If a certain number of people, n, are in a circle and every other person is eliminated until one remains standing, what is the equation that gives the relation between n and the wining position, p?

Guest Jun 1, 2015

#1**+5 **

As yet I don't know how to prove this, but a formula that seems to work is

$$\displaystyle p=2\left(n-2^{\bmod\left(\frac{(\log(n)-0.001)}{\log(2)}\right)\right)-1.$$

The logs are to base 10 and mod (I hope, otherwise I need to find another operator,) delivers the integer part of the expression within the brackets.

p is measured from the first person to be eliminated, being the number of positions further on around the circle.

For example n = 6 will return a value of p = 3. So, from the first person eliminated count to the third position further round the circle.

Bertie
Jun 3, 2015