MathDB

Given is equilateral triangle

ABC

with side length

n \geq 3

. It is divided into

n^2

identical small equilateral triangles with side length

1

. On every vertex of the triangles there is a number. In a move we can choose a rhombus and add or subtract

1

from all

4

numbers on the vertices of the rhombus. Let point

D

have coordinates

(3,2)

where

3

is the number of the row and

2

is the position on it from left to right. On the vertices

A,B,C,D

there are

1

's and on the other vertices there are

0

's. Is it possible, after some operations, all the numbers to become equal?

Problem Statement