Generalization
The problem can be generalized to girls, where must be an odd multiple of 3 (that is n 3 (mod 6)), walking in triplets for ½(n-1) days, with the requirement, again, that no pair of girls walk in the same row twice. The solution to this generalisation is a Steiner triple system, an S(2, 3, 6t + 3) with parallelism (that is, one in which each of the 6t + 3 elements occurs exactly once in each block of 3-element sets), known as a Kirkman triple system. It is this generalization of the problem that Kirkman discussed first, while the famous special case was only proposed later. A complete solution to the general case was given by D. K. Ray-Chaudhuri and R. M. Wilson in 1968, but had already been settled by Lu Jiaxi in 1965.
Many variations of the basic problem can be considered. Alan Hartman solves a problem of this type with the requirement that no trio walks in a row of four more than once using Steiner quadruple systems.
More recently a similar problem known as the Social Golfer Problem has gained interest that deals with 20 golfers who want to get to play with different people each day in groups of 4.
As this is a regrouping strategy where all groups are orthogonal, this process within the problem of organising a large group into a small groups where no two people share the same group twice can be referred to as orthogonal regrouping. However, this term is currently not commonly used and evidence suggests that there isn't a common name for the process.
Read more about this topic: Kirkman's Schoolgirl Problem