• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.24 no.5
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• pp.83-88
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• 2024

In a grid board with 9 cells of 3×3, the sum clue Sujiko puzzle with 4 fixed sum clues(FSCs) and variable sum clues(VSCs) is an NP-complete problem with no known way to solve the puzzle in polynomial time. To solve this puzzle 9! in all possible cases, a brute-force method should be applied to substitute the number. This paper determined the unique combination number cell by reducing the number of candidates that can enter empty cells. If the only number combination cell no longer exists, this paper proposes a method for determining a common number network with numbers common to the intersection cell of FSC+VSC. Applying the proposed algorithm to 9 benchmarking experimental data showed that puzzles can be solved in polynomial time for all problems.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.24 no.5
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• pp.159-168
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• 2024

In a grid board with 9 cells of 3X3, the Sujiko puzzle with 4 sum clues and C number clues as one block is an NP-complete problem with no known way to solve the puzzle in polynomial time. To solve this puzzle (9-C)! in all possible cases, a brute-force method should be applied to substitute the number. This paper confirmed the clue of the unique number cell by reducing the number of candidates that can enter empty cells. When the unique number cell no longer exists, a method of selecting the intersection combination numbers between the sum clue blocks has been proposed. Applying the proposed algorithm to 52 benchmarking experimental data showed that puzzles can be solved in polynomial time for all problems.