HDTenEightyP/NetNews huggingface dataset:
From: pete@bignode.equinox.gen.nz (Pete Moore)
Subject: Re: Game of pentominos
Newsgroups: sci.math,rec.games.abstract
Followup-To: sci.math,rec.games.abstract
Organization: Equinox Networks
Reply-To: pete@bignode.equinox.gen.nz
X-Newsreader: TIN [version 1.1 PL8]
Date: 17 Dec 92 15:22:28 +1200
Organization: Equinox Networks

Torben AEgidius Mogensen (torbenm@diku.dk) wrote:
>martel@marvin.mr.sintef.no (Paulo Martel) writes:

>>After several tries I gave up a combinatorial analysis of the game of
>>pentominos. Would someone point me to a reference, or briefly explain
>>how one could compute the total number of solutions for a grid of a
>>given size (6x10, 5x12, 4x15, 3x20). 

>I saw a paper once that reported the number of solutions to each of
>these rectangle sizes. It used a heavily optimized machine code
>program to exhaustively search for all solutions. I remember that for
>the 3x20 case there are only two solutions barring reflections and
>rotations. These are quite easy to find by hand. The number of
>solutions for the 6x10 case was quite large, but I don't recall the
>number. I also don't recall the title or author of the paper.

I can't give an authoritative reference, but according to
some notes I made back in my young & innocent days when I used to note
information without references, there are:
     2  3x20 solutions
  2339  6x10 solutions
  1010  5x12 solutions
   368  4x15 solutions

If your pentominoes are 3-dimensional (i.e. each could be constructed by
joining 5 cubes together) rather than 2-dimensional, you can also form a
3x4x5 rectangular prism from the 12 pentominoes. 

--
 +-------------------  pete@bignode.equinox.gen.nz  -------------------+
 | The effort to understand the universe is one of the very few things |
 | that lifts human life above the level of farce, and gives it some   |  
 | of the grace of tragedy   -  Steven Weinberg                        |
 +---------------------------------------------------------------------+
Xref: sparky sci.math:17070 comp.edu:2211 misc.education:5349
Newsgroups: sci.math,comp.edu,misc.education
From: leemike@eecg.toronto.edu (Michael Lee)
Subject: Re: Integration  Was: Re: Student attitudes
Organization: CSRI, University of Toronto
Date: 17 Dec 92 01:51:54 GMT

In article <PCG.92Dec14175129@aberdb.aber.ac.uk> pcg@aber.ac.uk (Piercarlo Grandi) writes:
>On 11 Dec 92 14:23:13 GMT, hrubin@pop.stat.purdue.edu (Herman Rubin) said:
>I am not a mathematician, but I cannot keep my trap shout on this. The
>usual way I explain integrals is:
>
>	Integration is a purely formal exercise in which a formula is
>	transformed into another formula, using particularly odd rules.
>
>	It so happens that the new formula, in several useful and
>	usually simple cases, describes what we intuitively perceive as
>	the area or volume delimited in some way by the first formula,
>	if it seen as describing a geometrical shape.
>
>	That's why the particular transformation called integration has
>	been invented and defined that particular way; but having
>	defined integration in that particular way largely for that
>	purpose, mathematicians found out such definition had many other
>	fairly nonintuitive properties.
>
>Incidentally, I am one of those that think that infinitesimal quantities
>are a bad idea.
>--
>Piercarlo Grandi, Dept of CS, PC/UW@Aberystwyth <pcg@aber.ac.uk>
>  E l'italiano cantava, cantava. E le sue disperate invocazioni giunsero
>  alle orecchie del suo divino protettore, il dio della barzelletta

Why do you think infinitesimal quantities are a bad idea?

