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Dividing A Set Of Lines

Find the smallest positive integer NN that has the following property.

Suppose we have a set of 20142014 lines in 3 dimensions that pass through the origin, and no plane contains more than three lines. Then we can divide the lines into NN 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 20142014 lines, and not just a particular set that you chose.


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