HDTenEightyP/NetNews huggingface dataset:
From: cliff@watson.ibm.com (cliff)
Subject:  Cliff Puzzle 18: Difficult Nested Roots
Date: Wed, 11 Nov 1992 22:17:49 GMT
Disclaimer: This posting represents the poster's views, not necessarily those of IBM
Organization: A

Title: Cliff Puzzle 18: Difficult Nested Roots                                  
From: cliff@watson.ibm.com                                                      
                                                                                
If you respond to this puzzle, if possible please send me your name,            
address, affiliation, e-mail address, so I can properly credit you if           
you provide unique information.  PLEASE ALSO directly mail me a copy of         
your response in addition to any responding you do in the newsgroup.  I         
will assume it is OK to describe your answer in any article or                  
publication I may write in the future, with attribution to you, unless          
you state otherwise.  Thanks, Cliff Pickover                                    
                                                                                
      * * *                                                                     
                                                                                
Consider the following nested set of square roots.
                              
 ? = sqrt <1 + G sqrt <1+(G+1) sqrt < 1 + ... >>>                            
                                                                                
Here, G indicates "Googol" or  10**100.                                         
The "<" and ">" symbols indicate where the beginning and ends of the            
the nested roots.                                                               
                                                                                
1. What is the value for in this infinite set of nested roots.                  
2. What is the next term under the root?                                        
                                                                                
Hint:                                                                           
In 1911, a twenty-three-year-old Indian clerk named Srinivasa Ramanujan         
posed the following question (#298) in a new mathematical journal called        
the Journal of the Indian Mathematical Society.                                
                                                       
 ? = sqrt <1 + 2 sqrt <1+3 sqrt <1 + ... >>>
From: U34301@uicvm.uic.edu
Newsgroups: rec.puzzles
Subject: Triangles and area
Date: 12 Nov 92 15:56:42 GMT
Article-I.D.: uicvm.92317.095642U34301
Organization: University of Illinois at Chicago

I am developing an animation that depicts merging of two triangles of equal are
a, but different shapes, into one. In order to make the animation simple, one o
f the triangles is assumed to be a right angled triangle (triangle A) and the o
ther one (triangle B) of any shape but with magnitudes of base and altitude sam
e as that of triangle A.

The animation intitially has triangle A (right angled one) placed beside Triang
le B. Then triangle B starts breaking itself up into pieces (smaller triangles)
. Each piece moves over to triangle A and positions over A such that eventually
 there is nothing left of triangle B while its fragments fit neatly over A to f
orm the shape of A (right angled triangle in this case).

The problem is breaking up the triangle B into smaller pieces. Is there any spe
cific pattern in which the triangle can be fragmented into, say, the biggest ri
ght angled triangle into which B can be fragmented into is again fragmented int
o two right angled triangles in which the biggest among them is further fragmen
ted into two right angled triangles and so forth until the difference between t
he area remaining to be filled in triangle A and the area remaining to be moved
 over from triangle B is insignificant (say less than 1% of total area). At eac
h fragmentation of B, one piece shall/ may move over to A and shall be able to
fit into the remaining area in A.

If any simple solution is already available (that is probably the cas) would so
meone please sent me an email or at least the source.

Thanks in advance.

Abraham
Newsgroups: rec.puzzles
From: karr@cs.cornell.edu (David Karr)
Subject: Re: Balls in the urn puzzle (LONG explanat
Organization: Cornell Univ. CS Dept, Ithaca NY 14853
Date: Thu, 5 Nov 1992 15:02:27 GMT

In article <Bx74u9.JL7@ra.nrl.navy.mil> mclean@itd.nrl.navy.mil writes:
>	S_w = {i: (there exists j)(for all x)(x>j -> i is in S_x)}
>
>This definition may strike you as arbitrary, but I think it's the only
>natural one given the process descriptions.

