Mathematical Games and Pastimes

Mathematical Games and Pastimes focuses on numerical solutions to mathematical games and pastimes. The book first discusses the binary system of notation and the system of notation with the base three. Congruences, Pythagorean and Heronic triples, and arithmetical pastimes are explained. The text takes a look at the nature of numerical tricks. Guessing the results of operations with unknown numbers; determination of numbers thought of using three tables; and extraction of roots of multidigit numbers are explained. The selection also touches on rapid calculations, games with piles of objects, Meleda, solitaire, and Lucas’ game. Problems on determining ways to reach goals are also presented. Games that show the numerous ways to reach goals are discussed. The text also examines Euler squares, dominoes, and problems related to the chess board. Pastimes related to objects changing places are also highlighted. Topics include Lucas’ problem, Ruma, and Monge’s shuffle. The book is highly recommended for readers wanting to find solutions to mathematical games and pastimes.

Contents

Foreword

§ 1.Various Systems of Notation

§ 2.Some Facts from the Theory of Numbers

§ 3.Congruences

§ 4.Continued Fractions and Indeterminate Equations

§ 5.Pythagorean and Heronic Triples of Numbers

§ 6.Arithmetical Pastimes

§ 7.Numerical Tricks

§ 8.Rapid Calculations

§ 9.Numerical Giants

§ 10.Games with Piles of Objects

§ 11.Meleda

§ 12.Lucas' Game

§ 13.Solitaire

§ 14."The Game of Fifteen" and Similar Games

§ 15.Problems on Determining the Number of Ways of Reaching a Goal

§ 16.Magic Squares

§ 17.Euler Squares

§ 18.Pastimes with Dominoes

§ 19.Problems Connected with the Chess Board

§ 20.Making up Timetables

§ 21."The Problem of Josephus Flavius" and Similar Ones

§ 22.Pastimes Connected with Objects Changing Places

§ 23. The Simplest Methods of Constructing Page Pleasing Patterns

§ 24. Regular Polygons from Rhombi

§ 25. The Construction of Figures from Given Parts

§ 26. Construction of Parquets

§ 27. Re-cutting of Figures

§ 28. The Construction of Curves

§ 29. Mathematical Borders

§ 30. Models of Polyhedra

§ 31. Pastimes with a Sheet and a Strip of Paper

§ 32. The Four-Colour Problem

§ 33. Drawing Figures at One Stroke of the Pencil

§ 34. Hamilton's Game

§ 35. Arranging Points on a Plane and in Space

§ 36. Problems of a Logical Nature

§ 37. Rag-Bag

§ 38. Notes and Answers to Problems

Bibliography