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The Mathematics of Various Entertaining Subjects: Research in Recreational Math

Jennifer Beineke and Jason Rosenhouse (eds)

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691164038
eISBN:
9781400881338
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691164038.001.0001
Subject:
Mathematics, History of Mathematics

The history of mathematics is filled with major breakthroughs resulting from solutions to recreational problems. Problems of interest to gamblers led to the modern theory of probability, for example, ... More


The Mathematics of Various Entertaining Subjects: Research in Games, Graphs, Counting, and Complexity, Volume 2

Jason Rosenhouse and Jennifer Beineke (eds)

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691171920
eISBN:
9781400889136
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691171920.001.0001
Subject:
Mathematics, History of Mathematics

The history of mathematics is filled with major breakthroughs resulting from solutions to recreational problems. Problems of interest to gamblers led to the modern theory of probability, for example, ... More


The Mathematical World of Charles L. Dodgson (Lewis Carroll)

Robin Wilson and Amirouche Moktefi (eds)

Published in print:
2019
Published Online:
April 2019
ISBN:
9780198817000
eISBN:
9780191858697
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198817000.001.0001
Subject:
Mathematics, History of Mathematics

Charles Lutwidge Dodgson is best known for his ‘Alice’ books, Alice’s Adventures in Wonderland and Through the Looking-Glass, written under his pen-name of Lewis Carroll. He is also remembered as a ... More


The History and Future of Logic Puzzles

Jason Rosenhouse

in The Mathematics of Various Entertaining Subjects: Research in Games, Graphs, Counting, and Complexity, Volume 2

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691171920
eISBN:
9781400889136
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691171920.003.0003
Subject:
Mathematics, History of Mathematics

This chapter first considers the history of logic puzzles through the contributions of Lewis Carroll and Raymond Smullyan. These two figures are united not only by their love of logic, but also by ... More


Dragons and Kasha

Tanya Khovanova

in The Mathematics of Various Entertaining Subjects: Research in Games, Graphs, Counting, and Complexity, Volume 2

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691171920
eISBN:
9781400889136
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691171920.003.0002
Subject:
Mathematics, History of Mathematics

This chapter begins with the following teaser about hungry dragons stealing kasha from one another. “Suppose a four-armed dragon is sitting on every face of a cube. Each dragon has a bowl of kasha in ... More


Enumeration of Solutions to Gardner’s Paper Cutting and Folding Problem

Jill Bigley Dunham and Gwyneth R. Whieldon

in The Mathematics of Various Entertaining Subjects: Research in Games, Graphs, Counting, and Complexity, Volume 2

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691171920
eISBN:
9781400889136
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691171920.003.0007
Subject:
Mathematics, History of Mathematics

In a plenary talk by Colm Mulcahy at the Fall 2013 Meeting of the MD-DCVA section of the Mathematical Association of America, the authors were introduced to an interesting puzzle about paper folding. ... More


A Sequence Game on a Roulette Wheel

Robert W. Vallin

in The Mathematics of Various Entertaining Subjects: Research in Games, Graphs, Counting, and Complexity, Volume 2

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691171920
eISBN:
9781400889136
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691171920.003.0016
Subject:
Mathematics, History of Mathematics

This chapter takes a classic puzzle about coin-flipping and extends it to a roulette wheel. It examines Penney's Game, a two-player game played via the flipping of a fair coin. Player I picks a ... More


The Tower of Hanoi for Humans

Paul K. Stockmeyer

in The Mathematics of Various Entertaining Subjects: Research in Games, Graphs, Counting, and Complexity, Volume 2

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691171920
eISBN:
9781400889136
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691171920.003.0004
Subject:
Mathematics, History of Mathematics

This chapter discusses one of the great classics of recreational math—the Tower of Hanoi. The Tower of Hanoi was introduced in 1883 by Le Professeur N. Claus (de Siam), Mandarin du College ... More


Tangled Tangles

Erik D. Demaine, Martin L. Demaine, Adam Hesterberg, Quanquan Liu, Ron Taylor, and Ryuhei Uehara

in The Mathematics of Various Entertaining Subjects: Research in Games, Graphs, Counting, and Complexity, Volume 2

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691171920
eISBN:
9781400889136
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691171920.003.0009
Subject:
Mathematics, History of Mathematics

This chapter considers a topological manipulable toy known as a Tangle. Tangle can be twisted and turned in a variety of different ways, producing different geometric configurations. Some of these ... More


Crossing Numbers of Complete Graphs

Noam D. Elkies

in The Mathematics of Various Entertaining Subjects: Research in Games, Graphs, Counting, and Complexity, Volume 2

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691171920
eISBN:
9781400889136
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691171920.003.0013
Subject:
Mathematics, History of Mathematics

This chapter examines crossing numbers. When a particular graph is drawn on a given surface, what is the smallest possible number of crossings among the edges? The chapter is organized as follows. ... More


