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 orchard. 
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.