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I would like some help scheduling an event. I have done the scheduling matrix with up to 20 participants, but now the population has gotten too large and I need some help.

Previously, there were 20 participants competing in 10 events, so each participant competed in each event once (mandatory) against a random opponent. This made 10 rounds of competition with no Byes. It was not required that they compete against every opponent, but they could not compete against another participant more than once (mandatory).

Now the event has grown, and I need help scheduling. I was hoping someone could provide the scheduling for 22 and 24 participants. I am willing to increase the number of events for ease of scheduling, so 11 events for 22 participants and 12 events for 24 participants. The same mandatory constrictions would apply.

Any help would be greatly appreciated! Thank you!

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For $22$ people and $11$ events you can divide the people into two groups of $11$. Arrange the events in a circle. One group rotates around the circle clockwise. The other rotates around the circle counterclockwise. This is a variant on the Mitchell movement in bridge tournaments.

For $24$ people and $12$ events you can do the same with $11$ rounds. After the sixth event one group of people should skip an event so they don't meet the same opponent from the first.

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  • $\begingroup$ Thank you! I assume this same practice works if you continue ue to expand the number of events and participants in the same pattern. $\endgroup$ – WB1 Sep 26 '18 at 18:10

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