THE CANTERBURY PUZZLES
is of precisely the same length as two of the sides. The puzzle was
to discover the fallacy, because it is a very obvious fallacy if we admit
that the shortest distance between two points is a straight line. But
where does the error come in ?
Well, it is perfectly true that so long as our zig-zag path is
formed of " steps " parallel to the sides of the square that path must
be of the same length as the two sides. It does not matter if you
have to use the most powerful microscope obtainable—the rule is
always true if the path is made up of steps in that way. But
the error lies in the assumption that such a zig-zag path can ever
become a straight line. You may go on increasing the number
of steps infinitely—that is, there is no limit whatever theoretically to
the number of steps that can be made—but you can never reach a
straight line by such a method. In fact it is just as much a " jump "
to a straight line if you have a billion steps as it is at the very outset
to pass from the two sides to the diagonal. It would be just as false
to say we might go on dropping marbles into a basket until they
became sovereigns as to say we can increase the number of our
steps until they become a straight line. There is the whole thing in
a nutshell.
29.—Chaucer s Puzzle,
The surface of water, or other liquid, is always spherical; and
the greater any sphere is the less is its convexity. Hence, the top
diameter of any vessel at the summit of a mountain will form the
base of the segment of a greater sphere than it would at the bottom.
This sphere, being greater, must (from what has been already said)
be less convex ; or, in other words, the spherical surface of the
water must be less above the brim of the vessel; and consequently
it will hold less at the top of a mountain than at the bottom. The
reader is therefore free to select any mountain he likes in Italy—or
elsewhere !
30.—The Puzzle of the Canon's Yeoman.
The number of different ways is 63,504. The general formula
for such arrangements, when the number of letters in the sentence
144
