Talk:Ping-pong ball conundrum

Deletion debate

—Quarl ^(talk) 2006-11-20 01:41Z

Undefined

It's not zero. It's undefined. The explaination no longer works if you simple stop numbering the balls. We have this:

10 * infinity balls went in.

So if you believe this, your are stupid.... — Preceding unsigned comment added by 71.161.105.102 (talk) 22:46, 20 March 2012 (UTC)

infinity balls came out.

Thus, we have (10*infinity) - infinity, or infinity - infinity, which is undefined. Or at least, it says infinity - infinity is undefined on the infinity page. So yeah, this doesn't work.

Or, if you think further, the CYCLE is repeated infinite times. Every cycle 9 balls went in. Yet we have a time when ever ball came out. That's about as undefined as it comes. This is really a lot like the 1=2 "proof".

"The explanation no longer works if you simple stop numbering the balls." Of course, because that is the crux of the problem (and the solution). If you don't know which balls you are removing from the barrel, you can't determine if all of them or only some of them are removed. The numbering establishes a particular ordering to the steps of the procedure, and allows you to determine exactly which balls are removed. Specifically, it establishes that every ball inserted is eventually removed at a later step. — Loadmaster 17:35, 7 November 2006 (UTC)

Estimated solution

I think the answer can be estimated.

First put aside the physical conundrums(eg How do you throw balls and pull them out of the barrel so fast?).

Let x be each group of 10 balls that you throw in.

For x=1, you throw in 10 balls and have 30 (60/2)sec left on your timer. You then pull out one ball and have 9 balls left. For x=2, you throw in 10 balls and have 15 (60/4) sec left on your timer. You then pull out one ball from the 10+9 balls and have 18 balls left. For x=3, you throw in 10 balls and have 7.5 (60/8) sec left on your timer. You then pull out one ball from the 18+10 and have 27 balls left. For x=4, you throw in 10 balls and have 3.75 (60/16) sec left on your timer. You then pull out one ball from the 27+10 and have 36 balls left. You can see a pattern: For any group x, you throw in 10 balls and have 60/(2^x)sec left on your timer. You pull out one ball and have 9x balls left. If you can find a value for x such that the second formula 60/(2^x) is almost zero, you can estimate the number of balls left. However, if you use the exact value for x to fit the above requirement(which is infinity), you have 9*infinity balls left, which is infinity. So the "intuitive answer" actually is correct. UPDATE: The answer isn't infinity. When I say that the number of balls left is 9x, I'm actually simplifying things. The actual number of balls left is 10x-x. If x is ifinity, the answer is undefined.

The answer's certainly undefined; it's the inherent contradiction which makes it a though experiement. On the one hand, you have an infinite number of balls (each cycle t lasts .5t(60) seconds, so you have an infinite number of cycles of adding 9 balls, and 9(infinity) is infinity), but on the other hand you have 0 balls (because each ball can be accounted for being removed). That is exactly what makes it a thought experiment, that it has no rational answer. It demonstrates, among other things, the difficulty inherent with dealing with infinity. --jfg284 ^{you were saying?} 20:50, 8 January 2006 (UTC)

An anon. user fixed the only thing i percieved wrong with it and the only thing brought up on the talk page (the fact that it should be undefined), so I removed the disputed tag on 10 January 2005.--jfg284 ^{you were saying?} 12:51, 10 January 2006 (UTC)

Possible merge with Monty Hell problem?

While this one deals with Ping pong balls, and that deals with money, I think they are fundamentally the same problem. Thoughts? Kirbytime 00:25, 4 April 2006 (UTC)

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No, I think it should just be deleted. The original point of this was that you have no ping pong balls at the end, and an explanation oh how that could be. The explanation turned out to be wrong, and so was the idea that you have no ping pong balls left, so how this has been reduced to "you do something impossible: Theoretically, what happened? A: There's no answer, it's impossible, even theoretically, so it's just pointless.

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each time you add 10 and remove one. infinite amount of times. 10 x infinity - 1 x infinity = 9 X infinity = infinity. Hneche the answer is infinity??

Is this a mathematical puzzle, or a thought-experiment about the natural world?

This puzzle has made the rounds on sci.math recently. Since each ball is labelled with a natural number, we can ascertain exactly how many balls remain in the barrel for any time t. And at the end of the minute, since every ball labelled with a natural has been removed, there are none left.

In fact, given slightly different rules, yet almost the same mechanics, we can leave almost any number of balls in the barrel. For example, in each batch of ten you insert (say, balls 21-30), you remove the tenth one (the ball labelled '30'), one ball for ever natural number would remain in the barrel (an infinite number of balls), except for the ones that end in a zero. Or, if you only remove balls consecutively, but starting with ball '7', you'd be left with 6 balls in the barrel.

Regarding the article, I'd personally reword it to say that the answer is zero, the paradox arising only if you have the unrealistic idea that there is a valid physical interpretation of the experiment. Any thoughts? Tez 15:13, 22 May 2006 (UTC)

Substitute "marble" for "ping-pong ball". I think we can agree this changes nothing substantial. And yet, you put an infinite number of marbles into a barrel, and now you sincerely tell me there are none left. It therefore follows that you have lost your marbles. -Dan 17:39, 30 May 2006 (UTC)

Balls and vase problem

I created a very similar article with a different name, Balls and vase problem, before I found this one. I suggest that the two articles be merged. One thing that is missing from both is a History section that provides the background about who originally proposed the problem and why, as well as historic arguments about its solution(s). — Loadmaster 17:24, 7 November 2006 (UTC)