Actually this definition strikes me as being the most natural.  It
corresponds to the notion that the balls in the urn at the end are
precisely those that "come to rest" in the urn at some point in time
before the end of the process, i.e. they are not removed after step k
for some k.  A somewhat sloppier way of saying this would be that S_w
contains x for all x in S_i as i -> infinity, i.e. x must be in every
S_i when i is restricted to some "neighborhood" of infinity.

>  What is implicit in the approach is that we
>first describe S_w and then determine the cardinality of S_w, rather
>than trying to compute directly the limit of |S_i| as i -> infinity.

The "physical intuition" that some people seem to want to apply to the
problem is that the labels on the ball somehow don't matter, or
perhaps they are just an arbitrary bookkeeping mechanism.  But the
problem clearly states that the algorithm for adding and removing
balls depends entirely on the labels, so if you mess around with the
labels, you change the algorithm.  You are saying that the thing that
really matters in the problem is precisely WHICH LABELS are in the urn
(and after we've identified them, we can count them), and this is my
opinion also.

-- David Karr (karr@cs.cornell.edu)
Newsgroups: rec.puzzles
Subject: Re: gays and condoms
From: jhsegal@wiscon.weizmann.ac.il (Livian)
Date: Sat, 7 Nov 1992 08:51:54 GMT
Organization: Weizmann Institute of Science, Computation Center

In article <SUOPANKI.92Nov5001903@zombie.oulu.fi> heikki.suopanki@phoenix.oulu.fi writes:
>
>
>There are 6 gay men and they want to have safe sex.
>How many condoms they need if everybody wants to have anal sex with
>everybody, i.e. everybody wants to insert penis in all anuses (sp?)
>(except their own :). Of course all of them have to be the receiving end
>as many times.
>
>-Heikki
6 is pretty hard to think about,but for 7 gays,28 condoms will be enough if they
are smart enough!
CU
                                   ___
                                  (o o)
 ------------------------------ooO-(_)-Ooo------------------------------------
  __     __  __    ___ __     _     ___   __
    |      |   \     /   |     \       \    | VM/CMS:
    |      |    \   /    |    _ \       \   | JHSEGALL @ Weizmann.weizmann.ac.il
    |___   |       /     |    _  \    |  \  | UNIX:
        |  |      /      |   /    \   |     |  JHSEGAL  @ Wiscon.weizmann.ac.il
Xref: sparky rec.puzzles:7172 rec.org.mensa:8125
From: varhus@contra.seas.upenn.edu (Kristofor A Varhus)
Newsgroups: rec.puzzles,rec.org.mensa
Subject: Re: the question is the answer ?!
Date: 10 Nov 92 18:34:06 GMT
Followup-To: rec.puzzles
Organization: University of Pennsylvania

In article <1992Nov10.154338.8379@nntp.nta.no> stein@hal.nta.no (Stein Kulseth FBA) writes:
|>In article <1992Nov10.144701.390@blaze.cs.jhu.edu>, wilson@rhombus.cs.jhu.edu (Dwight Wilson) writes:
|>> In article <1992Nov5.213159.10826@sbcs.sunysb.edu> kthiruma@engws3.ic.sunysb.edu () writes:
|>> >
|>> >a question when repeated becomes its own answer.
|>> >
|>> 
|>> This reminds me of a (probably apocryphal) story I read somewhere
|>> long ago.  It seems a professor gave a final exam consisting of
|>> a single question.
|>> 
|>> "Write a question that you feel would be suitable for a 
|>> final exam and answer it."
|>> 
|>> One student thought for a few moments, then wrote the above
|>> sentence twice.
|>> 
|>> -Dwight
|>
|>Well, I hope he flunked, for he obviously did not answer the question.
|>
|>-- 
|>stein.kulseth@nta.no (Norwegian Telecom Research)
|>   'When murders are committed by mathematics, they can be solved by
|>   mathematics. Most of them aren't, and this one wasn't'
|>   - Nick Charles (Dashiell Hammett's "The Thin Man")

What do you mean he didn't answer the question?  Yes he did!!!!
He wrote the sentence *twice*!  Once for the question suitable for a final,
and once for its answer.  How could you possibly think he didn't answer the
question?!

Explain that!


