You are here

Kirkman's Schoolgirls Wearing Hats and Walking Through Fields of Numbers

Award: Carl B. Allendoerfer

Year of Award: 2009

Publication Information: Mathematics Magazine, vol. 82, no. 1, February 2009, pp. 3-15.

Summary: The historical basis for this interesting article is a problem in recreational mathematics posed by T. P. Kirkman in 1850.

"Fifteen young ladies of a school walk out three abreast for seven days in succession: it is required to arrange them daily so that no two shall walk abreast more than once."

The authors explore the theory and applications of block designs. In the process, solutions to the schoolgirls problem are uncovered in such seemingly unrelated areas as the subfield structure of algebraic number fields and the configuration of "spreads" and "packings" in finite projective geometry.

Read the Article

About the Authors (From the Prizes and Awards Booklet, MathFest 2010) 

Ezra (Bud) Brown grew up in New Orleans, has degrees from Rice and Louisiana State University, and has been at Virginia Tech since 1969, where he is currently Alumni Distinguished Professor of Mathematics. His research interests include number theory and combinatorics. He particularly enjoys discovering connections between apparently unrelated areas of mathematics and working with students who are engaged in research. He has been a frequent contributor to the Mathematical Association of America journals, and he just finished a term as the Maryland, District of Columbia, and Virginia Section Governor. He and Art Benjamin edited Biscuits of Number Theory, a collection of number theory articles published in 2009 by the Mathematical Association.

In his spare time, Bud enjoys singing (from opera to rock and roll), playing jazz piano, and talking about his granddaughter Phoebe Rose. Under the direction of his wife Jo, he has become a fairly tolerable gardener, and the two of them enjoy kayaking. He occasionally bakes biscuits for his students, and he once won a karaoke contest.

Originally from Lancaster County, Pennsylvania, Keith E. Mellinger graduated with his Ph.D. in mathematics from the University of Delaware and was a post-doc at the University of Illinois at Chicago before moving to the University of Mary Washington in 2003. He is currently an Associate Professor and Chair of the Department of Mathematics at the University of Mary Washington. His research interests are in discrete mathematics, usually connected to finite geometry, and he regularly mentors undergraduate researchers. In 2005 he earned a research grant from the National Security Agency, and in 2008 he won the Outstanding Young Faculty Award presented by the University of Mary Washington.

Outside of mathematics, Keith is a decent cook, an average tennis player, and an accomplished musician. He has performed in different bands over the years, usually on acoustic guitar. However, most of his time outside the office these days is spent with his two beautiful children, Gabriel and Cecilia.

MSC Codes: 
12-XX, 97A30
Author(s): 
Ezra Brown (Virginia Polytechnic Institute and State University) and Keith E. Mellinger (University of Mary Washington)
Flag for Digital Object Identifier: 
Publication Date: 
Wednesday, August 11, 2010
Publish Page: 
Summary: 

The historical basis for this interesting article is a problem in recreational mathematics posed by T. P. Kirkman in 1850.

"Fifteen young ladies of a school walk out three abreast for seven days in succession: it is required to arrange them daily so that no two shall walk abreast more than once."

Dummy View - NOT TO BE DELETED