X TABLE OP CONTENTS 



Chapter X. Kirkman's School-Giels Problem. 



PAGE 



History of the Problem 193 



Solutions by One-Step Cycles 195 



Examples when n=3, 9, 27, 33, 51, 57, 75, 81, 99 . 196 



Solutions by Two-Step Cycles 199 



Examples when n=15, 27, 89, 51, 63, 75, 87, 99 200 



Solutions by Three-Step Cycles 203 



Examples n=9, 21, 27, 33, 39, 45, 51, 57, 63, 69, 75, 81, 87, 98, 99 205 



Solutions by the Fooal Method 209 



Examples when n=33, 51 210 



Analytical Methods 211 



Application when n=27 with 13 as base 212 



Examples when n = 15, 39 216 



Number of Solutions 217 



Harison's Theorem 218 



Problem of n* Girls in n groups (Peirce) 219 



Examples when n= 2, 3, 4, 6, 7, 8 219 



Example when n is prime 220 



Kirkman's Problem in Quartets, *o 221 



A Bridge Problem. Arrangements in Pairs ...... 221 



Sylvester's Corollary to Eirkman's Problem ...... 222 



Chapter XL Miscellaneous Problems. 



The Fifteen Puzzle 224 



The Tower of Hanoi 228 



Chinese Rings 229 



Algebraic Solution 230 



Solution in Binary Scale of Notation 232 



Problems connected with a Pack of Cards 234 



Shuffling a Pack 235 



Arrangements by Bows and Columns 237 



Bachet's Problem with Pairs of Cards 238 



The Three Pile Problem 240 



Gergonne's Generalization 241 



The Mouse Trap. Treize 245 



