RE: Interesting Numbers

[Dave Cross]

From: Greg McCarroll <[EMAIL PROTECTED]>
Date: 10/19/01 9:48:51 AM

> And finally a quick riddle, where you have to work out 
> the age of Diophantus,
>
>  "Here lies Diophantus," the wonder behold . . .
>  Through art algebraic, the stone tells how old:
>  "God gave him his boyhood one-sixth of his life,
>  One twelfth more as youth while whiskers grew rife;
>  And then yet one-seventh ere marriage begun;
>  In five years there came a bouncing new son.
>  Alas, the dear child of master and sage
>  After attaining half the measure of his fathers life
>  chill fate took him.
>  After consoling his fate by this science of numbers for
>  four years,
>  he ended his life." 

S
P
O
I
L
E
R

S
P
A
C
E
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.
.
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.
.
.
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.
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.
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.

He was 84 when he died.

Dave...

-- 


"Let me see you make decisions, without your television"
   - Depeche Mode (Stripped)

Re: Interesting Numbers

[David Cantrell]

On Fri, Oct 19, 2001 at 09:48:51AM +0100, Greg McCarroll wrote:
> And finally a quick riddle, where you have to work out the age of
> Diophantus,
>   "Here lies Diophantus," the wonder behold . . .
>   Through art algebraic, the stone tells how old:
> "God gave him his boyhood one-sixth of his life,
> One twelfth more as youth while whiskers grew rife;
> And then yet one-seventh ere marriage begun;
> In five years there came a bouncing new son.
> Alas, the dear child of master and sage
> After attaining half the measure of his fathers life
> chill fate took him.
> After consoling his fate by this science of numbers for
> four years,
> he ended his life." 

This is trivial, but can give two answers depending on how you interpret
"half the measure of his fathers life".  Is it half the measure of his
father's *entire* life, or half the measure of his father's life up until
that point?

Yes yes, I know, immediately spotting the ambiguity.  Feel free to mutter
about typical bloody programmers.

Assuming the former ...

   x/6 + x/12 + x/7 + 5 + x/2 + 4 = x
=> 84x + 42x + 72x + 2520 + 252x + 1008 = 504x # multiply by 504
=> 2520 + 1008 = 3528 = 54x
=> x = 65 yrs 4 months, give or take a day or two

Assuming the latter ...

   x/6 + x/12 + x/7 + 5 + y + 4 = x # son's life is y
   y = (x/6 + x/12 + x/7 + 5 + y)/2

solving for x is left as an exercise for the reader.

-- 
David Cantrell | [EMAIL PROTECTED] | http://www.cantrell.org.uk/david

If you save all your money for three years, you'll be able to afford this
new computer.  If, however, you blow all your money on poker, booze and
loose women - you'll still be able to afford it in three years.
  -- anon, on Usenet

Re: Interesting Numbers

[Peter Haworth]

On Fri, 19 Oct 2001 09:48:51 +0100, Greg McCarroll wrote:
>4840 
>   Clue: Robin Szmeti I think will have the best chance. 

For some reason, this sounds like a tape drive to me

>3 , 7 , 31 , 127
> Clue: They are in sequence

2**p - 1, where p is prime

-- 
Peter Haworth   [EMAIL PROTECTED]
"Maybe you win, and maybe you lose.
 Life is tough sometimes.  And Larry is a fink."
-- Larry Wall

RE: Interesting Numbers

[Richard Clyne]

But Diophantus studied equations that are solvable in integers only.  I
reckon that that is a clue to the desired solution.

Richard

Re: Interesting Numbers

[Dave Cross]

From: David Cantrell <[EMAIL PROTECTED]>
Date: 10/19/01 12:31:29 PM

>On Fri, Oct 19, 2001 at 09:48:51AM +0100, Greg McCarroll wrote:
>> And finally a quick riddle, where you have to work out 
>> the age of Diophantus,
>>   "Here lies Diophantus," the wonder behold . . .
>>   Through art algebraic, the stone tells how old:
>>   "God gave him his boyhood one-sixth of his life,
>>   One twelfth more as youth while whiskers grew rife;
>>   And then yet one-seventh ere marriage begun;
>>   In five years there came a bouncing new son.
>>   Alas, the dear child of master and sage
>>   After attaining half the measure of his fathers life
>>   chill fate took him.
>>   After consoling his fate by this science of numbers for
>>   four years, he ended his life." 
>
> This is trivial, but can give two answers depending on 
> how you interpret "half the measure of his fathers 
> life".  Is it half the measure of his father's *entire* 
> life, or half the measure of his father's life up until
> that point?

