What happens when generous people sit in a circle, and share candy – under some conditions – with each other?
In this Math Circle activity, students learn a candy sharing game with a simple rule for passing candy around the circle. They are encouraged to explore different combinations of numbers of players and candy quantity, observing that some result in the game stopping, others in the game reaching a fixed point (where each player's pile of candy remains a constant size), and still others in the game becoming locked in a cycle. They may even notice that some combinations will have different outcomes, depending on the way that the candy is distributed initially to the players.
Extending this activity to include the use of an agent-based model written in NetLogo expands the practical limits of the students' ability to conduct experiments. The use of the BehaviorSpace tool for defining, executing, and capturing data from automated experiments expands these limits further still.
An activity extension still under development will be targeted to students with some programming experience, and will include the students' own development and iterative enhancement of a NetLogo model of the Candy Sharing game.
Note that NetLogo 6 is required to run a downloaded model from this page. However, the same model can run (without BehaviorSpace functionality) in NetLogo Web: Basic Candy Sharing implementation in NetLogo Web.
Copyright © 2022, Math Circles Collaborative of New Mexico