10

Part of 2014 Ukraine Team Selection Test

Problems(1)

n - 3 points inside a triangle with vertices on convex hull of n points

Source: Ukraine TST 2014 p10

Find all positive integers

n \ge 4

for which there are

n

points in general position on the plane such that an arbitrary triangle with vertices belonging to the convex hull of these

n

points, containing exactly one of

n - 3

points inside remained.

combinatorial geometrycombinatoricspointsConvex hull