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. In fact, depending on which ball is removed at the various steps, any chosen number of balls can be placed in the vase by noon, as the procedure below demonstrates. This is the solution favored by philosopher logician Tom Tymoczko and mathematician logician Jim Henle. This solution corresponds mathematically to taking the limit inferior of a sequence of sets.