After reading unreality's problems dealing with infinite numbers, I decided to post my own. To be honest, it's not "my own," since I read it in a book a few years ago (I don't remember which book, but it was really good. You should all read it).

Suppose you have 2 bins, labeled 'A', and 'B'. To start, bin A has an infinite number of ping pong balls, and they are numbered sequentially from 1 to infinity. Each ball has a unique number printed on it. Bins B is empty to start.

You begin an experiment that will last 1 minute, but will include an infinite number of iterations. Each iteration will take exactly half of the time remaining - ie, the first iteration will be completed after 30 seconds, the second after 45, the third after 52.5, etc. At each iteration, you do two things: 1st, take the two lowest numbered balls out of bin A and put them in bin B; 2nd, take the one lowest numbered ball out of bin B, and throw it away.

So, in the first 30 seconds, you take balls 1 and 2 out of A and put them in B, then take ball 1 and throw it away. In the next 15 seconds, you take balls 3 and 4 out of A, put them in B, then throw away ball 2. As you can see, the number of balls in bin A will decrease by 2 with every iteration, and the number of balls in bin B will increase by 1.

The question is this: after the entire minute has elapsed, how many balls will be in bins A and B?

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After reading unreality's problems dealing with infinite numbers, I decided to post my own. To be honest, it's not "my own," since I read it in a book a few years ago (I don't remember which book, but it was really good. You should all read it).

Suppose you have 2 bins, labeled 'A', and 'B'. To start, bin A has an infinite number of ping pong balls, and they are numbered sequentially from 1 to infinity. Each ball has a unique number printed on it. Bins B is empty to start.

You begin an experiment that will last 1 minute, but will include an infinite number of iterations. Each iteration will take exactly half of the time remaining - ie, the first iteration will be completed after 30 seconds, the second after 45, the third after 52.5, etc. At each iteration, you do two things: 1st, take the two lowest numbered balls out of bin A and put them in bin B; 2nd, take the one lowest numbered ball out of bin B, and throw it away.

So, in the first 30 seconds, you take balls 1 and 2 out of A and put them in B, then take ball 1 and throw it away. In the next 15 seconds, you take balls 3 and 4 out of A, put them in B, then throw away ball 2. As you can see, the number of balls in bin A will decrease by 2 with every iteration, and the number of balls in bin B will increase by 1.

The question is this: after the entire minute has elapsed, how many balls will be in bins A and B?

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