The Cyclic Prisoners

Peter Winkler

in The Mathematics of Various Entertaining Subjects: Research in Games, Graphs, Counting, and Complexity, Volume 2

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691171920
eISBN:
9781400889136
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691171920.003.0001
Subject:
Mathematics, History of Mathematics

This chapter describes two recent prisoner puzzles (really they are problems in an area of computer science known as “distributed computing”), which show that prisoners in almost complete isolation ... More


Duels, Truels, Gruels, and Survival of the Unfittest

Dominic Lanphier

in The Mathematics of Various Entertaining Subjects: Research in Games, Graphs, Counting, and Complexity, Volume 2

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691171920
eISBN:
9781400889136
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691171920.003.0011
Subject:
Mathematics, History of Mathematics

This chapter considers two generalizations of duels. The first generalization is to n players, like n-uels. The other generalization is an iterative duel. The main issue for both of these duel-type ... More


Trees, Trees, So Many Trees

Allen J. Schwenk

in The Mathematics of Various Entertaining Subjects: Research in Games, Graphs, Counting, and Complexity, Volume 2

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691171920
eISBN:
9781400889136
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691171920.003.0012
Subject:
Mathematics, History of Mathematics

This chapter considers the problem of counting trees. Every connected graph G has a spanning tree, that is, a connected acyclic subgraph containing all the vertices of G. If G has no cycles, it is ... More


Numerically Balanced Dice

Robert Bosch, Robert Fathauer, and Henry Segerman

in The Mathematics of Various Entertaining Subjects: Research in Games, Graphs, Counting, and Complexity, Volume 2

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691171920
eISBN:
9781400889136
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691171920.003.0014
Subject:
Mathematics, History of Mathematics

This chapter uses integer programming to find numerically balanced, twenty-sided dice (d20s). On most commercially available d20s, the numbers on opposite sides sum to 21. The chapter begins with a ... More


A TROUBLE-some Simulation

Geoffrey D. Dietz

in The Mathematics of Various Entertaining Subjects: Research in Games, Graphs, Counting, and Complexity, Volume 2

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691171920
eISBN:
9781400889136
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691171920.003.0015
Subject:
Mathematics, History of Mathematics

This chapter studies the board game, Pop-O-Matic Trouble by Hasbro, which has been a kid favorite for decades. Beyond the beloved “pop-o-matic bubble,” a dome-encased die that cannot be lost or ... More


Frenicle’s 880 Magic Squares

John Conway, Simon Norton, and Alex Ryba

in The Mathematics of Various Entertaining Subjects: Research in Games, Graphs, Counting, and Complexity, Volume 2

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691171920
eISBN:
9781400889136
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691171920.003.0005
Subject:
Mathematics, History of Mathematics

This chapter discusses magic squares. A magic square of order n is an arrangement of the numbers from 1 to n2 in an n × n array so that the two diagonals and all the rows and columns have the same ... More


A Triangle Has Eight Vertices But Only One Center

Richard K. Guy

in The Mathematics of Various Entertaining Subjects: Research in Games, Graphs, Counting, and Complexity, Volume 2

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691171920
eISBN:
9781400889136
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691171920.003.0006
Subject:
Mathematics, History of Mathematics

This chapter describes the nine-point circle. Every triangle has a nine-point circle associated with it. This circle, however, is better referred to as the Central Circle. The nine points are the ... More


The Color Cubes Puzzle with Two and Three Colors

Ethan Berkove, David Cervantes-Nava, Daniel Condon, Andrew Eickemeyer, Rachel Katz, and Michael J. Schulman

in The Mathematics of Various Entertaining Subjects: Research in Games, Graphs, Counting, and Complexity, Volume 2

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691171920
eISBN:
9781400889136
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691171920.003.0008
Subject:
Mathematics, History of Mathematics

This chapter analyzes a puzzle related to a classic problem first posed by English mathematician Percy MacMahon. MacMahon Given a palette of six colors, a 6-color cube is one where each face is one ... More


Making Walks Count: From Silent Circles to Hamiltonian Cycles

Max A. Alekseyev and Gérard P. Michon

in The Mathematics of Various Entertaining Subjects: Research in Games, Graphs, Counting, and Complexity, Volume 2

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691171920
eISBN:
9781400889136
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691171920.003.0010
Subject:
Mathematics, History of Mathematics

Leonhard Euler (1707–1783) invented graph theory in 1735, by solving a puzzle of interest to the inhabitants of Königsberg. The city comprised three distinct land masses, connected by seven bridges. ... More


Multinational War is Hard

Jonathan Weed

in The Mathematics of Various Entertaining Subjects: Research in Games, Graphs, Counting, and Complexity, Volume 2

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691171920
eISBN:
9781400889136
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691171920.003.0017
Subject:
Mathematics, History of Mathematics

War is a card game so simple that only a child could love it. In this game, the deck is divided into piles, one for each player. At the beginning of each round, each player reveals the top card of ... More


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