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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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An Introduction to Gilbreath Numbers

An Introduction to Gilbreath Numbers

(p.163) 12 An Introduction to Gilbreath Numbers
The Mathematics of Various Entertaining Subjects

Robert W. Vallin

Princeton University Press

This chapter mathematically analyzes the behavior of a card trick described by an undergraduate math major at the University of California, Los Angeles, named Norman Gilbreath. Stated succinctly, this trick can be performed by handing an audience member a deck of cards, letting them cut the deck several times, and then having them deal a number of cards from the top into a pile. The audience member takes the two piles (the cards in hand and the set now piled on the table) and riffle-shuffles them together. The magician now hides the deck (under a cloth, perhaps, or behind the back) and proceeds to produce one pair of cards after another in which one card is black and the other is red.

Keywords:   Gilbreath numbers, Norman Gilbreath, playing cards, card tricks, magic tricks, Gilbreath permutations, continued fractions

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