A group of students are sitting in a circle with the teacher in the center. They all have an even number of candies (not necessarily equal). When the teacher blows a whistle, each student passes half his candies to the student on his left. Then the students who have an odd number of candies obtain an extra candy from the teacher.
Show that after a finite number of whistles, all students have the same number of candies.
Update (20 May 2013):
Partial Solution posted by JDGM in comments. Completed by me.