310 Answers(9 feet) would be one-third of the width of the square (27 feet). In all the
successive higher cases the square will be increasingly too large for the pedestal
to be in agreement with the illustration.- A CUBE PARADOX
It is a curious fact that a cube can
be passed through another cube of
smaller dimensions. Suppose a cube to
be raised so that its diagonal AB is
perpendicular to the plane on which
it rests, as in Figure I. Then the re-
sulting projection will be a regular
l~'O
Bhexagon, as shown. In Figure 2 the
square hole is cut for the passage of
a cube of the same dimensions. But
it will be seen that there is room for
cutting a hole that would pass a cube
of even larger dimensions. Therefore,
the one through which I cut a hole
was not, as the reader may have
hastily supposed, the larger one, but
the smaller! Consequently, the larger
cube would obviously remain the
heavier. This could not happen if the
smaller were passed through the
larger.316. THE CARDBOARD BOX
There are eleven different shapes in all, if turning over is allowed, and they
are as shown. If the outside of the box is blue and the inside white, and everypossible shape has to be laid out with white uppermost, then there are twenty
different ways, for all except Nos. I and 5 can be reversed to be different.