Okay ,here is another argument to make the paradox more warped. Consider the function f(t) which tells you the number of balls at time t. Clearly f(t) is an increasing function. Since f(1)=9 therefore f(2)>f(1). So f(2) > 0.
This doesnt use Mathematical Induction.
The problem here is that f is increasing on the open interval (1,2) and so lim(t->2)f = infinity. However as you have no information about f outside the open interval(you dont know whether its continuous in particular) therefore you cannot say anything about f(2).