First time on this forum. Engineer undergrad, loved discrete math class but always struggled with stats. Here is a problem I am facing I was hoping to get some help with.
We are organizing a "speed networking" event for a business school alumni chapter. Expecting 80 participants, with ~20 tables. The goal is to allow everyone to give everyone else their 1 minute elevator pitch to break the ice, followed by a cocktail. Every table will have 4 people sitting at it. We will have 20 rounds of 4 minutes. At every round, we will ring a bell, at which point, one person will remain at his/her table, and the 3 others will move. The goal is to maximize the number of new people everyone meets, and avoid having 2 people run into each other a second time at a table at any given as much as possible.
The last time we tried it, we had a simple approach. The group was smaller, and the approach was one person stays, one person goes left and one goes right. As a perfect example of difference between pure math modeling and reality (especially when humans and free will gets involved), it quickly turned into total chaos. About the 3rd round, one person decided to stay at a table passed the bell to finish a chat. The person coming to take their spot then decided to bypass that table and join the second table. But came next round, decided to go back to the table they missed and another table had a static guest issue. The problem quickly compounded to a point where at every round, people would just look for a semi empty table and go there.
This time around, we'd like to give every participant a schedule of where they should be at what round. The goal is that if ever someone decides to not move, or moves to the wrong table, at the following round, instead of compounding the problem, everyone can simply look at their schedule, and from which round we are at, know where they should be. So the mess will be contained at a few tables per rounds, as opposed to compounding round after round.
So here lies the problem. We need to generate a schedule for every individual that we can print and handout. For example: PERSON 1, Round 1: Table 1, Round 2: Table 2, Round 3: Table 3, etc... PERSON 2, Round 1: Table 1, Round 2: Table 20, Round 3: Table 19, etc...
Question is, (is there, and if so) what kind of pattern can we use to generate these schedules? (like making groups of 20, groups 1 stays, groups 2 goes table +1, groups 2 goes to table -1, groups 3 goes to table +2?) Or what way could you suggest we can generate these roadmaps for guests (preferably in excel)? Would it be preferable to have 25 tables and smaller groups? Longer rounds? If so, is there an optimal number we could aim for that would minimize duplicate encounters? (like making 17 rounds with 24 tables)? If that optimization exists, what is it (always 80 participants, max 25 tables, and rounds between 3 and 5 minutes)?
I find the problem conceptually fascinating, and after hours in excel and forums... I have to admit defeat. Any help would be greatly appreciated.