$\displaystyle \text{One minute before 12:00, you place 10 balls labeled from 1 to 10 in the box.}$

. . $\displaystyle \text{Then you randomly remove one ball.}$

$\displaystyle \frac{1}{2}\text{ min before 12:00, you add 10 ball to the box, labeled 11 to 20.}$

. . $\displaystyle \text{Then you randomly remove one ball.}$

$\displaystyle \frac{1}{4}\text{ min before 12:00, you add 10 balls to the box, labeled 21 to 30.}$

. . $\displaystyle \text{Then you randomly remove one ball.}$

$\displaystyle \text{You continue in this manner until 12:00.}$

$\displaystyle \text{What is the number of balls in the box at 12:00?}$