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

Authors : Jang-woo PARK, Ali DOGAN, Ricardo TEIXEIRA

Pages : 970-981

Doi:10.15672/hujms.750167

View : 13 | Download : 3

Publication Date : 2021-08-06

Article Type : Research Paper

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.
Keywords : Discrete Mathematics, Josephus problem, function iterations