Chapter IX. Kirkman's School-Girls Problem.

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History of the Problem 193
Solutions by One- Step Cycles 19o
Examples when n=3, 9, 27, 33, 51, 57, 75, SI, 99 . . . 196
Solutions by Two-Step Cycles 199
Examples when w = 15, 27, 39, 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, 93, 99 205
Solutions by the Focal MeiLod 209
Examples when w = 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
Walecki's Theorem 218
Problem of w^ Girls in n groups (Peirce) ...... 219
Examples when n= 2, 3, 4, 5, 7, 8 219
Example when n is prime 220
Kirkman's Problem in Quartets, &c. 221
A Bridge Problem. Arrangements in Pairs , 221
Sylvester's Corollary to Kirkman's Problem 222
Steiner's Combinatorische Aufgabe ..... .4 . 223