• 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.