HDTenEightyP/NetNews huggingface dataset:
From: jkenton@world.std.com (Jeff Kenton)
Subject: Re: VCR Plus Codes
Organization: Kenton Systems Corporation, Weston MA
Date: Mon, 12 Oct 1992 17:00:47 GMT

In article <1992Oct12.154619.17062@draco.macsch.com> m_reymond@macsch.com writes:
>Has anyone out there figgered out how the VCR Plus codes are derived?  
>My inquiry is purely academic. I don't intend to invent my own device.
>I've tried to determine if there is a consistent pattern, but have found none.
>I suspect there is some sort of encryption. I have also noticed that prime time 
>shows on channels 2-13 have codes with the fewest digits.
>

Try sci.crypt.  They've been through this before.

-- 
-------------------------------------------------------------------------
=			Jeff Kenton	(617) 894-4508			=
=			    jkenton@world.std.com			=
-------------------------------------------------------------------------
From: carl@SOL1.GPS.CALTECH.EDU (Carl J Lydick)
Newsgroups: rec.puzzles
Subject: Re: Diameter of earth?
Date: 7 Oct 1992 22:59:22 GMT
Organization: HST Wide Field/Planetary Camera
Reply-To: carl@SOL1.GPS.CALTECH.EDU
NNTP-Posting-Host: sol1.gps.caltech.edu

In article <1992Oct5.031617.18844@cs.cornell.edu>, karr@cs.cornell.edu (David Karr) writes:
>Someone suggested that the same person could make the observations
>on consecutive days near a solstice with reasonable accuracy.
>In such a case, it obviously doesn't matter if the observations
>are made at the same time (they can be a day apart) and so it isn't
>even necessary for the two observers to be on exactly the same line of
>longitude.  They'll make their observations a few minutes apart since
>each goes according to local noon, but the difference will be wiped
>out by other errors of measurement.

True.  The important thing is to know how much further north one observation
point is than the other.  
--------------------------------------------------------------------------------
Carl J Lydick | INTERnet: CARL@SOL1.GPS.CALTECH.EDU | NSI/HEPnet: SOL1::CARL

Disclaimer:  Hey, I understand VAXen and VMS.  That's what I get paid for.  My
understanding of astronomy is purely at the amateur level (or below).  So
unless what I'm saying is directly related to VAX/VMS, don't hold me or my
organization responsible for it.  If it IS related to VAX/VMS, you can try to
hold me responsible for it, but my organization had nothing to do with it.
From: gisle@ifi.uio.no (Gisle Hannemyr)
Subject: Re: jabberwocky wanted
Organization: gisle@ifi.uio.no
Date: Thu, 8 Oct 1992 01:32:19 GMT
Originator: gisle@drott.ifi.uio.no

> 	Tjatterskott
> 
> Det bryning var, och slimiga tovar
> i styckern gyrade och norrade.
> Sma:ndiga var alla borogovar,
> och vilna rator skrorrade.
> 
> (Norway)
  NOT!
> 
> 	Jabberwocky
> 
> En slidig oedling borvlade
> i bryningen pa solvis ples.
> Och lumpingen var brynklig, och
> den villa grutten fnes.
> 
> (Sweden)

Both these are definetively Swedish.  It is interesting to note that
while these two translations only share a single similar major word
("vilna"/"villa" in the last line) they are easily recognizable as
"nonsense" Swedish, and they are just as easy to recognize as
translations of the same stanza of the poem (the first).

--
Disclaimer: THESE ARE MY OPINIONS!  MINE!  MINE!  ALL MINE!
 
- gisle hannemyr  (Norsk Regnesentral)
  OSI:   C=no;PRMD=uninett;O=nr;S=Hannemyr;G=Gisle (X.400 SA format)
         gisle.hannemyr@nr.no                      (RFC-822  format)
  Inet:  gisle@ifi.uio.no
  UUCP:  ...!mcsun!ifi!gisle
------------------------------------------------

Newsgroups: rec.puzzles,sci.math
From: tao@fine.princeton.edu (Terry Tao)
Subject: Re: math puzzle
Organization: Princeton University
Distribution: usa
Date: Thu, 15 Oct 1992 01:11:24 GMT

No, you can't do it.  All the constraints are convex, i.e. if
(x_1, x_2, ..., x_n) is a solution of the constraint, as is   
(y_1, y_2, ..., y_n), then so is any solution of the form 
\alpha x + (1-\alpha) y, where x and y are the two vectors shown above.
The desired result though, is not a convex constraint.  e.g. the vectors
(0, 1) and (1, -1) satisfy the constraint, but their average (0.5, 0)
doesnt.  Hence: impossible unless n = 1.

