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points in plane

Source: Federation of Bosnia, 2. Grades 2008.

April 23, 2008
floor functionfunctioncombinatorics proposedcombinatorics

Problem Statement

n n points (no three being collinear) are given in a plane. Some points are connected and they form k k segments. If no three of these segments form triangle ( equiv. there are no three points, such that each two of them are connected) prove that k≤⌊n24⌋ k \leq \left \lfloor \frac {n^{2}}{4}\right\rfloor
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