Date of Award


Document Type


Degree Name

Master of Science (MS)


College of Science and Mathematics


Mathematical Sciences

Thesis Sponsor/Dissertation Chair/Project Chair

Deepak Bal

Committee Member

Aihua Li

Committee Member

Jonathan Cutler


The Candy Game begins with a finite number of players sitting in a circle, each with an initial amount of candy. At each time step, each player passes half of their pile to the player on their left (with odd sized stacks receiving an extra piece of candy). The original question was whether every initial distribution of candy results in every player holding the same number of pieces after a finite number of turns. For arbitrary initial distributions, we prove asymptotically tight bounds on the final amount of candy. The diffusion chip firing game assigns integral chip amounts to each vertex of a graph. At each time step, a vertex sends a chip to each neighbor who has less chips than itself. We show that this game on the infinite path, with bounded chip labels remains bounded for all time.

Included in

Mathematics Commons