Candy for Everyone
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Ivars Peterson (MathTrek)  
Several students are sitting in a circle. Each student has an even (though not necessarily the same) number of wrapped pieces of candy. On a signal, each student passes half of his or her trove to the student on his or her right. Between signals, the teacher (reaching into an inexhaustible goody bag) gives any student left with an odd number of candies an extra piece to make the number even before repeating the maneuver. What happens to the distribution of candy among the students if the maneuver is performed over and over again? ... You can find the complete mathematical argument in the book Over and Over Again by Gengzhe Chang and Thomas W. Sederberg (see chapter 6), along with other entertaining and intriguing problems involving iteration and transformation.  


Levels:  High School (912), College 
Languages:  English 
Resource Types:  Articles, Books 
Math Topics:  Graph Theory 
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