MathDB

Let

A_1,A_2,...,A_{3n}

3n\ge 3

planar points such that

A_1A_2A_3

is an equilateral triangle and

A_{3k+1} ,A_{3k+2} ,A_{3k+3}

are the midpoints of the sides of

A_{3k-2}A_{3k-1}A_{3k} ,

for all

1\le k<n.

Of two different colors, each one of these points are colored, either with one, either with another.
a) Prove that, if

n\ge 7,

then some of these points form a monochromatic (only one color) isosceles trapezoid. b) What about

n=6?

Problem Statement