Off Topic : the cheating Major

Clive George said:

"Gonzalez" <[email hidden]> wrote in message
"]news:[email hidden]...

Quoted message said:

Clive George said:

"Gonzalez" <[email hidden]> wrote in message
"]news:[email hidden]...
> But what are the chances of exactly 50 heads and exactly 50 tails?

100! / 50! / 50! / 2^100.

Reduces to 3*3*3*3*11*13*17*19*29*31*53*59*61*67*71*73*79*83*89*97 / 2^97 (if I counted that
right), both of which are still very big numbers. The answer is about 0.08.

I admire your prime factorisation. Very neat!

I'm afraid I can't claim any credit for that - I just used it as an excuse to practise my STL a
bit, something I don't get to do very often.

I played a bit more, and the exact answer is:

.07958923738717876149812705024217046140293154042473332135734787051717376016 31321012973785400390625

The top number is 12611418068195524166851562157 and the bottom 158456325028528675187087900672

This shows how rusty my maths is becoming. I was going to come back with, "But surely this must be a
repeating decimal.", but, of course, the denominator 2^97, will give a terminating decimal.

I had Mathematica on my old PC, and that could handle such numbers, but, alas, I can't instal it
on this one.
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(Dave Kahn) said:

James Hodson <[email hidden]> wrote in message
news:<[email hidden]>...

Quoted message said:

According to the late, great Carl Sagan in his book Cosmos - why has the Cosmos programme series
never been repeated on TV, BTW? - the universe ain't large enough to actually write in
regular-sized text that number.

I thought the limiting factor was the estimated amount of matter in the universe - more zeroes are
required than there are particles to form them.

Whatever. I'm no expert on these things although I do enjoy reading such material. The book is
actually on my sitting room's floor so I could easily go and look for the relevant sentence, but I
won't - not just now. I have some 450 u.r.c posts to read.

However, Dave, I have an idea. Why don't you start writing out a googolplex? I'll get back to you
eventually ;-)

James

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James Hodson said:

Whatever. I'm no expert on these things although I do enjoy reading such material. The book is
actually on my sitting room's floor so I could easily go and look for the relevant sentence, but I
won't - not just now. I have some 450 u.r.c posts to read.

However, Dave, I have an idea. Why don't you start writing out a googolplex? I'll get back to you
eventually ;-)

A googolplex is relatively easy to write:

10^10^100.

However, it is dwarfed by Graham's number: "which cannot be expressed using the conventional
notation of powers, and powers of powers. If all the material in the Universe were turned into pen
and ink it would not be enough to write the number down." David Wells
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Gonzalez said:

Quoted message said:

However, Dave, I have an idea. Why don't you start writing out a googolplex? I'll get back to you
eventually ;-)

A googolplex is relatively easy to write:

10^10^100.

"Hello, Gonzalez, I'm back," to paraphrase the bloke in Independence Day.

Is that the same as saying 1*10^Googol?

BTW, smart ... erm ... person ;-) Try writing a Googolplex the other way: 1,000,000,000 etc

FWIW, I do like:

Quoted message said:

However, it is dwarfed by Graham's number: "which cannot be expressed using the conventional
notation of powers, and powers of powers. If all the material in the Universe were turned into pen
and ink it would not be enough to write the number down."

James

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James Hodson said:

Gonzalez said:

Quoted message said:

However, Dave, I have an idea. Why don't you start writing out a googolplex? I'll get back to you
eventually ;-)

A googolplex is relatively easy to write:

10^10^100.

"Hello, Gonzalez, I'm back," to paraphrase the bloke in Independence Day.

Is that the same as saying 1*10^Googol?

Yes. A googol is 10^100, so 10^googol is 10^10^100, but it's not the sate as (10^10)^100.

Quoted message said:

BTW, smart ... erm ... person ;-) Try writing a Googolplex the other way: 1,000,000,000 etc

FWIW, I do like:

Quoted message said:

However, it is dwarfed by Graham's number: "which cannot be expressed using the conventional
notation of powers, and powers of powers. If all the material in the Universe were turned into pen
and ink it would not be enough to write the number down."

James

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James Hodson <[email hidden]> wrote in message
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Quoted message said:

However, Dave, I have an idea. Why don't you start writing out a googolplex? I'll get back to you
eventually ;-)

You don't expect me to fall for that old one again, do you? :-)

It reminds me of the story of the 18th century primary school teacher who thought he'd keep his
class quiet for half an hour or so by getting them to sum the integers from 1 to 100. One of his
pupils, a 7 year old named Karl Friedrich Gauss, saw immediately that the sum of the integers from 1
to n is given by the formula n(n+1)/2 and produced the answer 5050 within a few seconds.

Or maybe it was just a lucky Gauss. :-)

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Dave...

Dave Kahn said:

who thought he'd keep his class quiet for half an hour or so by getting them to sum the integers
from 1 to 100. One of his pupils, a 7 year old named Karl Friedrich Gauss, saw immediately that the
sum of the integers from 1 to n is given by the formula n(n+1)/2 and produced the answer 5050
within a few seconds. Or maybe it was just a lucky Gauss. :-)

Probably his magnetic personality.
--
David Damerell <[email hidden]> Distortion Field!

In message <[email hidden]>, David Damerell
<[email hidden]> writes

Quoted message said:

Dave Kahn said:

who thought he'd keep his class quiet for half an hour or so by getting them to sum the integers
from 1 to 100. One of his pupils, a 7 year old named Karl Friedrich Gauss, saw immediately that
the sum of the integers from 1 to n is given by the formula n(n+1)/2 and produced the answer 5050
within a few seconds. Or maybe it was just a lucky Gauss. :-)

Probably his magnetic personality.

Such a thing encourages polarised opinions.
--
Michael MacClancy