what is the formula for the josephus problem
The formula for the Josephus problem is:
J(n, k) = (J(n-1, k) + k-1) mod n + 1
where:
- J(n, k) represents the survivor position in a circle of n people, counting every kth person.
- n is the total number of people in the circle.
- k is the number of steps to be taken for each count.
The Josephus problem is a theoretical problem related to a certain counting-out game. The formula for solving the Josephus problem is as follows:
1. Start with a circle of n people, numbered from 1 to n.
2. Choose a starting point, typically person 1.
3. Count m positions clockwise around the circle, starting with the starting point as position 1.
4. Remove the person in the mth position from the circle.
5. Continue counting m positions and removing the mth person until there is only one person left.
The position of the last remaining person is the solution to the Josephus problem.