Let's say we have an infinitely large urn and an infinite number of balls, each labeled with its integer (1, 2, 3...). At 1 minute to 12PM, the balls with numbers 1 through 10 are placed into the urn, and one ball is then randomly taken out. At 30 seconds (half a minute) to 12PM, the balls with numbers 11 through 20 are placed in the urn, and one ball is then randomly taken out. At 15 seconds (1/4 minute) to 12PM, the same is done with the balls w/ numbers 21-30, and so on.

How many balls are in the urn at 12PM?

Please avoid Googling for full enjoyment.

This is a problem in the vein of Monty Python and the Doors with Yaks, airplane on a conveyor belt, does .999~infinite = 1, etc.

Infinity.

Since each time we place balls we wait half of the remaining time before doing it again, we end up placing/taking balls an infinite number of times, thus we end up with an infinite number of balls.

what's this jar business, i thought we were talking about an urn

But couldn't you say an urn is a modified jar?

balls in an urn? is this something like dick in a box?

String of 9s, eh? Appropriate math question for today.

A more interesting question to ask would be how many balls, on average, would be left out of the first 10 you put in.

i think it would be at least safe to say an urn is a stylized jar set aside for specific purposes...

Also I think he meant "11 - 20" instead of "1 - 20" as that makes more sense.

If I put the urn on a conveyor belt, will it take off at .999... miles per hour?

I laughed.

The answer is actually not infinity

[More accurately, this is a paradox and there is no conclusive answer, although the most commonly accepted/cited one is that the urn is empty (zero balls) at noon ]

This problem is also known as the Ross-Littlewood Paradox.

actualy, there is a finite answer, but it requires waiting till the time between inserting more balls gets smaller than a plank time, which according to quantum physics, is the smallest usefull time span (time it takes to move one plank length at the speed of light).

but this is getting into quantum physics here.

>.> <.<

A hooker is leaning against a wall. A man is 5 feet away. The pimp tells the man he can cut the distance between himself and the hooker in half every 10 seconds. A minute goes by and the pimp asks the man how close he is. The man replies "Close enough".