Revisiting Toom's proof of Bulgarian Solitaire

TL;DR

This paper revisits Toom's proof of Bulgarian Solitaire, providing detailed exposition and demonstrating how the Chinese Remainder Theorem can be used to generalize the proof.

Contribution

It offers a detailed explanation of Toom's original proof and introduces a generalization using the Chinese Remainder Theorem.

Findings

Detailed exposition of Toom's proof

Generalization of the proof via Chinese Remainder Theorem

Enhanced understanding of Bulgarian Solitaire's properties

Abstract

In this article we give an exposition of Toom's proof of Bulgarian Solitaire that appeared in \emph{Kvant}. We provide more details. We also show how an application of the Chinese Remainder Theorem allows us to generalize the proof.