<s>[INST] Create unique table rotation for an event I am planning to host an event with 14 people participating in it. There will be five tables in total. (4 tables with 3 people each and 1 with 2).
I want to rotate the tables 5-6 times and to ensure that everyone gets to meet as many people as possible and minimize (if not completely avoid) that some people see each other twice.
I figured out how to do tables of 2, but I struggle with tables of 3.
I would very much appreciate your help!
 [/INST] Here's a 7-round schedule with every pair covered exactly once, obtained via integer linear programming:
1  {6,8,11}  {10,12,14} {4,5,7}   {3,9,13}   {1,2}
2  {3,7,11}  {1,4,10}   {5,8,13}  {2,6,14}   {9,12}
3  {2,7,8}   {5,9,10}   {1,11,12} {3,4,14}   {6,13}
4  {1,3,8}   {4,6,9}    {2,5,12}  {10,11,13} {7,14}
5  {2,9,11}  {6,7,10}   {4,8,12}  {1,13,14}  {3,5}
6  {2,3,10}  {8,9,14}   {1,5,6}   {7,12,13}  {4,11}
7  {5,11,14} {3,6,12}   {2,4,13}  {1,7,9}    {8,10}

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