Mathematical_Recreations-Kraitchik-2e

!l60 Mathematical RecreJlions
4. Consider a rectangular chessboard of dimensions 4 and
k. Divide the set of cells into two domains, a and /3. Domain
a contains the cells marked A or a in Figure 133, do-
4
3
2
~
abcdefg ij
FIGURE 133.
main /3 contains those marked B or b. The cells on the outer
rows will be called exterior, those on the other two rows, interior.
Thus the board contains k cells of each of the followa4
bl c4 dl e4 II g4 hI
a3 22 8 8 16 13 8 10 33 118
b2 8 4 3 5 3 3 6 10 42
c3 8 3 2 2 3 3 3 8 32
d2 16 5 2 6 6 3 3 13 54
e3 13 3 3 6 6 2 5 16 54
f2 8 3 3 3 2 2 3 8 32
g3 10 6 3 3 5 3 4 8 42
h2 33 10 8 13 16 8 822 118
--
118 42 32 54 54 32 42 118 492
FIGURE 134.
ing four classes: exterior cells A, interior cells a, exterior
cells B, interior cells b. Each column contains one cell of
each class. The cells A and b have one color, B and a the
other.
The routes on this board are based on the theorem that a