32 43) (19 20 49) (44 24 45) (3 21 30) (28 5 46) (15 23 6) (40 31 48) (16 26 29) (41 4 51) (25 22 35) (50 10 47)
(1 14 39) (9 3 35) (34 10 28) (13 18 32) (38 7 43) (15 19 8) (40 33 44) (20 21 50) (45 25 46) (4 17 31) (29 6 42) (12 22 30) (37 5 47) (16 24 2) (41 27 49) (26 23 36) (51 11 48)
(1 15 40) (10 4 36) (35 11 29) (14 19 33) (39 8 44) (16 20 9) (41 34 45) (21 17 51) (46 26 42) (5 18 27) (30 2 43) (13 23 31) (38 6 48) (12 25 3) (37 28 50) (22 24 32) (47 7 49)
(1 16 41) (11 5 32) (36 7 30) (15 20 34) (40 9 45) (12 21 10) (37 35 46) (17 18 47) (42 22 43) (6 19 28) (31 3 44) (14 24 27) (39 2 49) (13 26 4) (38 29 51) (23 25 33) (48 8 50)
(1 17 42) (12 11 38) (37 13 36) (18 22 16) (43 41 47) (21 26 40) (46 15 51) (23 24 28) (48 3 49) (4 6 39) (29 14 31) (7 25 34) (32 9 50) (19 2 10) (44 35 27) (20 5 33) (45 8 30)
(1 18 43) (13 7 39) (38 14 32) (17 22 41) (42 16 47) (19 23 12) (44 37 48) (24 25 29) (49 4 50) (5 2 40) (30 15 27) (8 26 35) (33 10 51) (20 3 11) (45 36 28) (21 6 34) (46 9 31)
(1 19 44) (14 8 40) (39 15 33) (18 23 37) (43 12 48) (20 24 13) (45 38 49) (25 26 30) (50 5 51) (6 3 41) (31 16 28) (9 22 36) (34 11 47) (17 2 35) (42 10 27) (21 4 7) (46 32 29)
(1 20 45) (15 9 41) (40 16 34) (19 24 38) (44 13 49) (21 25 14) (46 39 50) (26 22 31) (51 6 47) (2 4 37) (27 12 29) (10 23 32) (35 7 48) (18 3 36) (43 11 28) (17 5 8) (42 33 30)
(1 21 46) (16 10 37) (41 12 35) (20 25 39) (45 14 50) (17 26 15) (42 40 51) (22 23 27) (47 2 48) (3 5 38) (28 13 30) (11 24 33) (36 8 49) (19 4 32) (44 7 29) (18 6 9) (43 34 31)
(1 22 47) (3 4 33) (28 8 29) (17 16 43) (42 18 41) (23 2 21) (48 46 27) (26 6 45) (51 20 31) (9 11 44) (34 19 36) (12 5 39) (37 14 30) (24 7 15) (49 40 32) (25 10 38) (50 13 35)
(1 23 48) (4 5 34) (29 9 30) (18 12 44) (43 19 37) (22 2 46) (47 21 27) (24 3 17) (49 42 28) (10 7 45) (35 20 32) (13 6 40) (38 15 31) (25 8 16) (50 41 33) (26 11 39) (51 14 36)
(1 24 49) (5 6 35) (30 10 31) (19 13 45) (44 20 38) (23 3 42) (48 17 28) (25 4 18) (50 43 29) (11 8 46) (36 21 33) (14 2 41) (39 16 27) (22 7 40) (47 15 32) (26 9 12) (51 37 34)
(1 25 50) (6 2 36) (31 11 27) (20 14 46) (45 21 39) (24 4 43) (49 18 29) (26 5 19) (51 44 30) (7 9 42) (32 17 34) (15 3 37) (40 12 28) (23 8 41) (48 16 33) (22 10 13) (47 38 35)
(1 26 51) (2 3 32) (27 7 28) (21 15 42) (46 17 40) (25 5 44) (50 19 30) (22 6 20) (47 45 31) (8 10 43) (33 18 35) (16 4 38) (41 13 29) (24 9 37) (49 12 34) (23 11 14) (48 39 36)

[depcdivr]

Thank you for much.  After looking through the matchups I had you are correct.  They certainly do duplicate.  I will use the sequences that you have created.  Once last favor.  can you run  matchup with 27  cars also.  