Newsgroups: sci.math,rec.games.abstract
From: nates@ll.mit.edu ( Nate Smith)
Subject: Re: Game of pentominos
Organization: MIT Lincoln Laboratory
Date: Wed, 16 Dec 92 21:54:37 GMT

In article <1992Dec16.182611.10896@progress.com> neil@progress.COM (Neil Galarneau) writes:
>>martel@marvin.mr.sintef.no (Paulo Martel) writes:
>>>After several tries I gave up a combinatorial analysis of the game of
>>>pentominos. Would someone point me to a reference, or briefly explain
>>>how one could compute the total number of solutions for a grid of a
>>>given size (6x10, 5x12, 4x15, 3x20). 
>
>Ah... Good old pentominoes.
>Several years ago, motivated by a passage in one of Clarke's novels, several
>of us programmed pentominoes.
>It is not very hard to solve it, it is a lot harder to solve it efficiently.
>The programming was a lot of fun.
>There are about 2100 solutions to the 6x10 case.
>
>Neil
>neil@progress.com

this has about as much to do with the game of pentominoes as the
elaborate solitaire games for the PC has to do with MahJongg....

the game of pentominoes, as described by martin gardner, consists
of the 12 pieces and an 8x8 board.  each of the 2 players takes one
of the unplayed pieces and positions it over 5 unoccupied squares.
the last player to move wins.  martin was impressed with its
complexity.

a LONG time ago, i was given a game called "Pan-Kai".  this is a
variant of the above played with 2 sets of pentominoes in 2
colors on a 10x10 board.  the objective was still the same - make
the last move.  the difference was that now you could make a "box"
in the shape of a piece you still had but your opponent didnt.  this
would give you an extra move at the end.  i played that game quite
a bit as a kid and found it quite intriguing.  i never got to play
the 8x8 version because by the time i found out about it, nobody
wanted to have anything to do with me & my pentominoes.  :-)  :-(

oh well....later i invented my best game, QuintHex, using ideas
from Pan-Kai...there are exactly 12 quintastix, for example.

the sequence 1,1,2,5,12,35,108,....  is still unsolved, i bet.

- nate
Newsgroups: sci.math
From: djoyce@black.clarku.edu (Dave Joyce)
Subject: Re: A word problem
Organization: Clark University (Worcester, MA)
Date: 15 Dec 92 18:36:16 GMT

In <1992Dec12.162349.29729@dcs.qmw.ac.uk> arodgers@dcs.qmw.ac.uk (Angus H Rodgers) writes:

>Are there any finitely generated infinite semigroups in which
>the idempotent law holds?
>
>The "free idempotent semigroup" (if that's the name for it) on
>2 generators has 6 elements. I don't know if the f.i.s. on 3
>generators is infinite, but it's certainly quite big.
>
[Description and comments for problem with an alphabet {a,b,c} deleted]
>
>Is there, nevertheless, a recipe or existence proof for arbitarily
>long reduced words?
>--
>Gus Rodgers,  Dept. of Computer Science, | 
>Queen Mary & Westfield College, Mile End | 
>Road, London, England.   +44 71 975 5241 | 
>E-mail (JANET):   arodgers@dcs.qmw.ac.uk | Post in haste, repent at leisure.

This is a very interesting problem, but I haven't made any progress on it yet.
As the length of the word increases, it looks like the number of reduced words
of that length increases, but ever more slowly (when n=3).

Sometimes the source of a problem helps in solving the problem.  I'd like to
know more about it.

Does anyone know examples of idempotent semigroups (or idempotent monoids)
besides the commutative ones?  (Commutative ones are semilattices and don't
help with this problem.)


-- 
David E. Joyce				Dept. Math. & Comp. Sci.
Internet:  djoyce@black.clarku.edu	Clark University
BITnet:    djoyce@clarku		Worcester, MA 01610-1477
From: vignat@lnp01.jinr.dubna.su
Newsgroups: sci.math
Subject: solve x^2+ax-xa+b=0
Date: Sat, 12 Dec 92 17:29:56 GMT
Distribution: world
Organization: unknown
Reply-To: vignat@lnp01.jinr.dubna.su

Ladies and Gentlemen!
I can say nothing about a simple nonlinear algebraic matrix equation
x^2+ax+xb+c=0
where a, b and c are noncommuting matrices. This equation can be
reduced to the form
x^2+Ax-xA+B=0
with noncommuting matrices A and B.
Can somebody help me with this equation. For what kind of matrices it
can be solved analytically?
I get this equation in dynamical diffraction theory.

