Slot car racing help please

[Top_Down]

I run a four lane slot car club and currently have manually produced race grids for 8, 12, 16, 20 and 24 people. We just use the nearest race grid if we don't have the full 8, etc.

As there are four lanes, there are always four rounds of heats. The number of heats per round is determined by the number of racers. 8 racers = 4 rounds of 2 heats, so 8 races. 12 racers = 4 rounds of 3 heats, so 12 races, etc.

In round one people are allocated numbers 1-8, 1-12, etc. and keep these numbers for the night. I then use this to rotate people through the lanes and against as many different competitors as possible.

Each person must race once on each lane and ideally never meet the same person twice.

I've got close, doing this by manually jigging the numbers round but there are instances where some people meet two or three times and it's driving me mad.

Does anyone have a solution to this please? Fixed groups as above would be fine, as people's names just get entered into the next meetings race grid in the winning order of the previous meeting.

However, as well as the 'Mini' solution (four separate grids and we just leave places empty if we don't get a full turnout) a 'Rolls Royce solution where I could just enter the exact number of names and it would sort them into rounds and heats would be a bonus - but as well as , rather than instead of, the 'Mini' solution would be brilliant. (I.E. it would cope with any number, leaving lanes empty in a heat if necessary.)

A lot to ask I know - but I've been struggling to get the 'perfect grid' for years! (I use Excel, by the way.)

[Ian Wakeling]

With 4 rounds then there will always be 12 opponents per player, so the "never meet the same person twice" criterion can only be met if there are 16 or more people.  There are also other problems with 8 or 12 people, if you require that the tournament can be played in rounds, where each player competes exactly once per round, then it will be impossible to get good balance for the number of times pair of players compete together in the same race.  So perhaps you should relax this requirement.

For 16, 20 ,24 or other higher multiples of 4 then there should be no problems in finding a balanced schedule.  I have pasted in some examples below.

16 players
           slot1 slot2 slot3 slot4
r1   h1    (15    14     7     4)
r1   h2    (12    16     2     5)
r1   h3    ( 9    10    13     1)
r1   h4    ( 6     8    11     3)

r2   h1    (13     6    12    14)
r2   h2    ( 8    15    16    10)
r2   h3    ( 5     1     3     7)
r2   h4    ( 2     4     9    11)

r3   h1    ( 3     9    15    12)
r3   h2    ( 7     2     8    13)
r3   h3    (10     5     4     6)
r3   h4    ( 1    11    14    16)

r4   h1    (11    13     5    15)
r4   h2    (16     7     6     9)
r4   h3    (14     3    10     2)
r4   h4    ( 4    12     1     8)


20 players
           slot1 slot2 slot3 slot4
r1   h1    ( 4    16     6    17)
r1   h2    (18     3     8    19)
r1   h3    ( 7     1     5     2)
r1   h4    (10     9    14    13)
r1   h5    (11    20    12    15)

r2   h1    (17     8     1    20)
r2   h2    (19     5    10     4)
r2   h3    (13     6    11    18)
r2   h4    ( 3    15     2     9)
r2   h5    (12    14     7    16)

r3   h1    ( 6     7     9     8)
r3   h2    (16    10    20     3)
r3   h3    (15    13    17     5)
r3   h4    ( 1    18     4    12)
r3   h5    (14     2    19    11)

r4   h1    (20    19    13     7)
r4   h2    ( 8     4    15    14)
r4   h3    ( 5    12     3     6)
r4   h4    ( 2    17    18    10)
r4   h5    ( 9    11    16     1)


24 players
           slot1 slot2 slot3 slot4
r1   h1    (11     6    16    10)
r1   h2    (15    19    13    24)
r1   h3    ( 8     9    20    22)
r1   h4    ( 3     1    21     5)
r1   h5    (14    18     7     2)
r1   h6    (12    17    23     4)

r2   h1    ( 2     5    10    19)
r2   h2    (23    15     1     8)
r2   h3    (16     4    22    14)
r2   h4    (24    12    18    20)
r2   h5    (13     7     6     3)
r2   h6    (21    11     9    17)

r3   h1    ( 1     2    11    12)
r3   h2    (18    23     3    16)
r3   h3    ( 9    14     5    15)
r3   h4    ( 4     8    19     6)
r3   h5    (20    10    17    13)
r3   h6    ( 7    22    24    21)

r4   h1    ( 6    20    14     1)
r4   h2    (17    16    15     7)
r4   h3    ( 5    24     4    11)
r4   h4    (19     3    12     9)
r4   h5    (10    21     8    18)
r4   h6    (22    13     2    23)

[Top_Down]

Thank you.  8-)

That's great and a big help. I hadn't appreciated there were problems below 16. I just thought it was me and that, eventually, I would hit on the right rotation/combination.  

