Indeed, the number of balls that one ends up with depends on the order in which the balls are removed from the vase. As stated previously, the balls can be added and removed in such a way that no balls will be left in the vase at noon. However, if ball number 10 were removed from the vase at step 1, ball number 20 at step 2, and so forth, then it is clear that there will be an infinite number of balls left in the vase at noon.
Certainly, the amount of balls remaining varies based on their removal sequence from the vase. As previously noted, the balls can be added and removed such that none are left by noon. Nonetheless, if ball number 10 were taken out at step 1, followed by ball number 20 at step 2, and so forth, it is clear that there would be an infinite number of balls remaining in the vase at noon.