Greatly apreciate any help.
-- 
----------------------------------------------------------------------------
Vladimir Ignatovich                      Tel. (09621)6-33-17
Laboratory of Neutron Physics                 (09621)4-70-65
Joint Institute for Nuclear Research     Fax 7(095)-975-23-81
From: koc@rize.ECE.ORST.EDU (Cetin Kaya Koc)
Newsgroups: sci.math
Subject: Re: What is the number
Date: 17 Dec 92 19:46:23 GMT
Article-I.D.: flop.1gqlefINN3e5
Organization: College of Engineering, Oregon State University
NNTP-Posting-Host: rize.ece.orst.edu

>    Whose sum of the factorials of the digits is the number itself
> Two examples come immediately to mind:  1, 145			

145 is correct: 1! + 4! + 5! = 1 + 24 + 120 = 145.
Also 40585 = 4! + 0! + 5! + 8! + 5! = 24 + 1 + 120 + 40320 + 120
                                    = 40585
From: allenk@ugcs.caltech.edu (Allen Knutson)
Newsgroups: sci.math
Subject: Long line headaches (was Re: more math puzzles)
Date: 12 Dec 1992 21:00:39 GMT
Organization: California Institute of Technology, Pasadena
NNTP-Posting-Host: torment.ugcs.caltech.edu

baez@ucrmath.ucr.edu (john baez) writes:

>3)  Prove that the tangent bundle of the long line is nontrivial.
>For extra credit, an obvious spinoff of 3) that I don't know the answer to:
>4)  Classify line bundles over the long line.

John doesn't mention one particularly amusing thing about this question 4.

Over any space, the isomorphism classes line bundles form a group under tensor 
product. A Euclidean line bundle comes with an obvious isomorphism to its
dual (which is its inverse). Over a paracompact space, any line bundle can
be made Euclidean. So this group is exponent 2, over a paracompact space.

But presumably it's a more interesting group in this case, the long line
not being paracompact. (If I remember right...)			Allen K.
From: koc@rize.ECE.ORST.EDU (Cetin Kaya Koc)
Newsgroups: sci.math
Subject: Apologies ..
Date: 17 Dec 92 19:59:45 GMT
Article-I.D.: flop.1gqm7hINN9u
Organization: College of Engineering, Oregon State University
NNTP-Posting-Host: rize.ece.orst.edu


Due to a newsfeed error, too many messages have been posted.

Cetin Koc

-- NewsGrazer, a NeXTstep(tm) news reader, posting --
M>UQR=&8P7&%N<VE[7&9O;G1T8FQ<9C!<9FUO9&5R;B!#;W5R:65R.WT*7&UA
M<F=L,3(P"EQM87)G<C$R,`I<<&%R9%QT>#$Q-3)<='@R,S`T7'1X,S0U-EQT
M>#0V,#A<='@U-S8P7'1X-CDQ,EQT>#@P-C1<='@Y,C$V7'1X,3`S-CA<='@Q
M,34R,%QF,%QB,%QI,%QU;&YO;F5<9G,R-%QF8S!<8V8P(%P*1'5E('1O(&$@
M;F5W<V9E960@97)R;W(L('1O;R!M86YY(&UE<W-A9V5S(&AA=F4@8F5E;B!P
6;W-T960N7`I<"D-E=&EN($MO8PI]"FYY
`
Newsgroups: sci.math
From: jbw@ponder.csci.unt.edu (WEST JASON BRUCE)
Subject: Descrete Math Questions - [PLEASE READ AND RESPOND]
Organization: University of North Texas, Denton
Date: Mon, 14 Dec 1992 05:24:43 GMT

Well, it's that time of the year - and I have some questions I hope you guys
could help me understand better.  PLEASE RESPOND BY MAIL AS SOON AS YOU CAN.
My final is tomorrow and I have lost my book - ARRRG.


