MathDB

Given a point

X

and

n

vectors

\overrightarrow{x_i}

with sum zero in the plane. For each permutation of the vectors we form a set of

n

points, by starting at

X

and adding the vectors in order. For example, with the original ordering we get

X_1

such that

XX_1 = \overrightarrow{x_1}, X_2

such that

X_1X_2 = \overrightarrow{x_2}

and so on. Show that for some permutation we can find two points

Y, Z

with angle

\angle YXZ = 60^o

, so that all the points lie inside or on the triangle

XYZ

Problem Statement