There are several
ways in which this problem might
be solved were it not for the condition that as few cherries and plums
as possible shall be planted on the north and east sides of the
The best possible arrangement is that shown in the diagram,
where the cherries, plums, and apples are indicated respectively by the
letters C, P, and A.
The dotted lines connect the cherries, and the
other lines the plums.
It will be seen that the ten cherry trees and
the ten plum trees are so planted that each fruit forms five lines with
four trees of its kind in line.
This is the only arrangement that
allows of so few as two cherries or plums being planted on the north
and east outside rows.