Kirkman's Schoolgirls Problem

Proposed by the Reverend Thomas P. Kirkman in 1850 this problem asks if it is possible for a schoolmistress to take her class of 15 girls on a walk arranged in five rows with three girls per row, on seven consecutive days such that no girl will walk with any of her classmates in a triplet more than once?

The problem was solved in the same year it was formulated, and leads to the study of Steiner triple systems and more generally combinatorial designs .

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An On-line Dictionary of Combinatorics