The Carl B. Allendoerfer Awards, established in 1976, are made to honor authors of outstanding expository articles published in Mathematics Magazine.  Carl B. Allendoerfer, a distinguished mathematician at the University of Washington, served as President of the Mathematical Association of America, 1959-60.  This year's awards were presented at the August 2001 MathFest, in Madison, Wisconsin.

James N. Brawner, Dinner, Dancing, and Tennis, Anyone?, Math. Mag. 73 (2000) 29-36.

Citation from the Allendoerfer Prize Committee  In the 1996 men's draw for the U.S. Open tennis tournament, Andrei medvedev was pitted against Jean-Phillipe Fleurian.  For reasons explained in the paper, a redraw was conducted.  Again, Medvedev was pitted against Fleurian.  A tennis official wondered about the probability of such an event and contacted the author of this paper.  After rephrasing the question in two ways, the author answers both questions and connects them to two classical problems: Montmort's problem of coincidences and the probleme des menages. The reader is engaged throughout by substantial mathematics, as well as numeric examples.  This well-written article concludes with some interesting problems, one of which has already inspired a follow-up article [see Barbara H. Margolius, Avoiding your spouse at a bridge party, Math. Mag. 74 (2001), 33-41].
 

Biographical Note  Jim Brawner grew up in Atlanta, Georgia and has spent his adult life bouncing up and down the Eastern United States.  He was an undergraduate at Williams College in Massachusetts, where he majored in English and Mathematical Sciences, and he received his Ph.D. in algebraic geometry at the University of North Carolina at Chapel Hill.  After spending several years at St. John’s University, just down the road from the U.S. Tennis Center in Queens, New York, he is now an assistant professor at Armstrong Atlantic State University in Savannah, Georgia.  In addition to algebraic geometry, his interests include combinatorics, number theory, balancing objects on his nose, and of course, dining, dancing, and playing tennis with his wife, Aubrey, and their two sons, Jimmy and Will.
 

Response  I am thrilled and honored to receive the Carl B. Allendoerfer Prize, and I am very grateful to the prize committee for this honor.  “Dinner, Dancing, and Tennis, Anyone?” grew out of a talk given for our wonderful weekly luncheon colloquium series at Armstrong Atlantic State University.  I am grateful to Ed Wheeler for his encouragement in writing a paper based on the talk, and for suggesting Mathematics Magazine as an appropriate forum.  I wanted to thank (former) editor Paul Zorn in the acknowledgments for his tremendous help, but he claimed he was just doing his job; I am pleased to be able to thank him now for his many helpful suggestions.  I have been delighted by several excellent solutions to the problems I posed at the end of the paper, most notably by Barbara Margolius’ article in this year’s Magazine.  Lastly, I would like to thank the USTA for asking an intriguing question, and my family for their love and support in listening to the answer.