# Dividing A Set Of Lines

**Discrete Mathematics**Level 4

Find the smallest positive integer \(N\) that has the following property.

Suppose we have a set of \(2014\) lines in 3 dimensions that pass through the origin, and no plane contains more than three lines. Then we can divide the lines into \(N\) groups, so that every line is perpendicular to **at most one** line in its group.

**Details and assumptions**

The statement has to be true for **any** set of \(2014\) lines, and not just a particular set that you chose.