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## Resolved Question

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# Given a collection of points P in the plane, a 1-set is a point in P that can be separated from the rest by a?

Given a collection of points P in the plane, a 1-set is a point in P that can be separated from the rest by a line, .i.e the point lies on one side of the line while the others lie on the other side.
The number of 1-sets of P is denoted by n1(P). The minimum value of n1(P) over all configurations P of 5 points in the plane in general position (.i.e no three points in P lie on a line) is
by chauncy
Member since:
15 October 2007
Total points:
22,228 (Level 6)

## Best Answer - Chosen by Voters

I think the answer is 3, when 3 of the points describe a triangle and the other 2 points are inside the triangle. The 3 points of the triangle form a 1-set. The 2 interior points cannot be members of a 1-set.
100% 1 Vote
If we have 10 points then maximum possibilities = 10
and minimum = 3

similarly for 5 points
Max = 5, Min = 3

for 19
max= 19 Min = 3

Detail solution by site admin at is below
http://www.m4maths.com/448-given-a-collection-of-points-P-in-a-plane-a-1-set-is-a-point-in-P-that-can-be-separated.html

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