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Candy Sharing Game



Students learn a candy sharing game with a simple rule for passing candy around the circle. Students will experiment to figure out how to make the game stop, end in a fixed point, or end in a cycle depending on the amount of starting candy, the number of people playing, and the initial distribution of candy.


Preparation Time

5 minutes

Activity Time

25 to 60 minutes for the introductory activity. It is possible to extend this into a sequence of classes relating to matrices or dynamical systems.





Advanced Prerequisites

Related Concepts


Boston Math Circle research page
Pass the Candy -- An Introduction to Recursive Equations. Maria Hernandez, NCSSM

National Common Core Standards

HS.Modeling Modeling is the process of choosing and using appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions. Quantities and their relationships in physical, economic, public policy, social, and everyday situations can be modeled using mathematical and statistical methods. When making mathematical models, technology is valuable for varying assumptions, exploring consequences, and comparing predictions with data.
HS.N-VM.6 Use matrices to represent and manipulate data, e.g. to represent payoffs or incidence relationships in a network.
HS.N-VM.11 Multiply a vector (regarded as a column matrix) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors.
Riverbend Community Math Center
(574) 339-9111
This work placed into the public domain by the Riverbend Community Math Center.