Off Topic : the cheating Major



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On Fri, 25 Apr 2003 12:36:13 +0100, Gonzalez <[email protected]> wrote:

>And I thought everyone in the World knew what a googol is, but perhaps its just because I'm a
>maths teacher!
>
>Now, who knows what a googolplex is?

As I said a day or two ago: 1*10^Googol

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.

For no particular reason, some time ago, I decided to do this on my very old Win3.1 / DOS PC. It was
actually quite fun watching it for a while:

CLS DIM Count AS DOUBLE Count = 1 DIM x AS DOUBLE DIM z AS DOUBLE z = 0

RANDOMIZE (TIMER)

DO UNTIL Count = 1D+100 + 1 x = RND(TIMER) IF x >= .5 THEN x = 1 ELSE x = 0 z = z + x PRINT "Count
is"; Count; " Coin flipped"; x; " Average is"; z / Count Count = Count + 1 LOOP

END

I gave up after several months of "flipping my coin to find the average". I stopped as I'd bought a
new PC and needed a those spare plug sockets.

James

PS I'd always thought it was spelt "Google". I was wrong but at least I knew what is was!

PP <Bless you, Gonzalez, my son>

--
http://homepage.ntlworld.com/c.butty/Larrau.jpg
 
James Hodson <[email protected]> wrote in
news:[email protected]:
> PS I'd always thought it was spelt "Google". I was wrong but at least I knew what is was!

Probably because they wouldn't have been allowed to trademark/copyright "Googol" whereas "Google" is
a made up word that sounds near to what they wanted.

Have fun!

Graeme
 
Gonzalez <[email protected]> wrote in news:[email protected]:

> And there exists a number with 369,693,100 digits that can be represented with just 3 digits and
> no additional symbols in standard decimal notation.
>

9^(9^9), guess what, I got the answers from Google (so named because it gives back loads of relevant
hits, or so their story goes).

Have fun!

Graeme
 
James Hodson wrote:

>For no particular reason, some time ago, I decided to do this on my very old Win3.1 / DOS PC. It
>was actually quite fun watching it for a while:
>
>CLS DIM Count AS DOUBLE Count = 1 DIM x AS DOUBLE DIM z AS DOUBLE z = 0
>
>RANDOMIZE (TIMER)
>
>DO UNTIL Count = 1D+100 + 1 x = RND(TIMER) IF x >= .5 THEN x = 1 ELSE x = 0 z = z + x PRINT "Count
>is"; Count; " Coin flipped"; x; " Average is"; z / Count Count = Count + 1 LOOP
>
>END
>
>I gave up after several months of "flipping my coin to find the average". I stopped as I'd bought a
>new PC and needed a those spare plug sockets.

Have you ever read/seen the play or watched the film, Rosencrantz and Guildenstern Are Dead? The two
men toss a coin about 100 times... it comes up heads every time.
--
remove remove to reply
 
James Hodson <[email protected]> wrote:
>
> <Cough. NO. Cough. Sneeze>
>

Hope that's not SARS you've got there.

Tony

--
http://www.raven-family.com

"All truth goes through three steps: First, it is ridiculed. Second, it is violently opposed.
Finally, it is accepted as self-evident." Arthur Schopenhauer
 
Thats the one!

One of the most useful aspects of broadband is that I can listen to those shows over the internet
instead of having to remember the exact broadcast time. Just wish they'd archive 'Jamming' with
Roland Rivron...

Pete.
---------------------------
Peter Connolly Acute Computing Derby UK

"Graeme" <[email protected]> wrote in message
news:[email protected]...
> "Peter Connolly" <[email protected]> wrote in news:b8b89p
> [email protected]:
>
> > There was a radio programme this week that suggested they were the first people to attempt a
> > fraud using a Morecambe and Wise sketch!
>
> "The Now Show"
>
> There seem to be a lot of closet Radio 4 listeners on URC.
>
> Have fun!
>
> Graeme
 
On Fri, 25 Apr 2003 22:39:20 +0100, "Peter Connolly" <[email protected]> wrote:

>One of the most useful aspects of broadband is that I can listen to those shows over the internet
>instead of having to remember the exact broadcast time.

Also the only way the poor peasants without DAB can listen to BBC7 :)

Guy
===
** WARNING ** This posting may contain traces of irony. http://www.chapmancentral.com (BT ADSL and
dynamic DNS permitting)
NOTE: BT Openworld have now blocked port 25 (without notice), so old mail addresses may no longer
work. Apologies.
 
"Just zis Guy, you know?" <[email protected]> wrote in message
news:[email protected]...

> Also the only way the poor peasants without DAB can listen to BBC7 :)

We don't have DAB. There were two reasons why we bought one of those digital TV boxes, and the
second one doesn't happen until July. Only downside is our video tapes are now full of radio
programmes...

cheers, clive
 
On Fri, 25 Apr 2003 21:20:54 +0100, Gonzalez <[email protected]> wrote:

>Have you ever read/seen the play or watched the film, Rosencrantz and Guildenstern Are Dead? The
>two men toss a coin about 100 times... it comes up heads every time.

