• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.22 no.4
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• pp.87-94
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• 2022

This paper researched a study to find a combination of acquisition scores for 9 dart throws, which is the minimum number of dart tactile throws in 501 point dart games. The maximum score that can be obtained by throwing once in a dart game is 60 points, which can end the perfect dart game with 60 points eight times according to 60×8+21×1=501, and if you earn 21 points once, you can finish the game with 9 throws. This is called 9-dart finish. As such, only 18 and 14 studies on the combination of scores that can obtain 501 points with 9 throws are known, and no studies have been conducted applying the exhaustive search algorithm. This paper proposed a division branch-and-bound algorithm as a method of simplifying the O(2ⁿ) exponential time performance complexity of the typical branch-and-bound method of a exhaustive search method, to polynomial time complexity. The proposed method limited the level to 8, jumped to a quotient level of 501/60, and backtracked to explore only possible score combinations in the previous level. The possible score combinations of the nine perfect games found with the proposed algorithm were 90(101 cases).