 The problem can be generalized to formula_1 girls, where formula_1 must be an odd multiple of 3 (that is formula_3), walking in triplets for formula_4 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, 6"t" + 3) with parallelism (that is, one in which each of the 6"t" + 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 formula_5 was only proposed later.