Yeah. Spotted that, but went with the most obvious one
(the first one).

> Assuming the former ...

As did I.

>   x/6 + x/12 + x/7 + 5 + x/2 + 4 = x

Well, we started with the same equation

> => 84x + 42x + 72x + 2520 + 252x + 1008 = 504x # multiply
by 504

I multiplied by 84. Giving

14x + 7x + 12x + 420 + 42x + 336 = 84x

> => 2520 + 1008 = 3528 = 54x

756 = 9x

>=> x = 65 yrs 4 months, give or take a day or two

x = 84

I believe your error was in the calculation of 4 x 504 :)

hth,

Dave...
-- 


"Let me see you make decisions, without your television"
   - Depeche Mode (Stripped)

RE: Interesting Numbers

[Wilson, Andrew (Belfast)]

> Assuming the latter ...
> 
>x/6 + x/12 + x/7 + 5 + y + 4 = x # son's life is y
>y = (x/6 + x/12 + x/7 + 5 + y)/2

Actually  y = (x - 4) / 2 is easier to work with.

cheers

Andrew

Re: Interesting Numbers

[David Cantrell]

On Fri, Oct 19, 2001 at 05:55:22AM -0700, Dave Cross wrote:
> I believe your error was in the calculation of 4 x 504 :)

Oh yeah.  Oops.

Look! It's the Goodyear blimp! [runs away]

-- 
David Cantrell | [EMAIL PROTECTED] | http://www.cantrell.org.uk/david

This is a signature.  There are many like it but this one is mine.

Re: Interesting Numbers

[Greg McCarroll]

To summarise the answers we have so far .

* Greg McCarroll ([EMAIL PROTECTED]) wrote:
> 
>4840 
>   Clue: Robin Szmeti I think will have the best chance. 
>1 , 9 , 36 , 84 , 126
> Clue: Don't use C to work this out
>3 , 7 , 31 , 127
> Clue: They are in sequence


SOLVED : Peter Haworth, although he noticed something I didn't.

>212
>   Clue: Mark Fowler should know this one
>714
>   Clue: Jack built something, but he wasn't the only one
>231
>   Clue: You'll need the revised edition of the book to work this
>   one out. (WARNING: I don't think anyone will get this one)
> 
> And finally a quick riddle, where you have to work out the age of
> Diophantus,

SOLVED : Dave Cross

So that leaves 5 reasonable ones, the last is nigh on impossible,
without either a quick fire guessing session or owning the book and
knowing how my mind words.

I reckon Dave Cross, Paul Mison, Richard Clamp, to name a few should
be able to answer `714' from the clue alone. People who IRC when
Trelane is on in the morning should get a clue to `212', Older people
should spot 4840, and as for the first sequence anyone who likes
puzzles should figure it out.

Greg

p.s. if you are the sort of johnny come lately, giving up, PHP
programming type of person, the answers are at .

http://217.34.97.146/~gem/perl/answers.txt

-- 
Greg McCarroll http://217.34.97.146/~gem/

Re: Interesting Numbers

[Newton, Philip]

Peter Haworth wrote:
> On Fri, 19 Oct 2001 09:48:51 +0100, Greg McCarroll wrote:
> >3 , 7 , 31 , 127
> > Clue: They are in sequence
> 
> 2**p - 1, where p is prime

aka "Mersenne numbers". (A subset of those numbers is the "Mersenne
primes".)

Apparently, they're important in factoring numbers and cryptography etc.
because of their special form. Or something.

Cheers,
Philip
-- 
Philip Newton <[EMAIL PROTECTED]>
All opinions are my own, not my employer's.
If you're not part of the solution, you're part of the precipitate.

Re: Interesting Numbers

[Newton, Philip]

Greg McCarroll wrote:
>1 , 9 , 36 , 84 , 126
> Clue: Don't use C to work this out

Ah! Got the joke. (Well, after peeking in the EIS.) Actually, C *does* have
something to do with those numbers.

>212
>   Clue: Mark Fowler should know this one

It's a NYC area code.

