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| Math Central | Quandaries & Queries |
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Question from Jamie: Looking to schedule a 12 week poker tournament with 18 players ...playing 2 separate 9 person tables...I'm looking to have a balanced schedule where everyone player with each other an equal amount of time |
Jamie,
I’ve had a program running for about 5 days to try to find the best possible solution. It has looked at about 1.5 billion schedules, but is less than half way done and I’m going to stop it. Here is the best schedule it found so far. The players are the positions and the numbers indicate the two tables. Here, player 1 is always at table 0, but if that matters you could switch the tables half of the time and the balance of the schedule will be unchanged.
Day 1 : (0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1)
Day 2 : (0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1)
Day 3 : (0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1)
Day 4 : (0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1)
Day 5 : (0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0)
Day 6 : (0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0)
Day 7 : (0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0)
Day 8 : (0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0)
Day 9 : (0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1)
Day 10 : (0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0)
Day 11 : (0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1)
Day 12 : (0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1)
—Victoria
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