12-player whist tournament - schedule adjustment

[larstm]

Hi there, 

Thanks for having me on the forum. I am currently breaking my head over the following: 
We are playing a 12 player whist card game tournament throughout the year. I have setup a schedule for it, and we have played 4 rounds, all good so far. However, I just noticed the software I used for the scheduling has everything correct for the first few rounds, but starts making mistakes then. I didn't check this properly when we started. The question now is whether there is a way to finish the round robin whist schedule for the rest of the rounds, keeping up the 4 rounds that were already played. 

Any input or help is much appreciated! 

Cheers,
Lars 

[Ian Wakeling]

Hi Lars,

I think it possible that there are many 4 round schedules that can not be completed into a full 11 round whist schedule, and that applies even if the 4 rounds in question don't have any mistakes.  It's a hard problem, as a computer search to complete the schedule is probably the only way.  Can you post the entire schedule as I may be able to see where things went wrong.

Thanks,

Ian

[larstm]

Hi Ian, 

I supposed so. The rounds played so far are as follows: 

Round 1: 
1, 5 vs 2, 11 
3, 7 vs 6, 12 
4, 8 vs 9, 10 


Round 2: 
1, 11 vs 4, 6 
2, 8 vs 7, 12 
3, 10 vs 5, 9

Round 3:
1, 6 vs 10, 12 
2, 4 vs 3, 8 
5, 11 vs 7, 9 

Round 4:
1, 8 vs 3, 5 
2, 12 vs 10, 11 
4, 9 vs 6, 7 

The main goal is to finish a proper 11 round whist schedule given these rounds. I assumed after quick assessment of these 4-5 rounds that all was correct, only to find out later that players in later rounds are in the same pair as earlier in the tournament. 

My conclusion so far is indeed that there is no easy solution to this, if any. 

Best,
Lars

[Ian Wakeling]

I tried, but I can not do any better than the schedule below.  All pairs of players partner exactly once, but the opposition pairings are not balanced - most players have 1 or 2 players who they oppose 3 times, and 1 or 2 other players who they oppose once.  The schedule may have less mistakes than your original, so it may be useful.

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