64

60

two transformations are the reverse of one another,
it follows, by the principle of contraposition that
the same is true within any odd number
of cuts. When the vacant enclosure is oddly
enclosed as in this figure
y, the
enclosure on whose area it stands is
evenly enclosed and can be erased by
Permission No 1. But when the vacant
enclosure is evenly enclosed as in the
next figure
z
all other graphs,
in the same enclosure (here
represented by x[)], being evenly enclosed
can be erased by Permission No 1, and
then Permission No 4 which allows a double
enclosure round any graph under even