After processing an infinite number of marbles, not once but
twice in solving the puzzle
Marbles Bonanza, you've grown rather tired of moving all these marbles around. Nevertheless, it is your duty to press on forward and try a third experiment. This time, though, you decide that you'll cut down on the amount of work by not
removing any balls ever.
At the start of the minute, you put marbles 1-9 in the bag, and then add a 0 to the end of marble 1 (so that you now have duplicate marble 10s, one in the bag that you just modified, one out). Therefore you now have marbles numbered 2-10 in the bag, as in scenario B of the previous puzzle, and marble 10 outside the bag as in scenario A. 30 seconds later, you put marbles 11-19 in the bag, and add a 0 to marble 2, so that now you have two marbles numbered 20 - one in, one out. You continuously repeat this process, with each interval half as long as the one before. In general, for the nth operation, you put marbles 10n-9 to 10n-1 in the bag, and add a zero to marble n in the bag, so that it becomes marble 10n in the bag.
- How many marbles are in the bag at the end of the minute?
- What are the numbers on the marbles ?
- Is the situation inside the bag identical to either of the previous two problems after 31 seconds? 50 seconds? at the end of the minute? How about the situation outside the bag?
(In reply to
re(5): No Subject by ajosin)
ajosin, let's try this. Suppose the problem were phrased as follows:
A bag starts out empty. At the end of 1/2 minute, you look at the bag and there are 9 marbles in it, numbered 1-9. At the end of another 1/4 minute, you look at it and there are 18 marbles in it, numbered 2-19. At the end of 3/4 minute, there are 27 marbles in it numbered 3-29. Furthermore, you know this pattern will continue for up to one full minute...the time intervals are cut in half every step, and and the end of each step the lowest numbered marble will be one higher than at the previous step, and the highest numbered marble will be 10 higher than at the previous step.
From this information, can you tell me how many marbles will be in the bag at the end of one minute? I'll let you answer, before I finish my point.
re(6): No Subject
