000RM.dvi

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1004 The Josephus problem and its generalization


Exercise


1.For what values ofnisf(n)=n?

2.For what values ofnisf(n)=n− 1?

3.Make a list of the deadly positions of the Josephus problem for
n=4, 5 ,..., 9.

4.Forn=7, there is only one deadly position 1. This means that one
other position is most likely to survive? Which one is it?

5.Find out the survivor in the Josephus problemJ(24,11).

2

3

4

5

8 7 6
9
10
11
12

13

14
15
16
17
18 19 20

21

22

23

24

1

1

2

3

4

6.The deadly positions forJ(24,k),k=1,..., 24 are 5, 12, 13, 16,
18, 19, 22. What is the one with the best chance of survival?
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