HDTenEightyP/NetNews huggingface dataset:
From: bs@gauss.mitre.org (Robert D. Silverman)
Subject: Re: Interesting Discrete Math Question
Organization: Research Computer Facility, MITRE Corporation, Bedford, MA
Date: Tue, 15 Dec 1992 22:11:24 GMT

In article <3548@carroll1.cc.edu> noffke@carroll1.cc.edu (Pat Noffke) writes:
:Here's a question we had on one of our last tests in Discrete.
:
:A jar contains 100 chips numbered 1 through 100.  I want to draw a
:subset of chips that satisfies the condition that at least two chips
:have values that differ by exactly 3.  What is the minimum number of
:chips I must draw to guarantee that I satisfy the condition?  Justify
:your response.
 
You can easily draw 50 without satisfying the condition, e.g.
1,3,5,7,....99

The next one you draw will be at distance 3 from one of these.

--
Bob Silverman
These are my opinions and not MITRE's.
Mitre Corporation, Bedford, MA 01730
"You can lead a horse's ass to knowledge, but you can't make him think"
Newsgroups: sci.math
From: brumleve@gauss (Dan Brumleve)
Subject: Re: Pi in beatiful form --lost
Organization: University of Illinois at Urbana
Date: Wed, 16 Dec 1992 04:12:55 GMT

sbardhan@uncc.edu (Soumendu Bardhan) writes:

>I  hope Mathematicians especially  Pi'ans  could help me remember this beautiful form of pi.
>I  can only faintly remember this beautiful form  invented by Ramanujam
>pi = (1*2)/(3*4) +(5*6)/(6*7)....

>All I remember is that it is very close to this representation ....it involved multiplication of two numbers
>and divsion by two very close numbers .. it was indeed  one of the fascinating forms.

>Thanks
>--bardhan

I'm pretty sure it's this...

4 * (2/1) * (2/3) * (4/3) * (4/5) * (6/5) * (6/7) * ... 

-Dan
From: deghare@daisy.uwaterloo.ca (Dave Hare)
Newsgroups: sci.math
Subject: Re: TO ALL !!!
Date: 19 Dec 92 14:12:42 GMT
Organization: University of Waterloo

In article <1992Dec19.022327.1125@leland.Stanford.EDU> ilan@leland.Stanford.EDU (ilan vardi) writes:
>In article <1gtunkINN3h5@usenet.INS.CWRU.Edu> ak005@cleveland.Freenet.Edu (Yona Webb) writes:
>>
>>*****************************************************************
>>*                                                               *
>>*         *                 M E R R Y                           *
>>*        <^>                                                    *
>>*        ***        CHRISTMAS   &   HANUKKAH                    *
>>*       *****                                        *          *
>>*      *******           HAPPY NEW YEAR      * * * * | * * * *  *
>>*     *********           - 1 9 9 3 -        | | | | | | | | |  *
>>*    ***********                              \|_|_|_|_|_|_|/   *
>>*   *************      May all your dreams     ~~~~~\|/~~~~~    *
>>*  ***************          come true                |          *
>>* *****************                                 _|_         *
>>*        ] [          Best wishes to all - Yona     ~~~         *
>>*****************************************************************
>>-- 
>
>I think I speak for a sizable minority of this secular newsgroup when
>I wonder why you feel the need to wish Jewish people a happy Hanukkah,
>yet failed to do anything for Simcha Torah, Suchot (I don't know how
>to spell these things), or any other myriad holidays that are more
>important to actual Jewish people. Since you are obviously ignorant of

I think I speak for a sizable minority of this newsgroup when I state that
I would like anybody who wants to wish me a nice day to just go to hell.
Not all of us have "nice days" and it is simply damnably insensitive
of all you jerks to suggest that we should have nice days.

In closing, I would say "Have a day", but I know that there are some people
reading this who don't feel up to having a day and I certainly wouldn't want
to risk offending them.  So I will just sign off with: "Whatever".

Dave Hare
Newsgroups: sci.math
From: pisul_cj@glutamic.uwlax.edu (Charles Pisula S92)
Subject: Need help with a constraint problem
Keywords: constraint, minimize area
Organization: University of Wisconsin - La Crosse Computer Science Department
Date: Thu, 10 Dec 1992 18:18:00 GMT

here's the problem that I'm sure will prove to be trivial although 
It's given me a hard time:

Minimize the area inside an elipse of form  x^2        y^2
                                            ---   +    ---   =  1
                                            a^2        b^2
such that it contains the circle x^2 + y^2 = 2y.