I am not sure how good/bad the turnout will be tomorrow.  Thank you in advance.

[depcdivr]

Thank you again.  I was plugging the numbers into my spreadsheet and noticed that for the 33 car races it always starts with car 1 in the first position.  The other schedules have the cars in various positions throughout the round robin.  Is it possible to do this for the 33 car race as well?

[Ian Wakeling]

Below are two schedule for 27 and 33 cars.  I have randomized the order of the triples within each round.

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

33 Cars (16 rounds of 11 races each) 
(26 12 3) (30 23 10) (13 31 18) (17 2 25) (14 32 11) (24 20 7) (27 1 9) (5 22 6) (8 16 4) (8 16 4) (29 21 15) (19 28 33)
(18 26 10) (12 27 6) (9 19 13) (23 24 1) (21 32 17) (28 5 20) (3 7 8) (30 33 4) (11 29 2) (11 29 2) (25 15 14) (22 31 16)
(16 12 20) (24 6 19) (7 10 27) (8 28 23) (5 13 4) (30 3 31) (11 15 17) (9 22 26) (1 18 33) (1 18 33) (29 25 32) (14 2 21)
(27 28 31) (22 33 7) (6 18 8) (12 23 13) (21 11 25) (5 1 3) (19 10 16) (2 32 15) (14 29 17) (14 29 17) (26 4 24) (20 30 9)
(10 11 6) (26 8 21) (33 17 13) (19 18 27) (7 29 12) (28 2 9) (3 4 20) (30 5 32) (22 23 14) (22 23 14) (15 24 16) (1 25 31)
(31 21 6) (10 29 1) (7 9 25) (20 27 22) (13 8 15) (23 4 18) (2 30 24) (11 33 26) (32 12 28) (32 12 28) (14 19 3) (16 17 5)
(15 10 28) (25 26 5) (12 21 1) (8 17 30) (18 20 14) (4 22 19) (23 27 3) (6 9 29) (24 13 32) (24 13 32) (31 7 11) (16 33 2)
(33 6 15) (23 20 19) (25 30 12) (11 9 16) (7 2 5) (32 8 1) (31 17 26) (13 10 21) (22 18 3) (22 18 3) (28 29 24) (27 14 4)
(9 31 33) (32 6 23) (15 26 20) (24 8 12) (10 14 5) (18 25 28) (3 16 29) (21 7 4) (11 30 22) (11 30 22) (1 19 17) (13 2 27)
(25 3 13) (2 26 23) (15 19 7) (17 20 6) (16 27 32) (4 11 1) (9 8 14) (33 24 10) (12 5 31) (12 5 31) (30 18 29) (21 22 28)
(29 13 22) (4 25 6) (12 14 33) (20 1 2) (10 31 8) (28 3 11) (5 24 9) (23 7 17) (18 21 16) (18 21 16) (30 15 27) (26 19 32)
(25 23 16) (1 15 22) (19 30 21) (9 10 12) (4 17 28) (31 14 24) (3 6 2) (32 7 18) (27 26 29) (27 26 29) (20 13 11) (8 5 33)
(29 20 8) (3 21 24) (6 14 30) (4 12 15) (28 1 13) (33 27 25) (26 16 7) (23 5 11) (31 19 2) (31 19 2) (32 22 10) (17 9 18)
(15 3 9) (32 31 20) (26 1 30) (2 4 10) (27 21 5) (8 25 19) (24 11 18) (13 14 7) (6 16 28) (6 16 28) (17 12 22) (33 23 29)
(15 31 23) (7 28 30) (20 33 21) (5 29 19) (22 24 25) (6 13 26) (18 2 12) (8 11 27) (10 3 17) (10 3 17) (1 16 14) (4 32 9)
(16 13 30) (29 4 31) (3 32 33) (19 12 11) (18 15 5) (17 24 27) (1 6 7) (20 25 10) (2 22 8) (2 22 8) (21 9 23) (14 28 26)