MathDB

Consider a regular

n

-gon with

n>3

, call a line acceptable if it passes through the interior of this

n

-gon. Draw

m

different acceptable lines, so that the

n

-gon is divided into several smaller polygons.
(a) Prove that there exists an

m

, depending only on

n

, such that any collection of

m

acceptable lines results in one of the smaller polygons having

3

4

sides.
(b) Find the smallest possible

m

which guarantees that at least one of the smaller polygons will have

3

4

sides.

1