TABLE OF CONTENTS ix 



PAOS1 



Re-Entrant Paths on a Chess-Board 122 



Knight's Ee-Entrant Path 122 



King's Ee-Entrant Path 133 



Rook's Ee-Entrant Path 133 



Bishop's Ee-Entrant Path 134 



Miscellaneous Problems 134 



Chapter VII. Magic Squares. 



Magio Squares and their History 138 



Construction of Odd Magio Squares 139 



Construction of Singly-Even Magic Squares 140 



Construction of Doubly-Even Magie Squares 143 



Bordered Magic Squares 144 



Number of SquareB of certain Orders 146 



Produot Squares 147 



Magio Stars, eto 147 



Magio Pencils 148 



Hyper-Magio Squares 150 



Pandiagonal Squares ISO 



Symmetrical Squares 156 



Doubly-Magio and Trebly-Magio Squares 156 



Allied Magio Problems 158 



Magio Card Square. Euler's Offioers Problem . . . .158 



Magio Domino Squares 159 



Coin and Stamp Squares 160 



Addendum on a Solution 161 



Chapter VIII. Bees and Their Cells. 



The Form of Bees' Cells 162 



Economy Conjecture to explain the form 163 



Mathematical Analysis of 164 



Ellis's Suggestion to explain the form 166 



The Density Theory .... 166 



Bryant's Application 168 



Chapter IX. Unicursal Problems. 



Euler's Problem 170 



Definitions 172 



Euler's Besults 172 



Illustrations 176 



Number of Ways in whioh a Unicursal Figure can be described . . 177 



Mazes 182 



Rules for traversing a Maze 183 



The History of Mazes 183 



Examples of Mazes 186 



Geometrioal Trees 188 



The Hamiltonian Game 189 



