MATC Mathematics Club
Lecture #51

Madison Area Technical College
Madison, Wisconsin


Spring 2006 Presentation #51 (Thursday March 9, 2006)
by John Frohliger

"One Potato, Two Potato, ..."

Abstract: In the children’s game, participants go around a circle reciting the poem, "One Potato, Two Potato." When they reach the end of the poem, that person is removed from the circle. The children continue this until only one player is left. This is a form of the classic Josephus Problem: Suppose there are m people in a circle, and you go around eliminating every kth person until only one person remains. Where should someone be in the original circle in order to be the last one? We will answer this question, consider specific cases, and discuss variations of the problem.

Biography:  Professor John A. Frohliger of St. Norbert College has been an Associate Professor of Mathematics at St. Norbert College since 1983. He received his B.A. from Indiana University and  M.S. and Ph.D. from Purdue University. He has served as the Wisconsin coordinator of the American High School Mathematics Examination (AHSME), 1987-92,  the Chair of the Wisconsin Section of the MAA 1998-1999 and a Reader for the AP calculus exam since 2000.

Thanks are extended to Flynn Dustrud for taking these pictures.
Click on any of the above pictures for the original sized image file, or on any image below to see notes on the lecture.
Click here to download Professor Frohliger's Powerpoint presentation.



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