8. 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
a) 3 b) 5 c) 2
Answer Posted / lion251
The answer is 3, for all P >= 3.
For all P >= 3, there exists a configuration where 3 points form a triangle, and all the other points lie within the triangle, and are thus protected from being 'singled out' from the rest by a line. In this configuration, only the three corner points can be singled out from the rest by a line.
2 points can only 'protect' the rest is all points are on a single line, but this case is excluded.
The answer is thus 3, for all P>=3
Is This Answer Correct ? | 10 Yes | 4 No |
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