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Journals / Hacettepe Journal of Mathematics and Statistics / 2021 / Cilt: 50 - Sayı: 4

Block Josephus Problem: When the reality is more cruel than the old story

Jang-Woo Park
Ali Doğan
Ricardo Teixeira
Pages
970–981
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

In particular, we present nonrecursive formulas for the initial positions of survivors in the Block Josephus Problem.

📌 3 Key Takeaways

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Objective & Hypothesis:In the Josephus Problem, there are $n$ people numbered from $0$ to $n-1$ around a circle and proceeding around the circle every second person is executed until no one survives.
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Key Findings & Data:Determining where to stand on the circle to be the last survivor is called the Josephus Problem.
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Conclusion & Impact:In particular, we present nonrecursive formulas for the initial positions of survivors in the Block Josephus Problem.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Discrete Mathematics · Josephus problem · function iterations

Abstract

In the Josephus Problem, there are $n$ people numbered from $0$ to $n-1$ around a circle and proceeding around the circle every second person is executed until no one survives. Determining where to stand on the circle to be the last survivor is called the Josephus Problem. In this paper, we present a generalized version of the Josephus Problem and study cases where multiple executions occur at each iteration. Especially, we focus on the Block Josephus problem where the number of skips and the number of executions are the same. In particular, we present nonrecursive formulas for the initial positions of survivors in the Block Josephus Problem.

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Cite This Article

Park, J., Doğan, A., Teixeira, R. (2022). Block Josephus Problem: When the reality is more cruel than the old story. Hacettepe Journal of Mathematics and Statistics, Cilt: 50 - Sayı: 4, 970–981. https://ajindex.com/articles/529459

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