Discrete Geometry Question

There are n distinct points in the plane, no three of which are collinear. Suppose that A and B are two of these points. We say that segment AB is independent if there is a straight line such that points A and B are on one side of the line, and the other n − 2 points are on the other side. What is the maximum possible number of independent segments?

#Combinatorics

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
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Comments

Nice question. What have you tried? What do you guess the numerical answer is?

Calvin Lin Staff - 3 years, 6 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$