



 
Mark, There is a schedule with no repeats, but you need 11 trips to have each person with each of the ten possible partners (one week is solo). Try this:
To get the schedule for the next trip, add one to every number in the current one, and wrap 11 back around to 1 as if on an odometer. If you continue long enough, this will give you the 11 trip schedule that was mentioned above. Using the first seven trips will give you a schedule that’s the best you can do, so you can stop after you have seven. —Victoria  


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