MathDB

There are

n

(

n \ge 4

) straight lines on the plane. For two straight lines

a

and

b

, if there are at least two straight lines among the remaining

n-2

lines that intersect both straight lines

a

and

b

, then

a

and

b

are called a congruent pair of staight lines, otherwise it is called a separated pair of straight lines. If the number of congruent pairs of straight line among

n

straight lines is

2012

more than the number of separated pairs of straight line , find the smallest possible value of

n

(the order of the two straight lines in a pair is not counted).

Problem Statement