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A study on solutions of Jisuguimundo using the range of magic sums

합의 범위를 이용한 지수귀문도 해의 탐구

  • Received : 2014.02.12
  • Accepted : 2014.04.14
  • Published : 2014.04.30

Abstract

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.

Keywords

References

  1. CHOE Heemahn, CHOI Sung-Soon, MOON Byung-Ro, A Hybrid Genetic Algorithm for the Hexagonal Tortoise Problem, Lecture Notes in Computer Science 2723 (2003), 850-861.
  2. CHOI Seok-Jeong, GuSuRyak (translated by JEON Hae-Nam, HUH Min), Kyo-Woo-Sa, 2006. 최석정, 구수략-조선시대 산학총서, 정해남, 허민 옮김, 교우사, 2006.
  3. C. COLBOURN, J. DINITZ (co-editors), Handbook of Combinatorial Designs, 2nd edition, Chapman & Hall/CRC, 2006.
  4. JEON Yong Hun, Mysteries of mathematics: The order of the universe hidden in numbers, Science Dong-A, July 1999, 68-77. 전용훈, 수학사의 미스터리 마방진, 과학동아 1999년 7월호, 68-77.
  5. KIM Dong Jin, OH Yung Hwan, Properties and solution-finding algorithm of Jisuguimundo (Turtle-shape Diagram), Proceedings of Korea Information Science Society 16(1) (1989), 405-408. 김동진, 오영환, 지수귀문도의 특성 및 해를 구하는 알고리즘, 한국정보과학회 봄 학술발표회 논문집 16(1) (1989), 405-408.
  6. KIM Young Wook, Seok-Jeong Choi, prime minster and mathematician in 17th century, Newsletter of Korean Mathematical Society, September 2013, 2-4. 김영욱, 최석정, 17세기의 영의정 수학자, 대한수학회 소식지 2013년 9월호, 2-4.
  7. MOON Byung-Ro, Genetic algorithm: the key to solving Jisuguimundo, Science Dong-A, July 2003, 146-149. 문병로, 지수귀문도 해결의 열쇠 유전자 알고리즘, 과학동아 2003년 7월호, 146-149.
  8. Arseniy V. POVOLOTSKIY, SHIN Haisoo, RI Bob MCKAY, Hexagonal Tortoise Problem Solving using Constraint Programming, Journal of KIISE: Software and Applications 38(1) (2011), 27-40. 아르세니 포볼로츠스키, 신해수, 밥 맥케이, 제약 프로그래밍을 이용한 지수귀문도 풀이, 정보과학회지논문지 : 소프트웨어 및 응용 제38권 제1호, 2011년 1월호, 27-40.
  9. SONG Hong-Yeop, Choi Seok-Jeong made orthogonal Latin squares at least 61 years earlier than Euler, Newsletter of Korean Mathematical Society, September 2013, 5-12. 송홍엽, 최석정 선생, 오일러를 최소 61년 앞서 직교라틴방진을 만들다, 대한수학회 소식지 2013년 9월호, 5-12.
  10. Wikipedia, Hexagonal tortoise problem, http://en.wikipedia.org/wiki/Hexagonal_ tortoise_problem (2014, February 1)

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