MathDB

Given

4

lines in the plane such that there are not

2

parallel to each other or no

3

concurrent, we consider the following

8

segments: in each line we have

2

consecutive segments determined by the intersections with the other three lines. Prove that: a) The lengths of the

8

segments cannot be the numbers

1, 2, 3,4, 5, 6, 7, 8

in some order. b) The lengths of the

8

segments can be

8

different integers.

Problem Statement