Master potato farmer Heikki Harrinen has ordered a new variety of potato for his farm in Lapua, and now he wants to determine the effect of the cultivation area on the variety’s growth rate.
For his test crops, Heikki has reserved an area of 13 × 13 meters, which he now has to divide into as many cultivation plots as possible, each of unique size. For planting, cultivation, and maintenance, rectangular plots are ideal.
How many rectangular cultivation areas can Heikki create in his test field?
On the right, we have provided an example of one possible division of plots, but it’s far from ideal, because it features only four areas differing in size.
Heikki Harrinen’s potatoes
Divide the field on the right into rectangular areas so that:
a) All rectangles differ in size
b) The borders of the rectangles follow the borders marked on the field
The goal is create as many possible plots of different sizes as possible.