Cheers,
Philip
-- 
Philip Newton <[EMAIL PROTECTED]>
All opinions are my own, not my employer's.
If you're not part of the solution, you're part of the precipitate.

Re: Interesting Numbers

[Chris Devers]

On Fri, 19 Oct 2001, Greg McCarroll wrote:

> I remembered one of my favourite books, "The Penguin Dictionary of
> Curious and Interesting Numbers".

Good book :)

> So hear we go (some are easy, some are pretty much impossible)..
> 
>4840 

Clue: page 158. Is it Robin Szmetia, esq?

>1 , 9 , 36 , 84 , 126
>3 , 7 , 31 , 127

I can't find these ones! I can't cheat! :)

>212

Page 130. No, the Manhattan area code is not the answer :)

>714

Page 146, and I don't get the hint about Jack...

>231

Not in the book! 
 
> And finally a quick riddle, where you have to work out the age of
> Diophantus,
> 
>   "Here lies Diophantus," the wonder behold . . .
>   Through art algebraic, the stone tells how old:
> "God gave him his boyhood one-sixth of his life,
> One twelfth more as youth while whiskers grew rife;
> And then yet one-seventh ere marriage begun;
> In five years there came a bouncing new son.
> Alas, the dear child of master and sage
> After attaining half the measure of his fathers life
> chill fate took him.
> After consoling his fate by this science of numbers for
> four years,
> he ended his life." 

Page 114. 
 
> Well I hope it gives someone some fun,
 
Yes. :) 



-- 
Chris Devers

"People with machines that think, will in times of crisis, 
make up stuff and attribute it to me" - "Nikla-nostra-debo"

Re: Interesting Numbers

[Greg McCarroll]

* Chris Devers ([EMAIL PROTECTED]) wrote:
> >1 , 9 , 36 , 84 , 126
> >3 , 7 , 31 , 127
> 
> I can't find these ones! I can't cheat! :)
> 

I did these ones myself ;-)

> Not in the book! 

Yes it is. Read the clue again carefully and think about it.

Greg

-- 
Greg McCarroll http://217.34.97.146/~gem/

Re: Interesting Numbers

[David H. Adler]

On Fri, Oct 19, 2001 at 04:30:51PM +0200, Newton, Philip wrote:
> Greg McCarroll wrote:
> 
> >212
> > Clue: Mark Fowler should know this one
> 
> It's a NYC area code.


It was, for many years, *the* nyc area code.


dha
-- 
David H. Adler - <[EMAIL PROTECTED]> - http://www.panix.com/~dha/
I expect my version of ESP::Psychic will be ready sometime last week.
More likely, yesterday (you know how schedules tend to slip).
- Eric The Read in comp.lang.perl.misc

SPOILERS : Re: Interesting Numbers

[Greg McCarroll]

* Peter Haworth ([EMAIL PROTECTED]) wrote:
> On Fri, 19 Oct 2001 09:48:51 +0100, Greg McCarroll wrote:
> >4840   
> > Clue: Robin Szmeti I think will have the best chance. 
> 
> For some reason, this sounds like a tape drive to me
> 
> >3 , 7 , 31 , 127
> > Clue: They are in sequence
> 
> 2**p - 1, where p is prime
> 

I didn't spot that, the actual answer I was looking for was they were
the first 4 Mersenne Primes, Mersenne Primes are all of the form of
2^x-1 and of course are primes. But I think your answer deserves a
bonus point! ;-) Cool!



-- 
Greg McCarroll http://217.34.97.146/~gem/

SPOILERS: Re: Interesting Numbers

[Greg McCarroll]

Dave's 84 is the correct answer for this riddle.

