Journal of Integer Sequences, Vol. 18 (2015), Article 15.2.7

A Prisoner Problem Variation

Jerry Metzger and Thomas Richards
University of North Dakota
Department of Mathematics
Witmer Hall Room 313
101 Cornell Street Stop 8376
Grand Forks, ND 58202-8376


Consider a fair n-sided die with faces numbered 1 to n. Several different methods are used to compute the probability that every face has come up at least once when face n appears for the kth time. The results lead to a number of summation identities. The probabilities are related to several sequences in Sloane's On-Line Encyclopedia of Integer Sequences.

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(Concerned with sequences A000012 A001008 A001240 A027459 A027462 A028037 A072913 A099946 A103878 A126646 A131689.)

Received October 28 2014; revised version received January 13 2015. Published in Journal of Integer Sequences, January 25 2015.

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