• Title/Summary/Keyword: Hexagonal Tortoise problem

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A study on solutions of Jisuguimundo using the range of magic sums (합의 범위를 이용한 지수귀문도 해의 탐구)

  • Kwon, Gyunuk;Park, Sang Hu;Song, Yun Min;Choi, Seong Woong;Park, Poo-Sung
    • Journal for History of Mathematics
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    • v.27 no.2
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    • pp.111-125
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    • 2014
  • Jisuguimundo is an inimitable magic hexagon devised by Choi Seok-Jeong, who was the author of GuSuRyak as well as a prime minister in Joseon dynasty. Jisuguimundo, recorded in GuSuRyak, is also known as Hexagonal Tortoise Problem (HTP) because its nine hexagons resemble a tortoise shell. We call the sum of numbers in a hexagon in Jisuguimundo a magic sum, and show that the magic sum of hexagonal tortoise problem of order 2 varies 40 through 62 exactly and that of hexagonal tortoise problem of order 3 varies 77 through 109 exactly. We also find all of the possible solutions for hexagonal tortoise problem of oder 2.

A study on finding solutions to generalized Jisuguimundo(hexagonal tortoise problem) (일반화된 지수귀문도의 해를 구하는 방법에 관한 연구)

  • Park, Kyo-Sik
    • Journal of the Korean School Mathematics Society
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    • v.14 no.3
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    • pp.261-275
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    • 2011
  • Seok-Jung Choi's Jisuguimundo mentioned as a brilliant legacy in the history of Korean mathematics had been cloaked in mystery for 300 years. In the meantime there has been some efforts to find solutions, and some particular answers were found, but no one achieved full success mathematically. By the way, H-alternating method showed that to find solutions of Jisuguimundo is possible, even though that method restricted magic number to 88~92 and 94~98. In this paper, $n{\times}n$ Jisuguimundo is defined, and it is showed that finding solutions of it is always possible in case of partition $({\upsilon}+1)+{\upsilon}+({\upsilon}+1)$ & co-partition ${\upsilon}+({\upsilon}+1)+{\upsilon}$, partition $({\upsilon}+1)+({\upsilon}-1)+({\upsilon}+1)$ & co-partition $({\upsilon}-1)+({\upsilon}+1)+({\upsilon}-1)$, partition $({\upsilon}+1)+({\upsilon}+2)+({\upsilon}+1)$ & co-partition $({\upsilon}+2)+({\upsilon}+1)+({\upsilon}+2)$, and partition $({\upsilon}+1)+({\upsilon}+3)+({\upsilon}+1)$ & co-partition $({\upsilon}+3)+({\upsilon}+1)+({\upsilon}+3)$. And It is suggested to find solutions of $n{\times}n$ Jisuguimundo could be used as a task for problem solving.

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A Study on Making Jisuguimundo as a Problem Solving Task for Elementary Students (초등학생을 위한 문제해결 과제로서의 지수귀문도의 해결 방안 연구)

  • Park, Kyo-Sik
    • Journal of Elementary Mathematics Education in Korea
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    • v.15 no.1
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    • pp.77-93
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    • 2011
  • Jisuguimundo(地數龜文圖) is a magic hexagon created by Suk-Jung Choi in his book about three hundreds years ago in Korea. Recently attention is focused on jisuguimundo, and it is known that jisuguimundos exist when magic number is from 77 to 108, however a general method making jisuguimundos is not known so far. Up to now, methods of making jisuguimundos using computers are known. In this study, a method making jisuguimundos is suggested using pairs of two numbers with sum p and q ($p{\neq}q$) alternately when magic number is from 88 to 92, and from 94 to 98, without using computer in elementary math class as a task for problem solving. Mathematical theory is introduced for this method, and jisuguimundos are presented which are found out through this method. Elementary students are expected to make their own jisuguimundo using this method.

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