Terry

Newsgroups: rec.puzzles
From: baljeual@uther.calvin.edu (Alan Baljeu)
Subject: What's the answer to this ough problem?
Organization: Calvin College
Date: Thu, 8 Oct 1992 23:33:43 GMT

ough

A long time ago in a spelling book, I learned that there are 4 different
ways to pronounce the above 4 letter sequence, depending on the word that 
contains it.  However, that is wrong.  What's the real answer anyone?

(Bonus points if you get the answer without dictionaries or other helps)
Please exhibit words that match.
From: pinto@neurocog.lrdc.pitt.edu (David Pinto)
Newsgroups: rec.puzzles
Subject: Re: Packing problem
Date: 9 Oct 92 16:37:06 GMT

In article <67423@cup.portal.com>, ISW@cup.portal.com (Isaac S Wingfield) writes:
|> In article <1992Oct6.020647.4651@ils.nwu.edu> blum@news.ils.nwu.edu 
|> (Daniel Blu
|> m) writes:
|> >A few years ago, this puzzle appeared in the newsletter of the company
|> >I was working for:
|> >
|> >   Given an infinitely long rectangular strip which is two units wide,
|> >and circles with diameters of one unit, one can pack them in parallel
|> >rows of two, like so:
|> >                      _____________________________
|> >                      |oooooooooooooooooooooooooooo...
|> >                      |oooooooooooooooooooooooooooo...
|> >                      -----------------------------
|> >However, there is a more efficient packing.  What is it?
|> 
|> If the strip is *infinitely long*, as stated, no alternate packing strategy 
|> is more efficient, in the sense that it would allow more circles to be fit 
|> into it...
|> 
|> Isaac   isw@cup.portal.com

In fact, one can get a more efficient packing in terms of number of circles
per unit length (i.e. packing density).

Without too much analysis, it seems one way to do this is to pack the circles
in 'egg crate' fashion

---------------------------------
|o o o o o o o o o o o o o o o o
| o o o o o o o o o o o o o o o 
---------------------------------
(visualize it more compact, of course)

In this case, each circle would share a section of tube with two others.
The only wasted space would be in the beginning bottom section (not at
the open end since it is infinite).

Someone else can compute the packing densities to make sure it is greater
Newsgroups: rec.puzzles
From: sethb@fid.morgan.com (Seth Breidbart)
Subject: Re: Packing problem
Organization: my opinions only
Date: Fri, 9 Oct 1992 22:12:45 GMT

In article <6OCT199210284778@pearl.tufts.edu> lsonko@pearl.tufts.edu
(FLOCCINAUCHINIHILIPIPIFICATION- LOOK IT UP) writes:

>but let me give another question in reply to yours!
>
>a freighter was to carry a shipment of ball bearings to a bicycle plant down
>the river.  The captain of the ship noted the volume of his hold and the
>density of steel (what the bearings were made of, of course).  He then told the
>guy loading the ship to only fill the ship three quarters full, lest the ship
>sink under the weight of the bearings.  The loader thought about this for a
>moment and told the captain not to worry.  Despite the captain's objections, he
>loaded the holds to their maximums. Low and behold, the ship did not sink and
>everyone lived happily ever after (especially the captain who moved more
>bearings than he expected, making a large bonus).
>
>What did the loader know?

The loader knew that the captain only moved as many bearings as he
expected, so there was no large bonus.

