Oberhausen

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• Middelbare school
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• Leerjaar 2

Josephus problem

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Josephus problem

• Year 67
• Roman and Jewish at war
• Josephus and 40 soldiers

Josephus problem

• If you don't know how many soldier will be there, how can you know on what place you should place yourself to survive? 

Josephus problem

• If you don't know how many soldier will be there, how can you know on what place you should stand to survive? 

• How should we start solving the problem?

Make the problem easier

amount	spot
1
2
3
4

Josephus problem

Make a table containing the number of soldiers and the place that survives.

Try to get to get as far as you can.

amount	spot
1
2
3
4
etc.

amount	spot
9
10
11
12
13
14
15
16

amount	spot
1
2
3
4
5
6
7
8

amount	spot
17
18
19
20
21
22
23
24

Even numbers and powers of two

Find the solution for 28 persons

Find the solution for 28 persons

amount	spot
9	3
10	5
11	7
12	9
13	11
14	13
15	15
16	1

amount	spot
1	1
2	1
3	3
4	1
5	3
6	5
7	7
8	1

amount	spot
17	3
18	5
19	7
20	9
21	11
22	13
23	15
24	17

The Josephus problem

If there are 41 people, what position should Josephus choose?

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