No, Gonzalez, I haven't. I'll look out for it.

Of course, 100 heads in a row is quite possible. What does make me laugh is those people who believe
that as (say) 50 heads have been tossed, the next one HAS to be a tail. The coin obviously knows how
it's been previously flipped.

James

--
http://homepage.ntlworld.com/c.butty/Larrau.jpg
 
James Hodson wrote:

>Of course, 100 heads in a row is quite possible. What does make me laugh is those people who
>believe that as (say) 50 heads have been tossed, the next one HAS to be a tail. The coin obviously
>knows how it's been previously flipped.

If my maths is correct, the odds of 100 consecutive heads is about
1:126 765 000 000 000 000 000 000 000 000.

BUT the chances of the next flipped coin being heads is 1:2.
--
remove remove to reply
 
"Gonzalez" <[email protected]> wrote in message
news:[email protected]...
> James Hodson wrote:
>
> >Of course, 100 heads in a row is quite possible. What does make me laugh is those people who
> >believe that as (say) 50 heads have been tossed, the next one HAS to be a tail. The coin
> >obviously knows how it's been previously flipped.
>
> If my maths is correct, the odds of 100 consecutive heads is about
> 1:126 765 000 000 000 000 000 000 000 000.
>

Assuming your maths is correct - I CBA to work it out: the odds of 50 heads followed by 50 tails is
exactly the same, as is the odds of head, tail, head, tail... etc and all the other possible
sequences.
 
Whazzarke wrote:

>Assuming your maths is correct - I CBA to work it out: the odds of 50 heads followed by 50 tails is
>exactly the same, as is the odds of head, tail, head, tail... etc and all the other possible
>sequences.

But what are the chances of exactly 50 heads and exactly 50 tails?
--
remove remove to reply
 
"Gonzalez" <[email protected]> wrote in message
news:[email protected]...
> James Hodson wrote:
>
> >Of course, 100 heads in a row is quite possible. What does make me laugh is those people who
> >believe that as (say) 50 heads have been tossed, the next one HAS to be a tail. The coin
> >obviously knows how it's been previously flipped.
>
> If my maths is correct, the odds of 100 consecutive heads is about
> 1:126 765 000 000 000 000 000 000 000 000.
>
> BUT the chances of the next flipped coin being heads is 1:2.

Actually, it's ever so slightly less than that. There are THREE possible outcomes of the toss of a
coin - obverse (heads), reverse (tails), or EDGE! If the dynamics are calculated (very complex
differential equations!), I believe the probability of the coin landing on its edge is something
like 1:3E998 ("One in three times ten to the power of nine hundred and ninety eight").

The odds of the outcome being obverse or reverse are almost equal, at (.5-(3E998)^-1), although it
does depend on the coin - since the centre of mass is ever so slightly different for each design
emobossed.

This assumes, of course, that each coin toss has an equal force exerted to start the spin, and that
the "upper" face when the toss is initiated are normally distributed.

Other variables are air pressure, humidity and temperature - which can all affect the "air buoyancy"
and aerodynamics by a factor of around
1:7000 per degree of magnitude.

Would anyone care to prepare an uncertainty budget? :)

--
MatSav
 
Alex Noel-Tod <[email protected]> wrote in message news:<[email protected]>...
> Apologies for this off-topic request, but I need to cast my net wide (If 17m people watched it,
> someone must have recorded it ...)
>
> Does anyone have a video of the ITV 90 minute 'documentary' about the 'cheating' episode of "Who
> Wants to be a Millionaire" (broadcast Monday 21 April), and from which I could request a copy ? I
> need a copy for our collection (honest !).
>

Didn't actually see the show in question, but was highly amused upon discovering (having watched
Friday's HIGNFY) that Benylin commercials featured prominently in the ad breaks!

David E. Belcher

Dept. of Chemistry, University of York
 
James Hodson <[email protected]> wrote in message
news:<[email protected]>...

> 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.

--
Dave...
 
"Gonzalez" <[email protected]> wrote in message
news:[email protected]...
> 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.

cheers, clive
 
Thus spake Graeme <[email protected]>

> "Peter Connolly" <[email protected]> wrote in news:b8b89p
> [email protected]:

> > There was a radio programme this week that suggested they were the first people to attempt a
> > fraud using a Morecambe and Wise sketch!

> "The Now Show"

> There seem to be a lot of closet Radio 4 listeners on URC.

Closet? I do have Radio 4 there but also in every other room in the house...

--
Helen D. Vecht: [email protected] Edgware.
 
Clive George wrote:

>"Gonzalez" <[email protected]> wrote in message
>news:[email protected]...
>> 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!
--
remove remove to reply
 
"Gonzalez" <[email protected]> wrote in message
news:[email protected]...
> Clive George wrote:
>
> >"Gonzalez" <[email protected]> wrote in message
> >news:[email protected]...
> >> 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

cheers, clive
 
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