How to form pairs in a group so that each element is coupled with each other only once My question is derived from real life but I think it's a classic mathematical problem. 
My uncle wants to organize a group activity with 12 people and wants to start by pairing each person with each other person so they can meet shortly. Everyone has to see every other person, but only once. His initial question was if there could be an easy rotation system to organize this (like putting everyone in two rows or a circle or something like that), which I couldn't find. But now I'm even struggling just to find a way that it can organized at all, by just writing down one example of each of the 11 'meeting rounds' with the numbers of the persons that have to meet in each round. 
However I'm sure this is a standard mathematical question that has been discussed often before - can someone give me a solution? A not too complicated rotation system would be great, a way to write down the order in which it can be organized would be nice as well. Thanks!

You could look at the question Gay Speed Dating problem.  The bridge players call it a Howell movement
