Kirkman's Schoolgirls Wearing Hats and Walking through Fields of Numbers
Authors: Brown, Ezra; Mellinger, Keith E.
Source: Mathematics Magazine, Volume 82, Number 1, February 2009 , pp. 3-15(13)
Publisher: Mathematical Association of America
Abstract:The Kirkman schoolgirls problem, a famous gem due to T. P. Kirkman in the mid 19th century, asks for 7 distinct arrangements of 15 girls into 5 rows of 3 girls each with the condition that each girl walks in a row with every other girl exactly once. Solutions to this famous problem can be found in algebraic number fields, finite projective 3-space, and certain error-correcting codes. These connections are made in the present article, along with a thorough explanation of the underlying mathematical objects. Related questions are posed and surprising connections are realized.
Document Type: Research Article
Publication date: February 1, 2009
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