You have an empty container, and an infinite number of marbles, each numbered with an integer from 1 to infinity.
At the start of the minute, you put marbles 1 - 10 into the container, then remove one of the marbles and throw it away. You do this again after 30 seconds, then again in 15 seconds, and again in 7.5 seconds. You continuosly repeat this process, each time after half as long an interval as the time before, until the minute is over.
Since this means that you repeated the process an infinite number of times, you have "processed" all your marbles.
How many marbles are in the container at the end of the minute if for every repetition (numbered N)
A. You remove the marble
numbered (10 * N)
B. You remove the marble numbered (N)
after this problem has been put ot bed (apparently), I'd like to add my two cents worth. So far it has been a very interesting read...
The problem as stated in a and b are identical. There is a lot of places where we confuse the actual math of a situation by implying a local nomenclature that is irrelevant to the actual mathematics, but helps us process the information just the same. As with Fatboy, I am a mere Engineer, so the theoretical vocabulary may pose a problem for me, but the idea is that a marble is a marble, regardless of the number it has written on it. The way that the majority of people here are thinking, having the exact same process performed on the exact same marbles would have a different result if the numbers painted on them were in a different order. Clearly this is not the case. As an example, (and hopefully this will make sense, as its derived from an anaolgy my math teacher used to explain the chain rule in calculus), if we have twice as many apples as oranges, then we - in the math world - can define apples as "x" and oranges as "y" and then say that 2x=y. Now we want to find the relationship between the rate of change between these "variables". It is equally correct to ask for d(x)/d(y) as it is to ask for d(apples)/d(oranges) - with a properly set up naming system, these are equivalent.
What this problem has done is forced upon you a nomenclature, which certainly seems legitimate, but obviously leads astray as both parts of the question, which identical except for the nomenclature, do not produce the same mathematical result.
Finally for the case of the amended question posted about 7-8 comments ago. The rewording of the question has removed the problem of the nomenclature and allow a different mathematical result.
And just to clarify, I see how the math works for the answer you are all supporting (to leave no marbles in the bag for part b), I am trying to show the mis-step in the process. The only way that you can end up with no marbles is to remove as many as you've put in, and since in no interval do you remove more than you put in, if you ever have more than zero marbles you always will. Its very clear that the math produced is flawed.
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