Given an equilateral triangle with sidelength k cm. With lines parallel to it's sides, we split it into k2 small equilateral triangles with sidelength 1 cm. This way, a triangular grid is created. In every small triangle of sidelength 1 cm, we place exactly one integer from 1 to k2 (included), such that there are no such triangles having the same numbers. With vertices the points of the grid, regular hexagons are defined of sidelengths 1 cm. We shall name as value of the hexagon, the sum of the numbers that lie on the 6 small equilateral triangles that the hexagon consists of . Find (in terms of the integer k>4) the maximum and the minimum value of the sum of the values of all hexagons .
Problem
Source: Greece TST 2019 p1
Tags: combinatorics, minimum value, maximum value, hexagon, Equilateral