Seth		sethb@fid.morgan.com
From: drothar@ucscb.UCSC.EDU (The Omniscient)
Newsgroups: rec.puzzles
Subject: Re: blue eyes, brown eyes revisited.
Date: 16 Oct 1992 20:55:52 GMT
Organization: University of California; Santa Cruz
NNTP-Posting-Host: ucscb.ucsc.edu


I hate to seem pathetically naive, but could someone state the original problem
to me so I have a slightly clearer idea of what's going on?  :)
Newsgroups: rec.puzzles
From: karr@cs.cornell.edu (David Karr)
Subject: Re: Chess problem 2
Keywords: queens checkmate
Organization: Cornell Univ. CS Dept, Ithaca NY 14853
Date: Fri, 9 Oct 1992 18:13:16 GMT

In article <1992Oct9.105518.20766@news.cs.indiana.edu> "matthew drew" <mdrew@loanshark.cs.indiana.edu> writes:
>baljeual@uther.calvin.edu (Alan Baljeu) writes
>> Ok, What's the most queens you can have without causing checkmate.
>> Give a position with n queens (n is huge) so that you can place 
>> a lone king somewhere on the board where he won't be in checkmate.
>
>The obvious solution is to put the king in a corner and leave that
>row, column, and diagonal bereft of queens.  The other 42 squares
>can have queens that don't threaten our poor hopelessly outnumbered
>hero.

Rather than putting the king in the corner, put the 42 queens as you
described, put a 43rd queen in the corner, and put the king next to
the 43rd queen.  The king is in (multiple) check but not checkmate,
for on the next move the king takes the 43rd queen to move out of
check.

That gives 43 queens for an 8x8 board, in general n^2 - 3n + 3 queens
for an nxn board.

-- David Karr (karr@cs.cornell.edu)



Newsgroups: rec.puzzles
From: blum@news.ils.nwu.edu (Daniel Blum)
Subject: Re: PACKING DENSITY
Organization: The Institute for the Learning Sciences
X-Newsreader: Tin 1.1 PL5
Date: Fri, 9 Oct 1992 20:13:35 GMT

Remember, you have to take into account the ENTIRE WIDTH OF THE STRIP.
I agree, this IS a more efficient packing in general, but NOT within
the confines of the strip (unless you're explaining it wrong).  As I
said, the other solution that has been posted (by 2 people) looks
correct.
							Dan Blum
							blum@ils.nwu.edu






Newsgroups: rec.puzzles
From: bhayes@Xenon.Stanford.EDU (Barry Hayes)
Subject: Re: Height of a building
Organization: Computer Science Department, Stanford University.
Date: Thu, 8 Oct 1992 21:30:53 GMT

In article <1992Oct7.192415.217922@ns1.cc.lehigh.edu> dsbb@ns1.cc.lehigh.edu (D. SPENCER BEECHER) writes:
>How would you accurately measure the height of a ten or twelve
>story building?
>
>Tools at your disposal include [...]

The problem doesn't state that you are limited to these tools, just
that the tools at your disposal include these.  I would just take my
Acme Building Height Measurer and point it at the building.  QED.
From: dwr2560@zeus.tamu.edu (RING, DAVID WAYNE)
Newsgroups: rec.puzzles
Subject: Re: TRAPPED BUBBLE
Date: 14 Oct 92 16:59:00 GMT
Article-I.D.: zeus.14OCT199211594117
Organization: Texas A&M University, Academic Computing Services
News-Software: VAX/VMS VNEWS 1.41

tjgerman@53iss6.Waterloo.NCR.COM (Trevor German) writes...
>		Take a cylinder of _incompressible_ fluid. Attach a
>	balloon to the lid of the cylinder and seal the cylinder
>	with the lid such that there is no air trapped within.
>		Now flip the cylinder upside down.
>		The question is, what happens to the baloon. Does it
>	get bigger or smaller. What happens to the pressure in the 
>	baloon, does it change. What are the thermal effects if any.

From your next post I think you mean for the balloon to be filled with
air, sealed, and taped to the inside of the lid. If this is the case
then the balloon's volume cannot change when the cylinder is flipped.
So the pressure does not change, and the temp does not change.

This answer is valid until the cylinder is long enough that the pressure
in the balloon can no longer support the weight of the water. In that
case a vacuum will form at the top (bottom?) of the cylinder, and the
balloon will compress until its pressure is enough.

>		As a corolorary what would happen if the situation
>	was reversed and the baloon was stuck to the bottom before
>	the fluid was added, the tube sealed, and inverted.

Then the first answer is always valid.

