There are 255 different ways of cutting the board into two pieces of
exactly the same size and shape. Every way must involve one of the five
cuts shown in Diagrams A, B, C, D, and E. To avoid repetitions by
reversal and reflection, we need only consider cuts that enter at the
points a, b, and c. But the exit must always be at a point in a straight
line from the entry through the centre. This is the most important
condition to remember. In case B you cannot enter at a, or you will get
the cut provided for in E. Similarly in C or D, you must not enter the
key-line in the same direction as itself, or you will get A or B. If you
are working on A or C and entering at a, you must consider joins at one
end only of the key-line, or you will get repetitions. In other cases
you must consider joins at both ends of the key; but after leaving a in
case D, turn always either to right or left--use one direction only.
Figs. 1 and 2 are examples under A; 3 and 4 are examples under B; 5 and
6 come under C;
[Illustration]
and 7 is a pretty example of D. Of course, E is a peculiar type, and
obviously admits of only one way of cutting, for you clearly cannot
enter at b or c.