The Mathematics of Perfect n-Shuffles

Abstract

The purpose of this project has been to analyze and generalize the behavior of playing cards as they move through the deck via perfect shuffles. Using concepts based in number theory and abstract algebra, these movements can be followed and card positions can be predicted. A generalized equation has resulted for the number of perfect n-shuffles taken to return the deck to its original state, and another equation for predicting where the dth card will be in the deck after k shuffles.