Magic Hexagon Formulas

TL;DR

This paper explores the construction of magic hexagons of various orders, extends known results, and introduces a new theory for formula-based magic hexagons with arbitrary sums, proving their infinite existence for any order.

Contribution

It provides new constructions of magic hexagons for orders 3 to 7 and establishes a theorem on the infinite existence of such hexagons with arbitrary sums for any order.

Findings

Constructed magic hexagons for orders 3 to 7.

Proved the existence of infinitely many magic hexagons for any order and sum.

Introduced a new theory for formula-based magic hexagons.

Abstract

We give a variety of magic hexagons of Orders from 3 to 7, many of which are extensions of known results. We also give a theorem that their are an infinite number of magic hexagons of Order $n$ for any fixed positive integer $n$ for any arbitrary magic sum $M=m$ to be any desired integer $m$. We instigate theory and ideas associated with formula-based versions of the magic hexagons, which seem to be new.