Josephus Notes

              Joseph1 - The Flavius Josephus Permutation Problem
              Version 1.10, last revised: 1994-04-23, 0600 hours
              Copyright (c) 1981-1994 by author: Harry J. Smith,
        19628 Via Monte Dr., Saratoga CA 95070.  All rights reserved.

    The General Problem: There is an ordered set of n objects arranged in a
    circle with object i (1 <= i <= n) in position i. All n objects are
    selected and removed in a certain order and placed in a new circle with
    the new position number k beings the order of selection. Object f is
    selected first. After each selection, m minus 1 of the remaining objects
    following the one removed are skipped and the next object is then
    selected. We are interested in the nature of the permutation generated by
    this process, its fixed elements, and in particular the original position
    L of the last object selected. Note that m and f can be as low as 1 and
    can be larger than n.

    This program uses the mod function to speed up the solution.


              Joseph2 - The Flavius Josephus Permutation Problem
    This program uses Knuth's equation, The Art of C.P., Vol. 1, Page 181.


              Joseph3 - The Flavius Josephus Permutation Problem
    This program searches for permutations with many fixed elements.


             Joseph4 - Graphical Solution of the Josephus Problem


             Joseph5 - Graphical Orbits in Josephus permutations
    This program is the mose fun of them all.

 All source files are included.