Range of magic constant on Hexagonal Tortoise Problem

TL;DR

This paper investigates the range of possible magic constants in Hexagonal Tortoise Problems by decomposing vertices into groups, revealing the variability in their sums.

Contribution

It introduces a method of vertex decomposition in Jisugwimundo to determine the range of magic constants, a novel approach in studying HTP.

Findings

Range of magic constants identified for various HTP configurations

Vertex decomposition method enables analysis of sum variability

Demonstrates that magic constants can vary due to vertex counting differences

Abstract

Hexagonal tortoise problem (HTP), also known as Jisuguimundo or Jisugwimundo, is a magic square variety which was invented by medieval Korean Mathematician and minister Suk-Jung Choi (1646-1715).[1] Choi showed pattern 30 vertices 3 by 3 diagonal shape which has 93 as its magic constant. Unlike magic square, vertices in Jisugwimundo counted one times, twice or three times. This change makes magic constant of Hexagonal Tortoise Problem could be vary. We consider a range of hexagonal sums in various Jisugwimundo. In this paper, we decomposed vertices on Jisugwimundo to some groups. by this way we found the range of magic constant on several HTP.