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The Mathematics of Various Entertaining SubjectsResearch in Recreational Math$
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Jennifer Beineke and Jason Rosenhouse

Print publication date: 2015

Print ISBN-13: 9780691164038

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691164038.001.0001

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Gallia Est Omnis Divisa In Partes Quattuor

Gallia Est Omnis Divisa In Partes Quattuor

Chapter:
(p.139) 10 Gallia Est Omnis Divisa In Partes Quattuor
Source:
The Mathematics of Various Entertaining Subjects
Author(s):

Neil Calkin

Colm Mulcahy

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691164038.003.0010

This chapter presents a single unified proof for a certain move that could be performed on packets of cards which, when repeated four times, brought the cards back to their initial arrangement. That is, the move was “of period four.” The move gave rise to some interesting card effects, especially when applied just three times. At that time, the easiest known method for explaining how the move worked involved a decomposition of the packet into three parts. A decade later, a family of generalizations was stumbled upon, also of period four, with interesting consequences when applied only twice. This chapter arrives at proof which covers the whole spectrum of cases of period four, and it divides packets into four parts.

Keywords:   card moves, card effects, decomposition, generalizations, ice cream trick, dualism, period-four move, period-four principles, playing cards

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