HINTS:  Area of Ellipse = (Pi)ab

PLEASE SEND ANY SOLUTIONS TO :
****************************
pisul_cj@cowley.uwlax.edu
****************************

		-THANX-
Newsgroups: sci.math
From: Dave Dodson <dodson@convex.COM>
Subject: Re: Would Pi repeat, were it expressed in a base other than 10?
Originator: dodson@bach.convex.com
Date: Mon, 14 Dec 1992 15:24:39 GMT
Reply-To: dodson@convex.COM (Dave Dodson)
Organization: Engineering, CONVEX Computer Corp., Richardson, Tx., USA
X-Disclaimer: This message was written by a user at CONVEX Computer
              Corp. The opinions expressed are those of the user and
              not necessarily those of CONVEX.

In article <Bz4p1C.DtG@news.cso.uiuc.edu> brumleve@gauss (Dan Brumleve) writes:
>bennett@math.ksu.edu (Andy Bennett) writes:
>
>>werdna@cco.caltech.edu (Andrew Tong) writes:
>>:Intuitively (not saying much, that is), I'd say yes, but that it would re-
>>:quire a transcendental base....
>
>>Of course, pi to the base pi is 1.000000000....
>
>>:-)
>
>
>Not to nitpick, but it's 10.00000.... ;-)

Combining this with a previously-beaten-to-death result, we see that
pi to the base pi is 9.999... .

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

Dave Dodson		                             dodson@convex.COM
Convex Computer Corporation      Richardson, Texas      (214) 497-4234
Newsgroups: sci.math,misc.education
From: prener@watson.ibm.com (Dan Prener)
Subject: Re: The Continuum Hypothesis:  Must it be {True or False}, or Not?
Date: Tue, 15 Dec 1992 06:47:02 GMT
Distribution: usa
Disclaimer: This posting represents the poster's views, not necessarily those of IBM
	<1992Dec14.200024.6435@nas.nasa.gov>
Organization: IBM T.J. Watson Research Center, Hawthorne, New York

In article <1992Dec14.200024.6435@nas.nasa.gov> asimov@wk223.nas.nasa.gov (Daniel A. Asimov) writes:

  [ ... citations, occasionally three deep ... ]

> I don't think I succeeded in conveying my question clearly in this case.

> Let me ask a similar question in perhaps a simpler setting:

>	ASSUME that Fermat's Last Theorem is undecidable from the 
> 	usual axioms of arithmetic. 

> 	Then there is a meta-argument which can now conclude that FLT is in fact
> 	true.  For if it were false, then there must exist a counterexample.
> 	Now simply doing the arithmetic to show that the counterexample
> 	really is one, constitutes a disproof of FLT, contradicting undecidability.  
> 	Therefore, undecidability implies that FLT cannot be false, so it is true.

> 	Do people buy this, that FLT must be {true or false}, regardless of
> 	whether it is provably true or false (i.e., decidable)?

Of course I buy it.  And your argument has nothing to do with the meaning
of FLT; it depends only on the logical form.  Thus it applies to any statement
of the form 

        It is false that ( there exist integers a_1, a_2, ..., a_n such that
                             ( P(a_1, a_2, ..., a_n) ) )

But, to avoid leading people into a common fallacy, one must repeat in every
such discussion, as you have done, that this notion of truth is not the same
as the notion of provability that is the stuff with which formal mathematics
deals.
--
                                   Dan Prener (prener@watson.ibm.com)
From: burchell@cse.unl.edu (David Burchell)
Newsgroups: sci.math
Subject: Marilyn Vos Savant's error?
Date: 14 Dec 1992 23:31:39 GMT
Organization: University of Nebraska--Lincoln	
Distribution: world
NNTP-Posting-Host: cse.unl.edu
Keywords: savant

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.
--
Dave Burchell                   |
burchell@cse.unl.edu            |        Review your options.
djburche@jwendnelnc.cr.usgs.gov |              Amiga. 
Newsgroups: sci.math
From: sbardhan@uncc.edu (Soumendu Bardhan)
Subject: Re: Interesting Discrete Math Question
Reply-To: sbardhan@uncc.edu
Organization: University of NC at Charlotte
Date: Wed, 16 Dec 1992 00:09:28 GMT

Here is  my try:( may sound dumb to you !)
To find the minimum number of chips, first we have to find the maximum number of possible chips 
which will not contain that pair;
If we can  select numbers like the following ---

