Solution for Heikki Harrinen’s potatoes
We can calculate that, because the total area of the field is 169 m², it may comprise no more than 17 plots of different sizes:
the minimum area of 17 plots is 1+2+3+…+17 = 153 m²
the minimum area of 18 plots is 171 m²
Therefore, the field can be divided into 17 plots at most. The challenging part is to make all the plots different in shape.
On the right, we present one possible solution to the problem.