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On the generalized Josephus problem

Published online by Cambridge University Press:  18 May 2009

F. Jakóbczyk
F. Jakóbczyk
Affiliation:
Katolicki Uniwersytet Lubelski, Lublin, Poland
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The problem of Josephus and the forty Jewsis well known [1, 3]. In its most general form, this problem is equivalent to the problem of m-enumeration of a set, as described below.

Define the ordered set

We choose and remove cyclically, from left to right, each with element of Zn until the set is exhausted. The chosen elements are ordered into a new ordered set

which is therefore a permutation of Zn, obtained by what we call m-enumeration of theset Zn.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 14 , Issue 2 , September 1973 , pp. 168 - 173
Copyright
Copyright © Glasgow Mathematical Journal Trust 1973

References

REFERENCES

1.Ahrens, W., Mathematische Unterhaltungen und Spiele (Leipzig, 1918), 118–169.Google Scholar
2.Rankin, R. A.(R. A. MacFhraing), Aireamh muinntir Fhinn is Dhubhain, agus sgeul Iosephuis is an da fhichead Iudhaich, Proc. Roy. Irish Acad.Sect. A. 52 (1948), 87–93.Google Scholar
3.Ball, W. W. Rouse and Coxeter, H. S. M., Mathematical recreations and essays (London, 1939),32–35.Google Scholar