1)  Eisiest way to determine if a Relation is transitive or not.

2)  Using a progression techniques to determine "things into boxes" problems.
ie.  10 choose 3 is the number of ways to put 7 balls in 4 boxes (3 "1"s in
a ten digit number "seperate" the boxes, while the 7 "0"s in the ten digit 
number are the balls in each box).  How do this and keep a certain number of
boxes empty (atleast).

3)  Any explanations of finding equivalence classes is greatly appreciated.
I need a decent explanation.  GOD I NEED MY BOOK.

4)  I'm sure I'll have more as the night progresses.

Thanks a million, in advance.
Any examples problems or anything are greatly appreciated.

Please respond by mail - I'll be checking in about every hour.

Ciao....



                                       - Jay.

Newsgroups: sci.math
From: dennis@cadkey.com (Dennis Paul Himes)
Subject: Re: What is the number
Organization: cadkey
Date: Sat, 19 Dec 1992 19:47:22 GMT

In article <BzFE6H.BCr@mentor.cc.purdue.edu> ags@seaman.cc.purdue.edu (Dave Seaman) writes:
>In article <1gqm29INN9f@flop.ENGR.ORST.EDU> koc@rize.ECE.ORST.EDU (Cetin Kaya Koc) writes:
>>>    Whose sum of the factorials of the digits is the number itself
>>
>>1, 145, 40585
>
>and also 2.
>
     What about 0000000010 ?   :-)

==============================================================================

               Dennis Paul Himes    <>    dennis@cadkey.com
 
"In watermelon sugar the deeds were done and done again as my life is done
in watermelon sugar."           - Richard Brautigan
Newsgroups: sci.math
From: solan@smauguio.no (Svein Olav G. Nyberg)
Subject: The genius of Marilyn Vos Savant
Keywords: savant
Reply-To: solan@smauguio.no (Svein Olav G. Nyberg)
Organization: University of Oslo, Norway
Date: Tue, 15 Dec 1992 21:02:08 GMT

In article <1gj5grINNk05@crcnis1.unl.edu>, burchell@cse.unl.edu (David
Burchell) writes:
|> I ask the net Gods: Can this be correct??
|> 
|> From ``Ask Marilyn'' by Marilyn Vos Savant, Parade magazine, December
|> 13, 1992.
|> 
|> You have a hat in which there are three pancakes.  One is golden on
|> both sides, one is brown on both sides, and one is golden on one side
|> and brown on the other.  You withdraw one pancake and see that one side
|> is brown.  What is the probability that the other side is brown?
|> 
|> ---Robert H. Batts, Acton, Mass.
|> 
|> It's two out of three.  The pancake you withdrew had to be one of only
|> two of them: the brown/golden one or the brown/brown one.  And of the
|> three brown sides you could be seeing, two of them also have brown on
|> the other side.

This is similar to a problem she got a lot of noise for answering:

It is a TV show - a game. There are 3 doors, behind which are 1 car
and 2 goats, respectively. The participant gets to choose one door.
The host then opens one of the two _other_ doors, revealing a goat.
The contestant gets the option: You can change your choice of doors.

Now: Would it pay to change doors?

The answer: Yes. The probability that the car was behind the first
chosen door is just 1/3, while the probability that it is behind
the remaining door is 2/3.

---

This angered a lot of people, even a lot of math PhDs, I am told.
They protested that an arbitrary person coming in instead of the
person just choosing would have equal knowledge about the two doors,
and that they would thereby have equal probability, i.e. 1/2, of
having the car behind.

But it IS true. Probability is partial knowledge _for_a_given_person_.
Thus probabilities are not the same for you and for me. For instance,
if I throw a coin up in the air, let it land in my fist, and peek at
it [and see it is "tails"], the probability that the coin ended tails
up is 100% _for_me_, while it is just 50% _for_you_ who have not seen it.

That is essentially what is the key to understanding Marilyns
answer to the question. The contestant was not just some arbitrary
person, but a person with more knowledge from which to measure the
probability. 


