Subject:
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Re: Is lego *truly* unlimited? (some thoughts)
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Newsgroups:
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lugnet.off-topic.geek
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Date:
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Thu, 9 Dec 2004 19:34:05 GMT
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Viewed:
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1675 times
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In lugnet.general, David Eaton wrote:
> [1] Ok, at a very rough guess, 500 billion choose 250 billion is at least
> 1x10^(4x10^11) or 1x10^400000000000, which... is a lot. Guessed based on how
> quickly the "middle number" in Pascal's triangle increases. Every other row's
> middle number seems to grow logarithmically, at hits at LEAST 4 long before
> it gets even halfway to the billionth row. Hence, I used a factor of 4 to
> guess at the number of 0's that the center number goes up by after 500
> billion rows (250 iterations, since it's counting every other row). In
> actuality, there's probably a better factor to use to guess with.
Ok, so it's asymptotic, not logarithmic, and it approaches 4, so 4 was a
perfectly cromulent guess. However. Since the sum of any line N of Pascal's
triangle is apparently 2^N (starting at row 0), and you'd theoretically count
EVERYTHING within a row, not including the empty set, there are roughly
2^200000000000-1 (about 1x10^60205999133) different groups of pieces possible
with all the Lego on the planet, not including piece orientation.
Dunno about the orientation thing.
2x4 bricks, only 90 degree angles:
1 => 1 combo (200 assuming 200 different colors)
2 => 24 combos (48 counting 2 diff. colors, 40000 assuming all colors)
3 => 1060 combos (approx 1392204000 assuming all colors)
4 => ?
5 => ?
6 => 102981500 combos (roughly 6x10^21 assuming all colors)
Given that progression, that's CRAZY. Still probably peanuts to a gogol plex,
but but crazy nonetheless.
DaveE
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Message has 1 Reply:
 | | Re: Googolplex (was: Is lego *truly* unlimited?)
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| (...) I found the following amusing description of how to visualise a googolplex: "...if one put this black hole into a hypothetical rigid nonpermeable box, a few million light years in size, and looked at the contents once a year, it would look (...) (20 years ago, 9-Dec-04, to lugnet.off-topic.geek)
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Message is in Reply To:
| | Re: Is lego *truly* unlimited? (some thoughts)
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| (...) Well, 1st off, there's probably on the order of several hundred billion pieces on the planet. I remember reading in some FAQ the estimated number of pieces in the world, but I can't seem to find it at the moment. I know they make about 20 (...) (20 years ago, 8-Dec-04, to lugnet.general)
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