Dave Ring
dwr2560@zeus.tamu.edu
Newsgroups: rec.puzzles
From: cooper@cbnewsg.cb.att.com (Ralph 'Hairy' Moonen)
Subject: Re: What's the answer to this ough problem? (SPOILER)
Organization: AT&T
Date: Fri, 9 Oct 1992 08:33:58 GMT

In article <baljeual.718587223@uther>, baljeual@uther.calvin.edu (Alan Baljeu) writes:
> ough
> 
> A long time ago in a spelling book, I learned that there are 4 different
> ways to pronounce the above 4 letter sequence, depending on the word that 
> contains it.  However, that is wrong.  What's the real answer anyone?
> 
> (Bonus points if you get the answer without dictionaries or other helps)
> Please exhibit words that match.

cough
tough
thorough
bough
though
through
thought

That's 7 already!, I know there's at least 1 more, but I can't think of it 
now.

--Ralph
Xref: sparky rec.puzzles:6660 rec.puzzles.crosswords:686
From: clong@remus.rutgers.edu (Chris Long)
Newsgroups: rec.puzzles,rec.puzzles.crosswords
Subject: 7C and 9C Available?
Date: 7 Oct 92 16:52:04 GMT
Followup-To: rec.puzzles
Organization: Rutgers Univ., New Brunswick, N.J.


I know that the complete 7C was available at some point, so someone
*must* have it, and I'd really like a copy of it (or at least the list
of words that appear in it).  I also have reason to believe that
9C is available, and it would be really great if someone had a list
of the words from there.  I have quite a few other lists myself,
and I'd be more than happy to trade or simply pay expenses.  These
list would only be used for logological research, e.g. constructing
word squares, and not for any commercial purpose.

I've also been looking for the complete Levine Webster's 2nd
International wordlist forever, despite a standing offer of $500 for
it or for the complete 3rd International.  Any clues?
-- 
Chris Long, 265 Old York Rd., Bridgewater, NJ  08807-2618
Newsgroups: rec.puzzles
From: myrberger@elmer.e.kth.se (Johan Myrberger)
Subject: PS-file on Square-1?
Reply-To: myrberger@elmer.e.kth.se (Johan Myrberger)
Organization: School of EE, Royal Institute of Technolgy
Date: Thu, 15 Oct 1992 16:13:05 GMT

A while ago someone posted a PostScript file showing how
to get the Square-1 into the cubic shape.

Is there someone out there who can MAIL me a copy of it
since I lost it?

Thanks 

Johan Myrberger

MAIL: myrberger@elmer.e.kth.se
From: tjgerman@53iss6.Waterloo.NCR.COM (Trevor German)
Newsgroups: rec.puzzles
Subject: TRAPPED BUBBLE (STILL NO RIGHT ANSWER)
Date: 16 Oct 92 12:46:17 GMT
Organization: Imaging Systems Division, NCR Corp, Waterloo, Ont., CANADA


	----------------------------------------------------


	OK so far NO right answers to the puzzle on the board.
	(I did get one mailed to me though). It appears that
	some of you thought the cylinder was open at the end
	and the balloon was attached open ended over the mouth
	at one end. Not.

		The cylinder is closed at one end and capped
	at the other. The baloon is a closed baloon containing
	air at 1 atmos + rubber pressure (The initial pressure  in the
	baloon does not make much difference). Actually in the
	original version of this the baloon was only a bubble
	stuck to the bottom but there were so many questions
	as to how to "stick" a bubble to the bottom that I
	changed it to baloon to save the traffic.

	The fluid is assumed to be a perfect incompressible fluid
	in that it neither expands not contracts under the influence
	of pressure. 

	The walls of the cylinder are very strong and will not deform
	at the pressures in the puzzle.

	So restated the puzzle goes like this.

	------------------------------------------------------------

		Take a cylinder closed at one end filled
	with a perfect _incompressible_ fluid. Attach a 
	balloon filled with air and tied 
	inside the lid of the cylinder and seal the cylinder
	with the lid such that there is no extra air trapped within.
	

		Now flip the cylinder upside down.

		The question is, what happens to the baloon. Does it
	get bigger or smaller. What happens to the pressure in the 
	baloon, does it change. What are the thermal effects if any.
	


		As a corolorary what would happen if the situation
	was reversed and the baloon was stuck INSIDE the bottom before
	the fluid was added, the tube sealed, and inverted.

		You may, for the purpose of discussion ignore atmosheric
	effects.