Solan

Newsgroups: sci.math
From: slory@onyx.cuc.ab.ca (stuart lory)
Subject: Please help with INTEGRATION for final exam!
Organization: Wanna be
Date: Sat, 12 Dec 1992 23:36:05 GMT
X-Newsreader: Tin 1.1 PL5

If anyone can help me out I would be very grateful.  I've got a final exam
in calculus on Monday morning and I do not understand how to do a couple of
integration questions.  This is beginners calculus so please explain step
by step how you go about solving the equation and don't assume I know anything.

Question #1:  Evaluate the following definate integral:

           _ 5                                              2
          |                             y                  y 
          |     (a - b) dy      if a = --- + 4   and  b = ---
          |                             6                  9
         _|  0 

		Note:  we currently have been taught methods of substitution
                       so I let u = (a-b) but I don't know how to get du,
		       unless du = 0 because you are taking the derivative of
		       a constant.


Question #2:  Find the equation of a particular curve whose slope is shown
	      by the given equation and it passes through the point x = 1.8
	      and y = -1.048.

                         3        2
		m =  20 x  -  24 x   -  4 x  + 12


		Note: The answer is supposedly the constant of integration.


Any help is greatly appreciated.  Please email replies to slory@onyx.cuc.ab.ca
so I can hopefully understand this before Monday.


+---------------------------------------------------------------+
| Stuart Lory		Internet:	slory@onyx.cuc.ab.ca    |
| Calgary, Alberta	  -or-  :	slory@onyx.cuug.ab.ca   |
| Canada				FAX: (403) 289-1893     |
+---------------------------------------------------------------+
From: israel@unixg.ubc.ca (Robert B. Israel)
Newsgroups: sci.math
Subject: Re: Forcing f(x) to have horizontal asymptote at +infinity
Date: 16 Dec 92 18:01:28 GMT
Organization: The University of British Columbia
NNTP-Posting-Host: unixg.ubc.ca
Keywords: none

In <2317@sjfc.UUCP> dmc@sjfc.UUCP (Cass Dan) writes:


>My question is: what conditions must be imposed on the derivative
>f'(x) of a function f(x) in order to cause it to necessarily have
>a horizontal asymptote as x --> +infinity ?

It's very simple.  The necessary and sufficient condition is that
the improper integral int_a^infinity f'(x) dx converges (for some fixed a).
-- 
Robert Israel                            israel@math.ubc.ca
Department of Mathematics             or israel@unixg.ubc.ca
University of British Columbia
Vancouver, BC, Canada V6T 1Y4
Newsgroups: sci.math
From: jbaez@riesz.mit.edu (John C. Baez)
Subject: Re: another math trivia puzzle - SPOILER
Organization: MIT Department of Mathematics, Cambridge, MA
Date: Mon, 14 Dec 92 18:41:50 GMT

In article <24372@galaxy.ucr.edu> baez@guitar.ucr.edu (john baez) writes:
>Which famous mathematician wrote: "I had graduated from the Ecole Normale
>and I did not know what an ideal was, and only just knew what a group was!
>This gives you an idea of what a young French mathematician knew in 1930."

Two folks have gotten it so far so I might as well give it away:
Dieudonne.   I ran into this quote in an interesting description of the
impact of Emmy Noether's work in a recent issue of L'Enseignement
Mathematique (sorry, forget which).
Newsgroups: sci.math
From: li@sce.carleton.ca (Yao Li)
Subject: math problem
Organization: Indiana University
Date: Fri, 11 Dec 1992 18:51:02 GMT
X-Mailer: ELM [version 2.3 PL11]

                            Math Problem
                            ------------

Getting bored? Here is a math problem.

There is a polynomial:
       -a*y**n + y**(n-1) + y**(n-2) + ... + y + 1 = 0
where real number a>0 and the notation "y**n" represents the nth power of y.

It's conjectured that this polynomial has a unique positive real solution y.

Can you prove it or find a counter example?

