MHB Darts league question (maths related)

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To create a fair schedule for a darts league with 14 players and start times between 7:30 and 10:30 in 30-minute intervals, a balanced distribution is essential. The goal is to ensure that each player has an equal number of early and late starts to avoid complaints about unfair scheduling. The current alphabetical order method favors players with names starting with 'A', leading to imbalanced start times. A potential solution involves developing a rotation system that assigns start times based on a set formula, ensuring equitable distribution across all players. Further adjustments may be needed to account for the fact that the same players face each other weekly.
teeach
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Hi, wondering if anyone can help solve a query I have.
I've been tasked with setting up a local darts league and want to make it fir regarding start of play times.

We have 14 players and i wish to distribute these players between 7:30 and 10:30 for start times in 30 minute intervals.

Any sort of formula/cheat table so everyone gets the same amount of 7:30 starts and 10:30 starts this is because people may complain if they keep getting late starts and the online league software we are using seems to prefer alphabetical order so someone with the letter 'A' at the start of their name gets to play at 7:30 14 times out of 26 games.

any advice?
 
Mathematics news on Phys.org
think i may have solved it

2m6rj1k.png


if i continue in that vein i think it will pan out fairly?
 
Ahhh ok i havent, as the same players play each other every week dohhhelppppp
 
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