max and min sum of numbers of overlapping hexagons in a triangular grid
Source: Greece TST 2019 p1
June 7, 2020
combinatoricsminimum valuemaximum valuehexagonEquilateral
Problem Statement
Given an equilateral triangle with sidelength cm. With lines parallel to it's sides, we split it into small equilateral triangles with sidelength cm. This way, a triangular grid is created. In every small triangle of sidelength cm, we place exactly one integer from to (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 cm. We shall name as value of the hexagon, the sum of the numbers that lie on the small equilateral triangles that the hexagon consists of . Find (in terms of the integer ) the maximum and the minimum value of the sum of the values of all hexagons .