If succeed, please send me your solution. I will post the results later.

Happy challenge!

Li Yao
li@sce.carleton.ca
Xref: sparky sci.math:16826 sci.physics:21066 sci.bio:4552 sci.chem:5380 misc.education:5219
From: rickert@cco.caltech.edu (Keith Warren Rickert)
Newsgroups: sci.math,sci.physics,sci.bio,sci.chem,misc.education
Subject: Re: TIME HAS INERTIA - BASS JEALOUS AND INSECURE-ABIAN VALIDATED
Date: 14 Dec 1992 02:51:54 GMT
Organization: California Institute of Technology, Pasadena
NNTP-Posting-Host: sandman.caltech.edu

In <Bz81F4.Lqt@quake.sylmar.ca.us> brian@quake.sylmar.ca.us (Brian K. Yoder) writes:


>I think that before anyone even addresses this incredible claim (that "Time
>Has Inertia") they have to explain how something which is not an entity (time)
>can have properties.  Any definition of time I can think of (even ones I
>very much disagree with) define time as something other than an entity.
>If you claim that your definition of time is something new, that it IS an
>entity, then you need to have some means by which to prove this.  What do you
>think would constitute evidence of this amazing claim?

>A similar problem exists for physicists who consider light to be a wave (or
>a wave and something else too).  Waving is something an entity does, not a
>thing in itself.  There can no more be a wave traveling through space than
>there can be a room with some "jumping" going on outside of any entities which
>are doing the jumping.

>I think these kinds of problems both arise from physicists getting too tied up
>with their equations to remember that they apply to things in the real world.

The ability of light to behave as a wave, and as a particle, have
both been able to lead to concrete predictions about real world experiments,
and provided correct results.
THe ability to predict experimental behaviour correctly is the real
test of a theory, not whether or not it can be visualized.
From: arodgers@dcs.qmw.ac.uk (Angus H Rodgers)
Newsgroups: sci.math
Subject: Re: Negative Zero
Keywords: -0
Date: 19 Dec 92 18:06:01 GMT
Organization: Computer Science Dept, QMW, University of London

In <1992Dec15.174003.203407@uctvax.uct.ac.za>
naturman@uctvax.uct.ac.za writes:

>In article <1992Dec12.010711.15778@leela.cs.orst.edu>, jeremy@atlantis.CS.ORST.EDU ((-| Jeremy |-) Smith) writes:
>> 
>>       Some guy in Southern California proposed a method of naming multiples 
>> of ten which included a `logical' system for naming very large numbers 
>> (the largest being milli-decilli-fiveillionillion).
>> [...]

>All this reminds me of a student I encountered once who had written a program
>to check whether infinity existed. He was incrementing and printing out a
>counter in a continuous loop and sat looking at the screen enthusiastically.
>Shame.

On "The Best of the Worst" (an occasionally slightly amusing American TV
show), they invited into the studio a man with a very, very unusual hobby.
His great aim in life is to count up to 1 billion -- using a printing desk
calculator, by starting at 0.0, and adding 1.0 again and again and ...

He'd been doing this for 10 years. They'd had him on the show 3 years before,
and he'd been such a great hit with the viewers that they invited him back to
see how he was getting on. Sitting at a desk in the studio, surrounded by
buxom lovelies, and by rolls and rolls of calculator paper, he added 1.0, and
added 1.0, and kept on adding 1.0, until (the highlight of the show) his
current total, displayed in bright lights, changed from (I think) 3,539,999
to 3,540,000; whereupon a band struck up a tune and marched through the studio.

It's a good thing he picked a billion. If the number was small enough for
him ever to reach it in this way, I suspect that his life would lose all
meaning.

He had a really nice goofy smile.
--
Gus Rodgers,  Dept. of Computer Science, | 
Queen Mary & Westfield College, Mile End | 
Road, London, England.   +44 71 975 5241 | 
E-mail (JANET):   arodgers@dcs.qmw.ac.uk | Post in haste, repent at leisure.
Newsgroups: sci.math,sci.math.symbolic