The Candy-Passing Game for c\geq3n-2

TL;DR

This paper analyzes Tanton's candy-passing game for distributions with at least 3n-2 candies, proving that the game configuration stabilizes over time for any initial distribution.

Contribution

It establishes that for all initial distributions with at least 3n-2 candies, the candy configuration in the game eventually becomes fixed.

Findings

Game configuration stabilizes for all distributions with ≥ 3n-2 candies.

The behavior is predictable and reaches a fixed state.

Applicable to any initial distribution under the specified condition.

Abstract

We determine the behavior of Tanton's candy-passing game for all distributions of at least 3n-2 candies, where n is the number of students. Specifically, we show that the configuration of candy in such a game eventually becomes fixed.