		The solution to the first case is relatively simple
	the second case is less expected.
	------------------------------------------------------------
--
       >|  "Only average people            | Trevor J German BSc    |<
       >|        never make mistakes."     | NCR, Waterloo, Ontario |<
       >| tjgerman@53iss6.Waterloo.NCR.COM | Canada.                |<
From: carl@SOL1.GPS.CALTECH.EDU (Carl J Lydick)
Newsgroups: rec.puzzles
Subject: Re: TRAPPED BUBBLE
Date: 14 Oct 1992 18:04:28 GMT
Organization: HST Wide Field/Planetary Camera
Reply-To: carl@SOL1.GPS.CALTECH.EDU
NNTP-Posting-Host: sol1.gps.caltech.edu

In article <1992Oct14.161505.5533@alw.nih.gov>, singley@helix.nih.gov (Erick Singley) writes:
=>> The question is, what happens to the baloon. Does it
=>>       get bigger or smaller. What happens to the pressure in the
=>>       baloon, does it change. What are the thermal effects if any.
=
=>The balloon remains the same size.  Since the volume of the fluid filling the
=>rest of the cylinder can't change, and the volume of the cylinder is fixed, the
=>volume of the balloon can't change either.
=
=Well, consider a glass cylinder of Hg (like a thermometer) attatch a baloon
=to the end, turn it upside down and you'll have a vaccum. Said incompressable
=[Hg is the lowest I could fing in the CRC) will flow into the balloon untill the
=weight of the liquid is support by the strength of the vaccum above it (and the 
=pressure of the atmosphere below it probably factors in)
=Yes? No?


True.  My mistake.  Sorry.
--------------------------------------------------------------------------------
Carl J Lydick | INTERnet: CARL@SOL1.GPS.CALTECH.EDU | NSI/HEPnet: SOL1::CARL

Disclaimer:  Hey, I understand VAXen and VMS.  That's what I get paid for.  My
understanding of astronomy is purely at the amateur level (or below).  So
unless what I'm saying is directly related to VAX/VMS, don't hold me or my
organization responsible for it.  If it IS related to VAX/VMS, you can try to
hold me responsible for it, but my organization had nothing to do with it.
From: sjsmith@cs.umd.edu (Stephen Joseph Smith)
Newsgroups: rec.puzzles
Subject: Re: Word ending in 5 Consonants
Date: 8 Oct 92 13:06:25 GMT
Organization: Dept. of Computer Science, University of Maryland at College Park

asimov@wk223.nas.nasa.gov (Daniel A. Asimov) writes:
>I am thinking of a word which ends with 5 consecutive
>consonants (no, none of them is a 'w' or a 'y').
>There is only one vowel in the entire word.
>The word is Scrabble-admissible, and not particularly 
>uncommon.

Ok...


>Another one of its strengths is that this word does not
>appear in this sentence.

Ooh!  Tough!


>Can you think of a word fitting this description?

I can't, but I hear that eleven twelfths of the English-speaking population
of the world can't either...

(Hmm... I had a sudden attack of improper hyphenation...)

- Stephen
Newsgroups: rec.puzzles
From: msb@sq.sq.com (Mark Brader)
Subject: Re: New, obscure number sequence puzzle...
Supersedes: <1992Oct9.184945.8178@sq.sq.com>
Organization: SoftQuad Inc., Toronto, Canada
Date: Fri, 9 Oct 92 19:01:32 GMT

[Replacement for buggy version posted just before; apologies if you see both.]

I wrote:

> 561, 1105, 1729, 2465, ?

These are the first few Carmichael numbers.  For prime numbers X it is
true that, for ALL positive integers i, i%X == (i^X)%X [where the ^ means
exponentiation while == and % have their C meanings].  But this is also
true for a few composite numbers X, and these are called Carmichael numbers.

Small Carmichael numbers are easily found with, say, a C program; you only
have to check values of i from 2 to X-1, and (i^X)%X can be calculated
without use of bignums, most straightforwardly by doing prod = (prod*i)%X
X times.  The next two Carmichael numbers are 2821 and 6601.

