er and the fly, and the straightened course which
the spider must take without going off the cardboard. These are the four
most favourable cases, and it will be found that the shortest route is in
No. 4, for it is only 40 feet in length (add the square of 32 to the
square of 24 and extract the square root). It will be seen that the
spider actually passes along five of the six sides of the room! Having
marked the route, fold the box up (removing the side the spider does not
use), and the appearance of the shortest course is rather surprising. If
the spider had taken what most persons will consider obviously the
shortest route (that shown in No. 1), he would have gone 42 feet! Route
No. 2 is 43.174 feet in length, and Route No. 3 is 40.718 feet.

[Illustration]

I will leave the reader to discover which are the shortest routes when
the spider and the fly are 2, 3, 4, 5, and 6 feet from the ceiling and
the floor respectively.

76.--_The Perplexed Cellarman._

Brother John gave the first man three large bottles and one small
bottleful of wine, and one large and three small empty bottles. To each
of the other two men he gave two large and three small bottles of wine,
and two large and one small empty bottle. Each of the three then receives
the same quantity of wine, and the same number of each size of bottle.

77.--_Making a Flag._

The diagram shows how the piece of bunting is to be cut into two pieces.
Lower the piece on the right one "tooth," and they will form a perfect
square, with the roses symmetrically placed.

[Illustration]

It will be found interesting to compare this with No. 154 in _A. in M._

78.--_Catching the Hogs._

A very short examination of this puzzle game should convince the reader
that Hendrick can never catch the black hog, and that the white hog can
never be caught by Katruen.

Each hog merely runs in and out of one of the nearest corners and can
never be captured. The fact is, curious as it must at first sight appear,
a Dutchman cannot catch a black hog, and a Dutchwoman can never capture a
white one! But each can, without difficulty, catch one of the other
colour.

So if the first player just determines that he will send Hendrick after
the white porker and Katruen after the black one, he will have no
difficulty whatever in securing both in a very few moves.

It is, in fact, so easy that there is no necessity whatever to give the
line of play. We thus, by means of t