In combinatorics, a Steiner Triple System of order v is a collection of triples or 3-subsets of a set X of size v such that each pair of elements of X occurs in exactly one triple. In other words a Steiner Triple System is a 2-design with parameters (v, 3, 1, (v-1)/2, v(v-1)/6) . Since the design parameters must be integers, it is necessary that v = 6n + 1 or v = 6n + 3. Kirkman showed that this is a sufficient condition that a Steiner Triple System exists (see Reverend Kirkman's Schoolgirls).

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