newbie trying to organize a Petanque melee triplette tourney

[atlpetanqueleague]

hello
searching for solution I found your forum very promising but as I have limited mathematics or programming skills I could not find any existing topic that seems to match my problem, so here it is :

1/ I would want to use excel or similar opensource calc sheets to be able to manage the tourney.
2/ we have 11 courts where 2 teams of 3 players can face each other every rounds, also as we doing this in one afternoon we only can play 4 or 5 rounds.
3/ we have a currently 47 players who want to participate so probably we need 8 courts only and one team will have only 2 players.
4/ each round we would like the players in the team to change (so they meet other people when playing)
5/ we would like that individual players do not play with the same partner as much as possible

all those parameters push me to search for Nested Balanced Incomplete Block Designs on internet, but I'm not sure this is really what I'm suppose to use and I certainly do not know how to translate this into an excel sheet.
any suggestion how to do this ? Thanks in advance for your support
The game we play is Petanque by the way ... atlpetanqueleague.com if you are interested ;-)
Rdgs Emmanuel
ps: in the past I build a excel sheet for 10 triplette team but as you will see a spread the player manually, it did the trick but I would like to build something more effective.

ps2: we do double full melee tourney using a great tool call https://kickertool.com/ Monster-DYP tournament model, it works perfectly for the double teams,  that will give you and idea of what we aiming for with triplette

[Ian Wakeling]

Hello Emmanuel,

I think in mathematical terms you do not need the complexity of the NBIBD. The number of rounds is sufficiently small, and the number of players sufficiently large that it should be possible to make a schedule where all of a player's partners and opponents are different people.  Then the design problem reduces to using part of a resolvable BIBD, or part of a resolvable covering.  Each time six people are scheduled to have a game you can decide on the 2 teams of 3 at random, or let themselves decide on the teams.  After some experimenting I found the schedule below.  Player 48 is the ghost player, so wherever it appears, this is a group of 5 people who must form one team of two and one team of three players.

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

If you play the first 4 rounds above, there will be no two players who play together in the same group twice.  If you play 5 rounds the pair (25 47) will occur twice.  If you play 6 rounds the pair (27 46) will also occur twice.

Hope that helps,

Ian

[atlpetanqueleague]

Whaoo !!, thanks, I was able to update my spreadsheet and I'm ready for our next tournament.

If I could ask for another question:
if we end up with more players let's say 6 more (another court) so the variable would be: 54 players, 9 courts and still 4 games round.
Then 6 more players want to join and we hit our max courts capacity today : 60 players, 10 courts still 4 games round.

would it be ok for you to suggest 2 more schedules ?
Thank you so much for your help.
Rdgs
Emmanuel

ps: I forwarded your response to Helmut Poppen who is developing Kikertool, that may give him some ideas.

[Ian Wakeling]

I have put two more schedules below.  Hope that helps.

9 rounds for 54 players where no 2 players meet more than once (no two players from the same column ever meet)

R1
1 10 19 28 37 46
9 18 27 36 45 54
5 14 23 32 41 50
3 12 21 30 39 48
8 17 26 35 44 53
4 13 22 31 40 49
2 11 20 29 38 47
7 16 25 34 43 52
6 15 24 33 42 51

R2
9 17 25 33 41 49
5 13 24 29 37 48
1 12 20 34 45 53
8 16 27 32 40 51
4 15 23 28 39 47
3 11 19 36 44 52
7 18 26 31 42 50
6 14 22 30 38 46
2 10 21 35 43 54

R3
5 15 22 35 45 52
1 11 21 31 41 51
9 16 26 30 37 47
4 14 24 34 44 54
3 10 20 33 40 50
8 18 25 29 39 46
6 13 23 36 43 53
2 12 19 32 42 49
7 17 27 28 38 48

R4
3 18 24 32 38 53
8 14 20 28 43 49
4 10 25 36 42 48
2 17 23 31 37 52
7 13 19 30 45 51
6 12 27 35 41 47
1 16 22 33 39 54
9 15 21 29 44 50
5 11 26 34 40 46

R5
8 13 21 34 42 47
4 12 26 33 38 52
3 17 22 29 43 51
7 15 20 36 41 46
6 11 25 32 37 54
2 16 24 28 45 50
9 14 19 35 40 48
5 10 27 31 39 53
1 18 23 30 44 49

R6
4 11 27 30 43 50
3 16 23 35 42 46
8 15 19 31 38 54
6 10 26 29 45 49
2 18 22 34 41 48
7 14 21 33 37 53
5 12 25 28 44 51
1 17 24 36 40 47
9 13 20 32 39 52

R7
2 14 26 36 39 51
7 10 22 32 44 47
6 18 21 28 40 52
1 13 25 35 38 50
9 12 24 31 43 46
5 17 20 30 42 54
3 15 27 34 37 49
8 11 23 33 45 48
4 16 19 29 41 53

R8
7 12 23 29 40 54
6 17 19 34 39 50
2 13 27 33 44 46
9 11 22 28 42 53
5 16 21 36 38 49
1 15 26 32 43 48
8 10 24 30 41 52
4 18 20 35 37 51
3 14 25 31 45 47

R9
6 16 20 31 44 48
2 15 25 30 40 53
7 11 24 35 39 49
5 18 19 33 43 47
1 14 27 29 42 52
9 10 23 34 38 51
4 17 21 32 45 46
3 13 26 28 41 54
8 12 22 36 37 50


Here are 5 rounds for 60 players where no 2 players meet more than once:
R1
28 37 46 43 41 35
49  1 11  2 45 29
13 48  8 51 33 19
50 20 60 44 24 55
38 57 27 53  9 26
 3 22 36 16 47 23
40 12 17 56 42 39
59 31  5  7 58 52
54 25 32  4 34 15
14 30 10 18  6 21

R2
29 38 47 44 42 31
50  2 12  3 41 30
14 49  9 52 34 20
46 16 56 45 25 51
39 58 28 54 10 27
 4 23 37 17 48 24
36 13 18 57 43 40
60 32  1  8 59 53
55 21 33  5 35 11
15 26  6 19  7 22

R3
30 39 48 45 43 32
46  3 13  4 42 26
15 50 10 53 35 16
47 17 57 41 21 52
40 59 29 55  6 28
 5 24 38 18 49 25
37 14 19 58 44 36
56 33  2  9 60 54
51 22 34  1 31 12
11 27  7 20  8 23

R4
26 40 49 41 44 33
47  4 14  5 43 27
11 46  6 54 31 17
48 18 58 42 22 53
36 60 30 51  7 29
 1 25 39 19 50 21
38 15 20 59 45 37
57 34  3 10 56 55
52 23 35  2 32 13
12 28  8 16  9 24

R5
27 36 50 42 45 34
48  5 15  1 44 28
12 47  7 55 32 18
49 19 59 43 23 54
37 56 26 52  8 30
 2 21 40 20 46 22
39 11 16 60 41 38
58 35  4  6 57 51
53 24 31  3 33 14
13 29  9 17 10 25

[atlpetanqueleague]

You Rock !! 
took this and prepared 3 set of excel files for our pétanque tournament, we ready for all our members and new one to join the fun !
Thanks again
Rdgs
Emmanuel