I'm hosting a speed networking session where there are 10 people at 5 tables (2 people per table.) Each table is hosted by a different person. There will be four rotations. It does not matter if everyone meets everyone - the objective is for everyone to meet the 5 "hosts."
Is there a formula for calculating the rotations so everyone gets to visit each table and meet each table's host AND not be matched with the same person twice? I'm having flashbacks to my high school pre-calc classes and studying probability, so I know this is a math problem but I can't figure out the next step.
EDIT: I misstated the conditions of the problem; I'm sorry about that. I've edited the question accordingly.
Not everyone will meet everyone (as that would require everyone to meet 9 other people, i.e. at least 9 rounds). With fourrotations, i.e. 5 sessions, the best you can do as in speed dating, i.e. each of five (men, say) meets each of the other five (women, say). A simple method is to let the ladies remain seated and the gents rotate.
To really let all pairs meet, you need 9 rounds. This can be achieved as follows: One person remains seated an dthe other nine rotate: $$\begin{matrix}A&\to&B&\to&C&\to&D&\to &E\\ \uparrow&&&&&&&\swarrow\\ I&\leftarrow&H&\leftarrow&G&\leftarrow&F&&X\end{matrix} $$