So, yours truly has somehow found himself organising the rota for an online quiz team - it's a squad of seven, where everyone is of a similar standard, and an 11-round season for a team of four, so somehow have to rotate in such a way that everyone gets equal game (i.e. all 7 would get 6 games, and two would get a seventh). Pen and paper has defeated me to date, but perhaps the mathematical minds of OTF will consider it a trifle.
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A mathematical conundrum
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Trial and error towards the end but it gives you an answer.Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7 Week 8 Week 9 Week 10 Week 11 No. of turns 1 1 1 1 1 1 6 2 2 2 2 2 2 6 3 3 3 3 3 3 3 7 4 4 4 4 4 4 4 7 5 5 5 5 5 5 6 6 6 6 6 6 6 6 7 7 7 7 7 7 6
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WFD's solution works, but if I were you, I'd shuffle the weeks around to make it feel more fair to the participants as the schedule unfolds. In the current schedule, persons 3 and 4 will have played three rounds before 7 played their first.
As order, I'd propose: week 1, 5, 2, 6, 3, 7, 4, 8, 9, 10, 11. Further optimizations are definitely still possible; I haven't given it a lot of thought.Last edited by Wouter D; 15-01-2021, 14:22.
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Originally posted by Wouter D View PostWFD's solution works, but if I were you, I'd shuffle the weeks around to make it feel more fair to the participants as the schedule unfolds. In the current schedule, persons 3 and 4 will have played three rounds before 7 played their first.
As order, I'd propose: week 1, 5, 2, 6, 3, 7, 4, 8, 9, 10, 11. Further optimizations are definitely still possible; I haven't given it a lot of thought.
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Originally posted by Rogin the Armchair fan View PostWhy don't you find an eighth member and enter 2 teams of 4?
Originally posted by Walt Flanagans Dog View PostTrial and error towards the end but it gives you an answer.Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7 Week 8 Week 9 Week 10 Week 11 No. of turns 1 1 1 1 1 1 6 2 2 2 2 2 2 6 3 3 3 3 3 3 3 7 4 4 4 4 4 4 4 7 5 5 5 5 5 5 6 6 6 6 6 6 6 6 7 7 7 7 7 7 6
* - some combinations do remain more likely than others. Specifically 1&3, 5&7 and 4&6. Each of these pairings happens 5 times in total. Rather than a problem this can be sold as a 'feature' - either putting couples of particularly good friends together more often than not, or (if you are feeling more competitive!) matching complimentary knowledge sets up, say a sport specialist being paired with an entertainment one. There are also pairing that happen less often than average, such as any odd number with any even number. Which, again, gives a way to 'tailor' teams whilst still maintaining overall fairness and (the impression of) neutrality.
Running that pattern, and sticking with it all the way through gives the following:-
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