# Dividing A Set Of Lines

Probability 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.

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