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      A Variant on the Feline Josephus Problem

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          Abstract

          In the Feline Josephus problem, soldiers stand in a circle, each having \(\ell\) `lives'. Going around the circle, a life is taken from every \(k\)th soldier; soldiers with 0 lives remaining are removed from the circle. Finding the last surviving soldier proves to be an interesting and difficult problem, even in the case when \(\ell=1\). In our variant of the Feline Josephus problem, we instead remove a life from \(k\) consecutive soldiers, and skip 1 soldier. In certain cases, we find closed formulas for the surviving soldier and hint at a way of finding such solutions in other cases.

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          The Josephus problem

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            2876. The Josephus Problem

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              The Feline Josephus Problem

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                Author and article information

                Journal
                30 March 2018
                Article
                1803.11340
                4319e3b3-9944-401d-90c4-755e59a11e2c

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                9 pages
                math.CO

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