--
-------------------------------------------------------------------------------
Kristofor A. Varhus			|       THIS SPACE AVAILABLE
varhus@eniac.seas.upenn.edu		|        E-MAIL IMMEDIATELY!
-------------------------------------------------------------------------------
From: ags@seaman.cc.purdue.edu (Dave Seaman)
Newsgroups: rec.puzzles
Subject: Re: Balls in the urn puzzle (LONG explanat
Date: 9 Nov 92 21:05:02 GMT
Organization: Purdue University

In article <1992Nov9.193750.12054@cs.cornell.edu> karr@cs.cornell.edu  
(David Karr) writes:

[Mostly correct analysis deleted.]

> If you want to SWAP the labels between two balls, I don't mind.  It will
> make no difference in the results.  But all your proposals involve
> deleting some labels altogether or introducing new labels or duplicating
> existing labels.  And not surprisingly, it changes results.

Swapping labels may make a difference in the outcome. For example, suppose  
that at step n, after adding balls #10*n-9, 10*n-8, ..., 10*9, we then  
swap the labels on balls n and n+1, and remove the ball that now has label  
n. The result is that the original ball #1 gets relabelled infinitely many  
times, but is never removed from the urn. All other balls are removed one  
step sooner than they would have been in the original scenario.

Result: one ball remains in the urn on the hour. Don't ask what label it  
has on it; that's undefined.

--
Dave Seaman
ags@seaman.cc.purdue.edu
From: chris@questrel.com (Chris Cole)
Newsgroups: rec.puzzles
Subject: Re: Balls in urn (SPOILER)
Date: 12 Nov 92 05:22:35 GMT
Article-I.D.: questrel.1992Nov12.052235.8442
Organization: Questrel, Inc.

In article <Nov.10.14.24.02.1992.4763@remus.rutgers.edu> clong@remus.rutgers.edu (Chris Long) writes:
%In article <BxI7x2.772@mentor.cc.purdue.edu>, Dave Seaman writes:
%
%> I suppose this would be the wrong time to bring up the Monty Hall puzzle,  
%> then.
%
%You know, I consider the Monty Hall puzzle to be the *best* puzzle
%ever invented, and I believe the majority of rec.puzzles veterans
%would agree.
%-- 
%Chris Long, 265 Old York Rd., Bridgewater, NJ  08807-2618

Say, just what is the Monty Hall puzzle anyway?
--
Chris Cole, chris@questrel.com
From: bickford@jimmy.dfci.harvard.edu (Paul Bickford)
Newsgroups: rec.puzzles
Subject: Re: Does anybody know what a TRYPTYCH is?
Date: 6 Nov 1992 13:46:13 GMT
Organization: Dana-Farber Cancer Institute
NNTP-Posting-Host: jimmy.harvard.edu

A tryptych is a three paneled painting, usually hinged so that the two
panels on the left and the right fold over to cover the third inner panel.
The subject matter of the painting is usually boring religious dogma (sorry!),
and usually accents the altar.
From: sirkeinen@ntc01.tele.nokia.fi
Newsgroups: rec.puzzles
Subject: Re: Break Time Head Work
Date: 5 Nov 92 14:25:59 GMT
Organization: Nokia Telecommunications.



	Careful, careful!  The problem setting does not contain
	sufficient information to get any other answer but that
	the average speed should lie somewhere between 2 and 
	6 mph. Only on the assumption that the downhill and
	uphill sections are of equal length (i.e. sloping
	symmetrically up and down) you will get the 3 mph 
	average.