So if I relax the criteria below 16 are there optimum grids that minimise the number of times the same people would meet in an 8 and 12 group please? If we don't get a full turnout I could prioritise on leaving these lanes empty then.  

[Ian Wakeling]

Here are some schedules for 8 and 12 players.

(6 4 3 2)
(1 2 4 7)
(4 6 8 5)
(5 3 1 8)
(2 5 6 1)
(7 8 2 3)
(3 7 5 4)
(8 1 7 6)


(12  7  9  6)
(11  5  7  8)
( 4  3  8  9)
( 5  9  2  4)
(10  4  1  7)
( 8  1 12  2)
( 3 12 10  5)
( 7  2  3 11)
( 2  8  6 10)
( 1  6  5  3)
( 6 11  4 12)
( 9 10 11  1)


Along similar lines if you had 13 players there is a perfect schedule where each player gets to race against all 12 others exactly once.

( 1  2  4 10)
( 2  3  5 11)
( 3  4  6 12)
( 4  5  7 13)
( 5  6  8  1)
( 6  7  9  2)
( 7  8 10  3)
( 8  9 11  4)
( 9 10 12  5)
(10 11 13  6)
(11 12  1  7)
(12 13  2  8)
(13  1  3  9)

[Top_Down]

thank you. Much appreciated.

[Top_Down]

I just wanted to let you know that we're adopting the 16, 20 and 24 person rotations you came up with - and if you ever have time to do a 28 and 32 we'd adopt those too.
 
I couldn't follow the 8 and 12 rotations though, so we stuck with those we already have.
 
Thank you so much for your help.
 

[Ian Wakeling]

Good to know that you are making use of these schedules.

Here are some 28 and 32 player rotations.

28 Players

r1   h1   (28 22 13 21)
r1   h2   (17  1 19 23)
r1   h3   (16  9 15  4)
r1   h4   (26 25 14  7)
r1   h5   ( 3 24 20  5)
r1   h6   ( 8 11  6 12)
r1   h7   (10 27 18  2)
 
r2   h1   (27 12 28 17)
r2   h2   (24 15 25 13)
r2   h3   (20  2  1 14)
r2   h4   ( 5 21  4  8)
r2   h5   (23 16 11 18)
r2   h6   ( 7  3 10 22)
r2   h7   ( 6 19 26  9)
 
r3   h1   ( 2  4 24  6)
r3   h2   (21 10 17 15)
r3   h3   ( 1 18  8 25)
r3   h4   (14 28  9 11)
r3   h5   (19  7  5 27)
r3   h6   (22 20 12 16)
r3   h7   (13 23  3 26)
 
r4   h1   ( 4 14 23 10)
r4   h2   (15  6 22  1)
r4   h3   (18 26 21 20)
r4   h4   ( 9  8 27  3)
r4   h5   (11 17  7 24)
r4   h6   (25  5 16 28)
r4   h7   (12 13  2 19)


32 Players

r1   h1   (16 14 22 25)
r1   h2   ( 2 18  4 11)
r1   h3   (20 10 15 30)
r1   h4   (32  7 21  5)
r1   h5   (12  6  8 29)
r1   h6   (17 31 27  9)
r1   h7   ( 3 24 13 19)
r1   h8   (28 26 23  1)
 
r2   h1   (14 20  1 13)
r2   h2   ( 6 25 11 23)
r2   h3   ( 9 15 26  3)
r2   h4   (24 16 18  7)
r2   h5   (29 22 19  2)
r2   h6   (27 12 30 32)
r2   h7   (31 28  5  8)
r2   h8   ( 4 21 17 10)
 
r3   h1   (18  1 29 21)
r3   h2   (10  8 25 24)
r3   h3   (26 17  6 16)
r3   h4   (22 27  3  4)
r3   h5   ( 5  9 12 14)
r3   h6   (30 19  7 28)
r3   h7   (11 13 32 15)
r3   h8   (23  2 31 20)
 
r4   h1   (15 29 16 31)
r4   h2   (19 11 14 17)
r4   h3   (21 23 24 27)
r4   h4   (25 30  9 18)
r4   h5   ( 8 32  2 26)
r4   h6   ( 7  3 20  6)
r4   h7   (13  4 28 12)
r4   h8   ( 1  5 10 22)

[Top_Down]

Wow! Thank you!  

I wasn't expecting such a quick response - or any at all, at this time of year, to be honest. That's wonderful.  

I'll build these into our Race Management System asap, ready for the new season. which starts on Jan 5th!