[322 
323] 
95 
ieir values, the 
323. 
«1=0, 
-¡3 = 0) as the 
ON A TACTICAL THEOREM RELATING TO THE TRIADS OF 
FIFTEEN THINGS. 
(x, y) of the 
[From the Philosophical Magazine, vol. xxv. (1863), pp. 59—61.] 
The school-girl problem may be stated as follows:—“With 15 things to form 
35 triads, involving all the 105 duads, and such that they can be divided into 7 systems, 
each of 5 triads containing all the 15 things.” A more simple problem is, “ With 
15 things, to form 35 triads involving all the 105 duads.” 
In the solution which I formerly gave of the school-girl problem (Phil. Mag. 
vol. xxxvii. 1850, [82]), and which may be presented in the form 
a 
b 
c 
d 
e 
/ 
y 
abc 
35 
17 
82 
64 
ade 
62 
84 
15 
37 
a fy 
13 
57 
86 
42 
bdf 
47 
16 
38 
25 
bge 
58 
23 
14 
67 
cdg 
12 
78 
56 
34 
cef 
36 
45 
27 
18 
b, c, 
d, e, f, g, 
1, 2 
, 3, 
L -5, 
6, 7, 8, t 
is abc, d 35, e 17, /82, <7 64, and so for all the seven pentads of triads), there is obviously 
a division of the 15 things into (7 + 8) things, viz. the 35 triads are composed 7 of