The Feline Josephus Problem

In the classic Josephus problem, elements 1, 2, . . . , n are placed in order around a circle and a skip value k is chosen. The problem proceeds in n rounds, where each round consists of traveling around the circle from the current position, and selecting the kth remaining element to be eliminated from the circle. After n rounds, every element is eliminated. Special attention is given to the last surviving element, denote it by j. We generalize this popular problem by introducing a uniform number of lives , so that elements are not eliminated until they have been selected for the th time. We prove two main results: 1) When n and k are fixed, then j is constant for all values of larger than the nth Fibonacci number. In other words, the last surviving element stabilizes with respect to increasing the number of lives. 2) When n and j are fixed, then there exists a value of k that allows j to be the last survivor simultaneously for all values of . In other words, certain skip values ensu...

• Type: Conference
• Year: 2010
• Where: FUN
• Authors: Frank Ruskey, Aaron Williams
• Keywords: Algorithms, Classic Josephus Problem, FUN 2010, Kth Remaining Element, Skip Values