Only using INDUCTION METHOD

[20 marks] Suppose a number of people are placed in a circle and numbered from 1 to x. Now, you start counting from 1 and eliminate the i - th person in the circle. The circle now has x - 1 people and you count again, starting from where you left off (after the last eliminated person), and eliminate the i-th person in the circle again. This goes on until only one person remains, and wins the game. Determine in a circle of x = 2" people, and count i = 2 (every second person is eliminated), where someone should stay to be the last one standing, i.e., never be eliminated. Clearly state the position and proof your answer using induction