1 2 3, 7 8 9, 13 14 15, .....   91 92 93,  97 98 99 
-----  -----   --------         --------    -------

the maximum number of numbers  such that no two chips have difference of 3 is 51. 
So, if we include any other chip to this group it will have a number in this group which satisfies our condition
Hence, the minimum number to be drawn is 52.
---bardhan
Newsgroups: sci.math
From: abian@iastate.edu (Alexander Abian)
Subject: Re: TIME HAS INERTIA - ABIAN REPLIES TO SOME QUESTIONS OF BOUCHER
Organization: Iowa State University, Ames, IA
Date: Mon, 14 Dec 1992 02:54:19 GMT

                              

In article <2235@newsserver.cs.uwindsor.ca> bouche2@server.uwindsor.ca (BOUCHER DAVID            ) writes:
>In article <abian.724200923@pv343f.vincent.iastate.edu> abian@iastate.edu (Alexander Abian) writes:
>  
>>(A2)   TIME HAS INERTIA (i.e. TIME IS MATTER)  AND SOME ENERGY IS 
>>       IRRETRIEVABLY DISSIPATEED TO MOVE TIME FORWARD
>>
>>AND NONE OF THE  existing theories is capable to explain the puzzling
>>loss of energy and that (A2) revolutionized both GR and QM

Dear Mr. Boucher                   12-13-92
  
For the lack of time, 	 will answer  only some of your questions:

>2. Since time IS moving forward and has been moving forward since the Big
>   Bang, how can there be any "dissipation of energy" to keep it moving?  
>   "A body in motion tends to remain in motion unless acted upon by some
>   external force"... that is inertia.
>

     	 I do not believe in the abovementioned Newton's Law.
         Any motion consumes energy - maybe extremely minute
         in some cases.






>6. Have you published this theory in any scientific journal subject to peer
   review?  If so, where?  If not, why not?

     The peer review banned Copernicus' writings for  70 years

     and

      
     The peer review sent Galileo to house arrest  and ex-communicated
     him for 300  years.
    
    Best regards,                       Alexander Abian




-- 
   The tendency of maintaining the status-quo, Reaction to provocation and
                The tendency of maintaining again a status-quo.  
    TIME HAS INERTIA  and some energy is lost to move Time forward  
  E = mcc  (Einstein)    must be replaced by    E = m(0) exp(-At) (Abian)
Xref: sparky sci.math:17183 rec.games.abstract:652
From: rcbaaw@rw6.urc.tue.nl (Angelo Wentzler)
Newsgroups: sci.math,rec.games.abstract
Subject: Re: Game of pentominos
Date: 18 Dec 92 15:24:24 GMT
Reply-To: rcbaaw@urc.tue.nl
Followup-To: sci.math

pete@bignode.equinox.gen.nz (Pete Moore) writes:

>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. 

Gee, this must be my lucky month! I like pentominoes, wrote a program
once (who didn't) and I rank them right up there along with life,
rubik's cube and tiled squares (See: tiling problem in this group :-)


C.J.Bouwkamp, a professor here at the TUE has computed all solutions
to this prism as well as to "the steps" which is a three dimensional
staircase. He's just as mad about pentominoes as I am.

The catalogues are:

"Catalogue of solutions to the rectangular 3x4x5 pentomino problem"
C.J.Bouwkamp, Eindhoven University of Technology.

"Packing the steps with solid pentominoes"
C.J.Bouwkamp, Eindhoven University of Technology.

The books are available here, but not in "computerised" format.


By the way, has anybody ever tried to write a program to compute all
(N+1)-ominoes from the set of N-ominoes? It's not difficult:
Just take one N-omino at a time and fit an extra square onto it. This
produces one extra (N+1)-omino. Fit a square on all possible positions,
(just "roll" it along the edge) then proceed with the next N-omino.
This leaves you with a *bag* of (N+1)-ominoes, of which you now have to
make a *set* (remove multiple copies).
It would be smart to check for multiples right at the start though...

It would take a lot of computation, but not an awful lot of time.

Angelo Wentzler
Newsgroups: sci.math,sci.physics,sci.bio,sci.chem,misc.education
From: dennis@cadkey.com (Dennis Paul Himes)
Subject: Re: The Continuum Hypothesis:  Must it be {True or False}, or Not?
Organization: cadkey
Distribution: usa
Date: Fri, 11 Dec 1992 16:22:39 GMT

In article <1992Dec9.183849.13004@nas.nasa.gov> asimov@wk223.nas.nasa.gov (Daniel A. Asimov) writes:
>Among those of you who are familiar with the statement of the
>Continuum Hypothesis, and the fact that it was proved to be
>independent of ZF + AC, I would like to know:
>
>Do you see the Truth or Falsity of the Continuum Hypothesis as 
>being exclusively dependent on a whether it can be proved or 
>disproved in some specific axiom system?
>
>Or rather, do you see the Continuum Hypothesis as being 
>{True or False}, in some sense independent of whether or 
>not it is decidable in any given axiom system?
>

