MathDB

We have constructed a rhombus by attaching two equal equilateral triangles. By putting

n-1

points on all 3 sides of each triangle we have divided the sides to

n

equal segments. By drawing line segements between correspounding points on each side of the triangles we have divided the rhombus into

2n^2

equal triangles. We write the numbers

1,2,\dots,2n^2

on these triangles in a way no number appears twice. On the common segment of each two triangles we write the positive difference of the numbers written on those triangles. Find the maximum sum of all numbers written on the segments.
(25 points) Proposed by Amirali Moinfar

Problem Statement