Forming all pairs in a minimal number of steps

How can N individuals in a closed space meet and greet each other most efficiently? This paper presents a general solution to this problem—an algorithm or “dance” that will achieve universal pairing in the least possible number of moves or steps. A proof of the suggested algorithm is included, showing that it guarantees that every two participants will greet each other once and only once, and that no procedure with this property can be accomplished with fewer steps. Slightly different procedures are required for the odd and even cases. The algorithm has been applied in classroom settings, and could be applied in any social setting where the objective is to initiate efficiently a sense of group cohesion and common purpose.