last, however (though not without
much difficulty), I discovered a subtle method for solving all cases, and
have written out schedules for every number up to 25 inclusive. The case
of 11 has been solved also by W. Nash. Perhaps the reader will like to
try his hand at 13. He will find it an extraordinarily hard nut.

The solutions for all cases up to 12 inclusive are given in _A. in M._,
pp. 205, 206.

91.--_The Five Tea Tins._

There are twelve ways of arranging the boxes without considering the
pictures. If the thirty pictures were all different the answer would be
93,312. But the necessary deductions for cases where changes of boxes may
be made without affecting the order of pictures amount to 1,728, and the
boxes may therefore be arranged, in accordance with the conditions, in
91,584 different ways. I will leave my readers to discover for themselves
how the figures are to be arrived at.

92.--_The Four Porkers._

The number of ways in which the four pigs may be placed in the thirty-six
sties in accordance with the conditions is seventeen, including the
example that I gave, not counting the reversals and reflections of these
arrangements as different. Jaenisch, in his _Analyse Mathematique au jeu
des Echecs_ (1862), quotes the statement that there are just twenty-one
solutions to the little problem on which this puzzle is based. As I had
myself only recorded seventeen, I examined the matter again, and found
that he was in error, and, doubtless, had mistaken reversals for
different arrangements.

Here are the seventeen answers. The figures indicate the rows, and their
positions show the columns. Thus, 104603 means that we place a pig in the
first row of the _first_ column, in no row of the _second_ column, in the
fourth row of the _third_ column, in the sixth row of the _fourth_
column, in no row of the _fifth_ column, and in the third row of the
_sixth_ column. The arrangement E is that which I gave in diagram form:--

A. 104603
B. 136002
C. 140502
D. 140520
E. 160025
F. 160304
G. 201405
H. 201605
I. 205104
J. 206104
K. 241005
L. 250014
M. 250630
N. 260015
O. 261005
P. 261040
Q. 306104

It will be found that forms N and Q are semi-symmetrical with regard to
the centre, and therefore give only two arrangements each by reversal and
reflection; that form H is quarter-symmetrical, and gives only four
arrangements; while all the fourteen others yield by re