MathDB

Kostya marked the points

A(0, 1), B(1, 0), C(0, 0)

in the coordinate plane. On the legs of the triangle ABC he marked the points with coordinates

(\frac{1}{2},0), (\frac{1}{3},0), \cdots, (\frac{1}{n+1},0)

and

(0,\frac{1}{2}), (0,\frac{1}{3}), \cdots, (0,\frac{1}{n+1}).

Then Kostya joined each pair of marked points with a segment. Sasha drew a

1 \times n

rectangle and joined with a segment each pair of integer points on its border. As a result both the triangle and the rectangle are divided into polygons by the segments drawn. Who has the greater number of polygons: Sasha or Kostya? (M. Alekseyev )

Problem Statement