	Truth is a relative term, although it is usually treated as absolute,
since when discussing the nature of reality it is relative to the universe.
When discussing mathematical hypotheses, however, it is relative to the
theory (axiom system) at hand.  We often speak of mathematical hypotheses as
being true or false as if those were absolute terms, but that is really a
shortcut used when the theory at hand is obvious (or when the hypothesis is
true in any of the more popular theories).
	On the other hand, theories become popular because they have models
which are useful in describing the universe.  Natural numbers and real
numbers are studied so extensively because they are useful when analysing
groups of objects and distances, among other things.  So it is a legitimate
question whether ZF + AC + CH or ZF + AC + ~CH is more useful when
describing physical phenomena, and if you answer that question you can say
whether CH is "true" in a very loose use of the term.  I personally have no
idea how you would go about answering that question.

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

               Dennis Paul Himes    <>    dennis@cadkey.com
 
... said the Cat: "we're all mad here.  I'm mad.  You're mad."
"How do you know I'm mad?" said Alice.
"You must be," said the Cat, "or you wouldn't have come here." - Lewis Carroll
From: mbeattie@black.ox.ac.uk (Malcolm Beattie)
Newsgroups: sci.math
Subject: Re: '-' operation
Date: 16 Dec 92 16:07:54 GMT
Organization: Oxford University Computing Service, 13 Banbury Rd, Oxford, U
Originator: mbeattie@black

In article <92350.145501B7D@psuvm.psu.edu> B7D@psuvm.psu.edu writes:
>Recently my daughter brought back Problem Set II of Wisconsin Mathematics
>Science and Engineering Talent Search, and Question 4 in it is as following:
>         Operation @ satisfies the conditions that
>                X @ (Y @ Z) = X @ Y + Z and X @ X = 0 for any real numbers
>          X, Y, Z. Show that @ must be subtraction.
>
>   Since my daughter does not care much whether she has talent so I tried to
> solve it myself:-). It took me more than an hour but still I am not sure I get
> a right answer. The problem I have is: How is operation '-' defined? How about
> other operations like '+', '*', and '/'? Although I do not have Ph.D
> in math but I consider myself one of the best in learning math in those
> math classes. It is sort of ashameful that I never learned or remember
> how the basic operation is defined. For the above question, is only
> thing I have to prove is X @ 0 = X?, which is not very difficult because
> X @ 0 = X @ (X @ X) = X @ X + X = 0 + X = X.
>
> I hope no one will blame me for bringing 'homework' to the net or trying
> to be 'talent' since the deadline was passed and it is already too late
> to send the answer in for that purpose:-). I just like to know what you
> have to do to say some operation MUST be one of the basic operations.
>
> Duane

Just show that x - y = x @ y for all x, y \in R.
Your conditions are that, for all reals x, y:
(1)   x @ (y @ z) = x @ y + z
(2)   x @ x = 0
Notice that x @ y + z brackets means (x @ y) + z
or else the question is wrong.
Take x,y \in R.
(x @ y) + y = x @ (y @ y)          by (1)
            = x @ (x @ x)          since y @ y = 0 = x @ x by (2)
            = (x @ x) + x          by (1)
            = x                    since x @ x = 0
Subtract y from both sides for your result.

--Malcolm
-- 
Malcolm Beattie <mbeattie@black.ox.ac.uk> | I'm not a kernel hacker
Oxford University Computing Services      | I'm a kernel hacker's mate
13 Banbury Road, Oxford, OX2 6NN (U.K.)   | And I'm only hacking kernels
Tel: +44 865 273232 Fax: +44 865 273275   | 'Cos the kernel hacker's late
Newsgroups: sci.math,rec.puzzles
From: k044477@hobbes.kzoo.edu (Jamie R. McCarthy)
Subject: Re: Naming Large Numbers (Re: Negative Zero)
Followup-To: poster
Organization: Kalamazoo College
Date: Fri, 18 Dec 1992 21:20:04 GMT

wilcox@vax.oxford.ac.uk writes:
>k044477@hobbes.kzoo.edu (Jamie R. McCarthy) writes:
>> I submit that one cannot write down, in scientific notation, the number
>> x, such that [blah blah blah]...
>
>Practically speaking, one cannot. Theoretically speaking, one can.

Because it's so trivial to write the number down in theory (you just
pull out your theoretical pencil and write down all 10^126 digits), I
didn't feel it necessary to point out that I was speaking of "writing"
in the practical, rather than the ideal, sense.