* Dave Cross ([EMAIL PROTECTED]) wrote:
> 
> From: David Cantrell <[EMAIL PROTECTED]>
> Date: 10/19/01 12:31:29 PM
> 
> >On Fri, Oct 19, 2001 at 09:48:51AM +0100, Greg McCarroll wrote:
> >> And finally a quick riddle, where you have to work out 
> >> the age of Diophantus,
> >>   "Here lies Diophantus," the wonder behold . . .
> >>   Through art algebraic, the stone tells how old:
> >>   "God gave him his boyhood one-sixth of his life,
> >>   One twelfth more as youth while whiskers grew rife;
> >>   And then yet one-seventh ere marriage begun;
> >>   In five years there came a bouncing new son.
> >>   Alas, the dear child of master and sage
> >>   After attaining half the measure of his fathers life
> >>   chill fate took him.
> >>   After consoling his fate by this science of numbers for
> >>   four years, he ended his life." 
> >
> > This is trivial, but can give two answers depending on 
> > how you interpret "half the measure of his fathers 
> > life".  Is it half the measure of his father's *entire* 
> > life, or half the measure of his father's life up until
> > that point?
> 
> Yeah. Spotted that, but went with the most obvious one
> (the first one).
> 
> > Assuming the former ...
> 
> As did I.
> 
> >   x/6 + x/12 + x/7 + 5 + x/2 + 4 = x
> 
> Well, we started with the same equation
> 
> > => 84x + 42x + 72x + 2520 + 252x + 1008 = 504x # multiply
> by 504
> 
> I multiplied by 84. Giving
> 
> 14x + 7x + 12x + 420 + 42x + 336 = 84x
> 
> > => 2520 + 1008 = 3528 = 54x
> 
> 756 = 9x
> 
> >=> x = 65 yrs 4 months, give or take a day or two
> 
> x = 84
> 
> I believe your error was in the calculation of 4 x 504 :)
> 
> hth,
> 
> Dave...
> -- 
> 
> 
> "Let me see you make decisions, without your television"
>- Depeche Mode (Stripped)
> 
> 
> 
> 
-- 
Greg McCarroll http://217.34.97.146/~gem/

Re: SPOILERS : Re: Interesting Numbers

[Newton, Philip]

Greg McCarroll wrote:
> * Peter Haworth ([EMAIL PROTECTED]) wrote:
> > On Fri, 19 Oct 2001 09:48:51 +0100, Greg McCarroll wrote:
> > >4840 
> > >   Clue: Robin Szmeti I think will have the best chance. 
> > 
> > For some reason, this sounds like a tape drive to me
> > 
> > >3 , 7 , 31 , 127
> > > Clue: They are in sequence
> > 
> > 2**p - 1, where p is prime
> > 
> 
> I didn't spot that, the actual answer I was looking for was they were
> the first 4 Mersenne Primes, Mersenne Primes are all of the form of
> 2^x-1 and of course are primes. But I think your answer deserves a
> bonus point! ;-) Cool!

2^p-1, actually. (Though I don't know whether any numbers of the form 2^x-1
are prime if x is not prime.)

The next numbers in the sequence are ..., 127, 8191, 131071, 524287, ... if
you mean the Mersenne primes, and ..., 127, 2047, 8191, 131071, 524287,
8388607, ... if you mean the Mersenne numbers (i.e. 2^p-1 regardless of
whether the result is prime or not).

Cheers,
Philip
-- 
Philip Newton <[EMAIL PROTECTED]>
All opinions are my own, not my employer's.
If you're not part of the solution, you're part of the precipitate.

Re: SPOILERS : Re: Interesting Numbers

[Dave Hodgkinson]

Greg McCarroll <[EMAIL PROTECTED]> writes:

*wibble*

Grep, get a life!



-- 
David Hodgkinson, Wizard for Hirehttp://www.davehodgkinson.com
Editor-in-chief, The Highway Star   http://www.deep-purple.com
All the Purple Family Tree news   http://www.slashrock.com
   Interim Technical Director, Web Architecture Consultant for hire

Re: SPOILERS : Re: Interesting Numbers

[Greg McCarroll]

* Dave Hodgkinson ([EMAIL PROTECTED]) wrote:
> Greg McCarroll <[EMAIL PROTECTED]> writes:
> 
> *wibble*
> 
> Grep, get a life!
> 

Dave,

trust me that isn't that sad, what would be sad is if i had already
started writing a quiz for next friday and dreamt some of the
questions, and was say for example write now at 7:20am on a saturday
morning reading email and writing some of the questions i dreamt into
a file in another window

Greg


-- 
Greg McCarroll http://217.34.97.146/~gem/

Re: SPOILERS : Re: Interesting Numbers

[Dave Cross]

On Fri, Oct 19, 2001 at 10:09:27PM +0100, Dave Hodgkinson ([EMAIL PROTECTED]) 
wrote:
> Greg McCarroll <[EMAIL PROTECTED]> writes:
> 
> *wibble*
> 
> Grep, get a life!

ITYM "get a _job_" :)

Dave...

-- 

  .sig missing...