The Josephus Problem

Who is left standing?

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Removing every second person, person 1 survives when n is a power of 2.
• Write n = 2ᵐ + L; the survivor is 2L + 1.
• In binary: move the leading 1 of n to the end.

Steps

1. Every second person
2. Five people
3. Watch the circle shrink
4. Spot the pattern
5. Forty-one people
6. A hundred people