# Urns of Infinity

A powerful sorcerer once summoned a pair of demons to perform some menial tasks. Just before midnight, when the demons' terms of servitude were about to expire, the sorcerer gave each demon one more task.

"Demon #1, before I fill out your timecard, I want you to place these numbered balls within this infinite urn. At one minute to midnight, place the balls numbered one through ten into the urn, and then take the ball numbered 10 out. At a half minute to midnight, place the balls numbered eleven through twenty into the urn, and remove the ball numbered 20. At a quarter of a minute to midnight, repeat this with the next ten balls, and so on until midnight. At that time you may leave for the weekend."

"Demon #2, I want you to place these other numbered balls into this other infinite urn. You will follow the same procedure as Demon #1, but instead of removing balls 10, 20, 30, etc., you will remove balls 1, 2, 3..."

The demons nodded and at a minute to midnight began their tasks. As creatures of magic, they had no difficulty with this seemingly impossible task. Each finished just before midnight, with one iotasecond to spare.

But Demon #2 was lazy. To save lifting effort, he took the liberty of following the spirit of the task, but not the letter. Instead, at one minute to midnight, he placed balls 1-9 into the urn. Then, he quickly painted a zero on the first ball, making it look like ball ten, which he shoved under the rug. At a half-minute to midnight, he placed balls 11-19 into the urn, and painted a zero on the ball numbered "2" turning it into a 20.

The next morning the sorcerer returned to inspect their work. Besides the fact that his carpet now had an infinite number of lumps in it, could he tell that the Demon had cheated?