# Separating points on a plane

BdMO 2011

There are $25$ points on a plane, no three of which lie on a line. Find the minimum number of lines needed to separate them from one another.

Can we assume that the points lie on a circle.I think not.I at first thought that the answer is 13,but realized that it probably isn't the correct answer.The way I tried to do it was by letting the points lie on a circle.Then I calculated the first few values and found a pattern and came to the (probably) erroneous conclusion that the answer is $13$.A nudge in the correct direction will be appreciated.

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Don't assume they lie on a circle, but try to see the cases for smaller amount of points ($2,3,4,5,6\dots$) –  Berci Jan 30 at 12:44
@Berci,it seems that the answer depends on the maximum number of divisions of plane using n lines. –  rah4927 Jan 30 at 12:47