Josephus Problem in Mathematica

Published on 28 April 2022 (Updated: 02 February 2023)

Josephus Problem in Mathematica

Welcome to the Josephus Problem in Mathematica page! Here, you’ll find the source code for this program as well as a description of how the program works.

Current Solution

(* Code *)

(* The code is trivial: *)

josephus[1, _] := 1
josephus[n_Integer, k_Integer] := Mod[josephus[n - 1, k] + (k - 1), n] + 1

(* The outer function provides the 'user interface': *)

josephusMain = Function[{people, skip},
   Catch[
    Module[{e = "Usage: please input the total number of people and number of people to skip."},
     josephus @@ Map[
       (* convert string to integer, or throw *)
       s \[Function] If[StringMatchQ[s, DigitCharacter ..],
         Module[{v = FromDigits[s]},
          If[Positive[v], v, Throw[e]]],(* make sure both numbers are positive *)
         Throw[e]],
       {people, skip}]]]];


(* Valid Tests *)

Print /@ Apply[josephusMain] /@ {
    {"5", "2"},
    {"7", "3"},
    {"41", "4"}
    };


(* Invalid Tests *)

josephusMain["", ""]
josephusMain["word", "word"]
josephusMain["0", "1"]

Josephus Problem in Mathematica was written by:

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How to Implement the Solution

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How to Run the Solution

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