	Yrjo Sirkeinen
 
Newsgroups: rec.puzzles
From: kanad@quip.eecs.umich.edu (Kanad Chakraborty)
Subject: Re: the question is the answer ?!
Organization: University of Michigan EECS Dept., Ann Arbor
Distribution: usa
Date: Thu, 12 Nov 1992 20:57:34 GMT

In article <1992Nov12.184220.17456@CSD-NewsHost.Stanford.EDU> amorgan@Xenon.Stanford.EDU (Crunchy Frog) writes:
>In article <DOUGG.92Nov12084243@kbsw3.kbsw1.uucp> 
>  dougg@kbsw1.uucp (Doug Gerecht 806 1031) writes:
>>>>>>> On 11 Nov 1992 14:44:30 -0500, 
>  berninge@cs.purdue.edu (James Berninger) said:
>>>>>>>
>>>>>>>Q: How many letters are there in the answer?
>>>>>>>A: Four
>>A: This one has eighteen
>
>A: This one has eighteen added to ten
>A: This one has eighteen added to ten added to ten
>A: etc
>
>C "Not original" Frog

A  : Look !  This one has twenty.
Newsgroups: rec.puzzles
From: 90tms@eng.cam.ac.uk (T.M. Speight)
Newsgroups: rec.puzzles,rec.org.mensa
Subject: Re: the question is the answer ?!
Date: 9 Nov 92 19:00:45 GMT
	<1992Nov6.122020.4432@nntp.nta.no>
Organization: Engineering Department, Cambridge University, England.

In article <1992Nov6.122020.4432@nntp.nta.no> stein@hal.nta.no (Stein Kulseth FBA) writes:

   This is more or less borrowed from DRH, yet interesting:

   What is the result of saying the following sentence twice: 
   'What is the result of saying the following sentence twice?' ?

Along a similar but diverging line, I once read that the following was
the first example of a single-statement paradox which is not
self-referential. (i.e. it does not contain `this sentence', and
therefore refers to all identical sentences).

`Yields a falsehood when appended to its own quotation'
Yields a falsehood when appended to its own quotation.

Anyone know who wrote this?

--
90tms@uk.ac.cam.eng      Cambridge University
Toby Speight             Engineering Department
Newsgroups: rec.puzzles
From: thomas@sees.bangor.ac.uk (Thomas Varsamidis)
Subject: Re: the question is the answer ?!
Organization: University of Wales (Bangor)
Date: Mon, 9 Nov 1992 20:53:12 GMT

This is somewhat different, but the idea is the same:

Q: How many letters are there in the answer?
A: Four






Thomas.
From: mct@praxis.co.uk (Martyn Thomas)
Newsgroups: rec.puzzles
Subject: New Magazine - puzzles needed
Date: 9 Nov 92 13:06:40 GMT
Organization: Praxis, Bath, U.K.

A publisher may be interested in producing a new puzzle magazine, and is
looking for original maths/logic puzzles, typewritten, 150-250 words long,
(including a worked solution, not involving computer search).

If you are interested in comtributing puzzles, write to Ian Adamson,
c/o Electronic Times, 30 Calderwood Street, Woolwich, London, SE18 6QH, UK.

They will pay a small fee, and need a regular stream of puzzles.

I have no connection with the publishers - I just saw it mentioned in
Electronic Times and thought it worth passing on.


-- 
Martyn Thomas, Praxis plc, 20 Manvers Street, Bath BA1 1PX UK.
Tel:	+44-225-444700.   Email:   mct@praxis.co.uk
Newsgroups: rec.puzzles
Date: Tuesday, 10 November 1992 22:21:20 PDT
X-Mailer: TMail version 1.06
From: "Anton Dovydaitis" <anton@anton.infoserv.com>
Organization: Ishi Press International
Subject: Re: Does anybody know what a TRYPTYCH is?
Newsgroups: rec.puzzles
Distribution: world

One of the most famous triptych's is a Japanese ukiyo-e wood block
print, titled `Raiko Tormented by the Ground Spider.'  The right panel
depicts aRaiko, a Japanese folk-hero, tormented by bad dreams, sent by
the Ground Spider (a demon), who holds a sinister web above Raiko, who
is sick in bed.  To the left, the web expands into a tapestry of bizzare
Buddhist demons, reminiscent of Bosch.  In the center panel, two of
Raiko's retainers play GO, one of them looking disquietly behind him
towards the demons.  The third panel show a single retainer, quite
concerned about the demons.

