Problem of the Week 882

A Cascading Candy Convergence

A number of students sit in a circle while their teacher gives them candy. Each student initially has an even number of pieces of candy. When the teacher blows a whistle, each student simultaneously gives half of his or her own candy to the neighbor on the right. Any student who ends up with an odd number of pieces of candy gets one more piece from the teacher. Show that no matter the starting configuration, after finitely many rounds everyone has the same amount of candy.
SOURCE: 1962 Beijing Olympiad
REQUEST FROM STAN
Please reply to: [email protected]
As many of you know, our DEC alpha software for running this list is feeble in some ways. We must delete bounces manually, and so many of you have been deleted when you did not want to be.
Swarthmore College is willing to take over the list next year, but they too do not have good software for recognizing bounces and deleting them only if four occur in two months or something like that. But they do have access to UNIX. I believe there are UNIX programs out there that would do this well. Can any of you help by suggesting some to me? A friend suggested "majordomo" but Swarthmore reports that that does not have an automated bounce-processing capability.
Many thanks, Stan Wagon

KONHAUSER PROBLEM FEST RESULTS
The 1999 Konhauser problem fest was held Saturday, February 27 at St. Olaf College in Northfield. As many POTW regulars know, the contest is held annually in honor of Joe Konhauser, Macalester faculty from 1968-1992 and founder of POTW at Macalester. The first place finishers win the right to display the coveted the pizza trophy at their college for one year. The pizza trophy is a Helaman Ferguson sculpture illustrating the pizza theorem, which I'm told was Joe's favorite.
Several teams from a number of local colleges (Gustavus Adolphus, Carleton, Macalester, St. Olaf and the University of St. Thomas) competed. The top six results are as follows:
  1. Macalester (Tamas Nemeth, Vahe Poladian, John Renze)              85
  2. Carleton (Dave Frohardt-Lane, Tim McMurry, Matt Riddle)           66
  3. Gustavus Adolphus (Andrew Shallue, Joshua Helston, Erik Tou)      59
  4. Macalester C (Jan Jamrich, Emilia Simeonova, Bill Owens)          50
  4. St. Olaf (Carl Larson, Matt Feig, Mike Raiter)                    50
  4. Macalester D (Erik Slivken, Ghaith Hiary, Andy Cantrell)          50
Well done to all.
BONUS
We will not use problems for the Konhauser Problemfest as POWs, but many of you might enjoy knowing which of them were interesting. George Gilbert made up the questions and perhaps the following was the nicest: Take a unit square and choose points randomly and uniformly on each side of the square: x on one side, y, on another, z, and w ditto. What is the probability that the quadrilateral xyzw will have area greater than 1/2?
© Copyright 1999 Rob Leduc. Reproduced with permission.

11 March 1999