The original article asserted that there was no rational number that
could not be "written" using standard symbols.  Since this is so
trivially true if "write" is used in the ideal sense, I assumed the
assertion intended the practical sense.
-- 
 Jamie McCarthy      Internet: k044477@kzoo.edu      AppleLink: j.mccarthy
 "As you should know by now, we're strong believers in the Apple II
  and always will be.  But we can't ignore reality forever."
    - Tom Weishaar
Xref: sparky sci.math:16962 sci.philosophy.tech:4569
From: arodgers@dcs.qmw.ac.uk (Angus H Rodgers)
Newsgroups: sci.math,sci.philosophy.tech
Subject: Re: Numbers and sets
Date: 15 Dec 92 18:11:58 GMT
Organization: Computer Science Dept, QMW, University of London

>>>>>>>>Is the cardinal interpretation or the ordinal interpretation more 
>>>>>>>>"natural"?  Which can be more easily understood?  Which is more 
>>>>>>>>suitable to the appropriate extensions?  These questions are non-
>>>>>>>>trivial.

How many `>' signs are there in that set? (This question is non-trivial.) :-)
--
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
From: bs@gauss.mitre.org (Robert D. Silverman)
Subject: Re: Peculiar limit?
Organization: Research Computer Facility, MITRE Corporation, Bedford, MA
Date: Thu, 17 Dec 1992 21:27:25 GMT

In article <1992Dec17.202531.20920@infonode.ingr.com> tdj@infonode.ingr.com (Ted Johnson) writes:
:Is the following true?
:
:                  g        g                        g        g      
:             (1/b)  - (1/a)                    (1/b)  - (1/a)       
:   lim      ------------------   =   lim      ------------------    
:   g->+inf.       g        g         g->-inf.       g        g      
:             (1/c)  - (1/a)                    (1/c)  - (1/a)       
:
:
:                          ln(1/b) - ln(1/a)
:                        = -----------------
:                          ln(1/c) - ln(1/a)
:
 
Unless I've made a mistake somewhere, this is wrong.

Take the original expression and multiply it by 1 in the form a^g/a^g.

This yields         (a/b)^g - 1
		    -----------
		    (a/c)^g - 1

If a = b this is 0. If a < b  and a < c, then both the numerator
and denominator go to -1  as g --> infinity. Thus, the limit is -1.
[note that since (a/b) < 1, that (a/b)^g goes to zero. ditto for (a/c)]

:If necessary:
:       0 < a <= b <= c <= 1;
 
As is easily seen, if a = b the limit is 0, unless a = c as well,
but you stated a < c.

--
Bob Silverman
These are my opinions and not MITRE's.
Mitre Corporation, Bedford, MA 01730
"You can lead a horse's ass to knowledge, but you can't make him think"
Newsgroups: sci.math
From: jimgar@scorch.apana.org.au (Jim Garner)
Subject: Re: Master Mind:A question.
Organization: Craggenmoore public Unix system , Newcastle , Oz
Date: Sun, 13 Dec 1992 22:15:51 GMT
Keywords: Master Mind Game

evant@coos.dartmouth.edu (Evan E. Thomas) writes:

|My question regards the game "MasterMind" where 4 pegs are chosen (from an
[deletions]
|You would be told that 1 color is exactly right and that two others are in
|the solution.  You have exactly 10 guesses to find the solution.  Is there
|an algorithm that will insure victory?

There is an optimal strategy that has been published. It is very long
and divided into cases, so I wouldn't call it an algorithm. But it
certainly can be done in less than 10 guesses every time. All I
remember is that your first guess should contain 2 colours only, 2
pegs of each.

-- 
Jim Garner - jimgar@scorch.apana.org.au

Xref: sparky sci.math:16810 sci.philosophy.tech:4556
From: goddard@NeXTwork.Rose-Hulman.Edu (Bart E. Goddard)
Newsgroups: sci.math
Subject: Re: Philosophy of Pi
Date: 11 Dec 1992 17:53:22 GMT
Organization: Computer Science Department at Rose-Hulman
Reply-To: goddard@NeXTwork.Rose-Hulman.Edu (Bart E. Goddard)
NNTP-Posting-Host: g214-1.nextwork.rose-hulman.edu

In article <1992Dec11.155846.10861@ee.ubc.ca> bdow@ee.ubc.ca (DOW BRUCE PAUL)  
writes:
> I'm looking for some opinions on Pi. 
> [...]
> Just wondering if any net.philosophers out there have any observations...
> 
> Bruce

Actually, I count by Pi's, so I have trouble dealing with integers, even
though they seem to pop up everywhere.  My banker insists on being  
closed-minded and intolerant about all this, but it's my numerical  
orientation:-)

bart