Answers, all correct (not surprising, you'd either know it or not),
were received from:

	courtes@ens.ens.fr
	jwr@math.Princeton.EDU
	grabiner@math.harvard.edu
	kubo@math.harvard.edu
	rmurphy@aludra.usc.edu
-- 
Mark Brader, Toronto		"The singular of 'data' is not 'anecdote.'"
utzoo!sq!msb, msb@sq.com				-- Jeff Goldberg

This article is in the public domain.
Newsgroups: rec.puzzles
From: gisle@ifi.uio.no (Gisle Hannemyr)
Subject: Re: Height of a building
Organization: gisle@ifi.uio.no
Date: Thu, 8 Oct 1992 15:46:48 GMT
Originator: gisle@gyda.ifi.uio.no

In article <1992Oct8.151218.10012@ifi.uio.no> dagjo@ifi.uio.no (Dag Espolin Johnson) writes:

> In article <1992Oct7.192415.217922@ns1.cc.lehigh.edu>, dsbb@ns1.cc.lehigh.edu (D. SPENCER BEECHER) writes:
>> How would you accurately measure the height of a ten or twelve
>> story building?
>> 
>> Tools at your disposal include a cigarette lighter, a plastic
>> ruler (12 inches, no metric calibration), a cheap wristwatch
>> (analog, no second hand), five thumb tacks, an altimeter that
>> reads kilometers plus or minus 1%, twelve meters of acrylic
>> plastic tubing (clear, rigid, one half inch diameter) with a
>> rubber stopper for each end, a large green wax marker (jumbo
>> crayon), fourteen empty beer cans (aluminum), three pencils,
>> eight marbles (clear glass, 12.7mm diameter), a thermometer
>> (0-100 degrees C), four feet of string (breaks at 60lbs),
>> twelve sheets of 8 1/2 by 11 inch paper, a pocket knife, and
>> a goldfish in a six inch (diameter) round goldfish bowl.
>> 
>> It is a dark night (no moon), and the solution is required
>> before morning.  Assume everything works for the purpose for
>> which it was designed.  You have access to the building which
>> has lights, running water, and no windows.  You are able to get
>> on the roof or outside the building at ground level with whatever
>> tools are on the list.  There are no lights outside the building.
>> All the stairway doors are locked (you must use the freight elevator).
>> 
>> Accuracy of plus or minus one meter is required.

> This one is realy a long shot, but I try:

>With the altimeter, try to read the preassure of the water at ground level.
>Then do the same on the top floor. Since waterpressure is more sensitive to
>hight than air (ie more heavy) it should make the +-1% error of the altimeter
>to no problem.


An even longer shot:

Put down all the other junk, and take the altimeter, thermometer,
wristwatch, pocket knife, goldfish and bowl to the caretaker of the
building.  Say: "I have here a precision altimeter, an excellent
thermometer, and exclusive wristwatch, a genuine "army style" pocket
knife and a live goldfish in a bowl!  These exquisite items will all
be yours if you can tell me the height of this building!"

--
Disclaimer: THESE ARE MY OPINIONS!  MINE!  MINE!  ALL MINE!
 
- gisle hannemyr  (Norsk Regnesentral)
  OSI:   C=no;PRMD=uninett;O=nr;S=Hannemyr;G=Gisle (X.400 SA format)
         gisle.hannemyr@nr.no                      (RFC-822  format)
  Inet:  gisle@ifi.uio.no
  UUCP:  ...!mcsun!ifi!gisle
------------------------------------------------
From: cb971@cleveland.Freenet.Edu (Marion L. Rappa)
Newsgroups: rec.puzzles
Subject: GRY
Date: 7 Oct 1992 12:08:39 GMT
Organization: Case Western Reserve University, Cleveland, Ohio (USA)
NNTP-Posting-Host: hela.ins.cwru.edu


   Are there more than three words in the English language
that end in gry?
-- 

Muntz Rappa
cb971@cleveland.Freenet.Edu

Newsgroups: rec.puzzles
From: de@cray.com (Duane Eitzen)
Subject: Re: Tell me more?
Organization: Cray Research, Inc.
Date: 9 Oct 92 15:36:59 CDT

In article <1992Oct9.135626.19742@hellgate.utah.edu> tolman%asylum.cs.utah.edu@cs.utah.edu (Kenneth Tolman) writes:
>Two good friends were walking in the woods on a hike, one was a mathematician,
>the other a logician.  The mathematician said, "The sum of the ages of
>my children is 12 years."
>
>The logician replied, "Don't tell me any more, there ages are: ... and ..."
>
>What were the ages 

7 and 4.

>and how did he know?

They're good friends. 

Duane.

P.S. the mathematician can't add very well, can he.