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JosephusCS is a program that solves the Josephus Permutation problem:

Original Problem: 1000 slaves in a circle, numbered 1 to 1000, are all

to be shot except one lucky survivor. The order of shooting is 1, 3,

5, etc., always alternating, and always immediately removing the

fallen bodies. Once a body has fallen, it is no longer considered part

of the circle for purposes of future counting and alternation.

Example, n=6: Shoot 1,3,5,2,6; 4 survives.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.n = The number of objects in the circle

f = index of first object to be selected [1, n]

m = difference in index of items selected, m = 2 => every otherReturn to Josephus Permutation Problems

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Changes last made on Sunday, 27-Jul-08 17:03:53 PDT