• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.24 no.3
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• pp.103-108
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• 2024

Kakuro puzzles are NP-complete problems where no way to solve puzzles in polynomial time is known. Until now, a brute-force search method or a linear programming method has been applied to substitute all possible cases. This paper finds a magic rule, a rule for box sizes and unfilled numbers according to sum clues. Based on the magic rule, numbers that cannot enter empty cells were deleted from the box for row and column sum clues. Next, numbers that cannot enter the box were deleted based on the sum clue value. Finally, cells with only a single number were confirmed as clues. As a result of applying the proposed algorithm to seven benchmarking experimental data, it was shown that solutions could be obtained for all problems.

• 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.

• Sim-seong Yeon-gu
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• v.36 no.1
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• pp.55-86
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• 2021

The initial situation in our tale shows that the earth-mother-feminine principle disappeared from the center of the collective consciousness into the collective unconscious. Therefore the heaven-father-masculine principle is dominant, which is represented by the king. And in the king's daughter, who is living without mother, the positive father complex is working. She stays in the heaven-spirit world playing with the golden ball, which can be seen as the state of inflation. She is disconnected from the earth-mother-feminine principle, which is important for a woman to find her genuine feminine identity. This demanded principle approaches her through the frog, a bewitched prince. Psychologically it means that a man is under the power of the negative mother complex. The disgusting, ugly frog is a symbol for the shadow, the earthly animal instincts of the princess. Only with his help she can find her golden ball again, which has fallen into the deep well. Their talk about the rewards to him for his help shows us very well the opposites. The frog wants the feminine value such as relation, earthly eros, but the princess offers the masculine value such as heavenly logos. After the frog brought her the lost ball, i.e. she regained her libido, she completely forgot her promise. Like this the content, which is becoming conscious, here the shadow, is easy to fall back into the unconscious and to be repressed. The frog cannot be with the princess without the help of the king, a father figure, a firm protector of the collective oder. At first unwillingly the princess obeys Logos of her father. But her authentic instinctual urge grows stronger and it causes that her ego is released from the power of her father complex. At just this moment the frog turns into a prince, i.e. he is liberated from the mother complex. The marriage of princess and frog-prince symbolize the unification of the opposites: heaven becomes earthly and earth becomes heavenly. Three iron bands, wrapped around the heart of Heinrich, a young king's servant, are snapped, while he brings the prince and princess back to his kingdom. The heart, the place of earth-mother-feminine consciousness, is now liberated. This principle, which disappeared into the unconscious, emerged into the collective consciousness and the wholeness is recovered. The Self is now leading the collective consciousness, which includes not only the principle of Logos but also Eros.