However, this was actually a political cartoon.  Raiko is the Shogun,
depicted as weak and ineffectual.  The demons are the spirits of popular
discontent (there was a famine at the time).  The retainers are the
Shogun's Ministers, shown to be callous (playing GO while the masses
starved).  The Shogun siezed the wooblocks and destroyed them, along
with all but four copies of the print.  It was later redrawn, and
reprinted by another artist.

Anton

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

Anton Dovydaitis
Ishi Press International
Newsgroups: rec.puzzles
From: cliff@watson.ibm.com (cliff)
Subject: Cliff Puzzle 17 - Follow up
Date: Mon, 09 Nov 1992 14:01:55 GMT
Disclaimer: This posting represents the poster's views, not necessarily those of IBM
Organization: A

Thanks for various comments I received.  For your information, the info
I reported came from Manfred Shroeder's book "Fractals, Chaos, and Power Laws"	
(Freeman: NY). page 59
Newsgroups: rec.puzzles
From: hoens@gmd.de (Guenter Hoens)
Subject: Re: gays and condoms
Organization: GMD, Sankt Augustin, Germany
Date: Tue, 10 Nov 1992 08:42:28 GMT

In <1992Nov7.085154.4225@wisipc.weizmann.ac.il> jhsegal@wiscon.weizmann.ac.il (Livian) writes:

>In article <SUOPANKI.92Nov5001903@zombie.oulu.fi> heikki.suopanki@phoenix.oulu.fi writes:
>>
>>
>>There are 6 gay men and they want to have safe sex.
>>How many condoms they need if everybody wants to have anal sex with
>>everybody, i.e. everybody wants to insert penis in all anuses (sp?)
>>(except their own :). Of course all of them have to be the receiving end
>>as many times.
>>
>>-Heikki
>6 is pretty hard to think about,but for 7 gays,28 condoms will be enough if they
>are smart enough!

i think, for 7 gays 14 condoms is the maximum. one for active use and one for
passive use by each person.

--
-----------------------------------------------------------------
* Guenter Hoens, GMD - I8, 
* German National Research Center for Computer Science
* hoens@gmd.de    (02241) 14-2408
From: ss7t+@andrew.cmu.edu (Steven C. Seel)
Newsgroups: rec.puzzles
Subject: SNAPS
Date: 9 Nov 92 19:56:41 GMT
Organization: Senior, Materials Science and Engineering, Carnegie Mellon, Pittsburgh, PA

Snaps is a game where a third party tells one of two people a certain
name.  Then, the one communicates the name to the other without
(hopefully) the third party knowing how the name was told to the other. 
The communication between the two people involves one acting as the
sender and the other as the receiver.  The sender says certain phrases
with certain numbers of finger snaps (you know, snapping) intermixed and
somehow tells the other person the name through some sort of code.  
	I have always been that third party and cannot for the life of me
figure it out.  Has anyone ever heard of it?  You don't necessarily have
to tell how it works exactly, but a hint would help.

Also, how about the game "Who's got the hat?".  Anyone heard of that one?


Steve
From: piz@cbnewsl.cb.att.com (G G ZIPFEL)
Newsgroups: rec.puzzles
Subject: Re: the question is the answer ?!(SPOLIER?)
Date: 12 Nov 92 19:57:56 GMT
Distribution: usa
Organization: AT&T

>>>>>>>
>>>>>>>Q: How many letters are there in the answer?

A: Exactly Ten.


-- 
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Zip   Steelers in 92!          | Illinois Basketball: More three point 
      Bubby's Benched!         | shooters than you can shake a stick at!
"I didn't lose, the Team lost" - Coach
From: Tim.Epstein@f526.n635.z3.fidonet.org (Tim Epstein)
Sender: acsnet@csource.oz.au
Newsgroups: rec.puzzles
Subject: balls in the urn puzzle
Date: Mon, 09 Nov 1992 21:18:00

* In a message originally to All, Teun Koetsier said:
 > >Suppose that we possess an infinitely large urn and an infinite collection 
 > >of balls labeled 1, 2, 3, and so on. There are exactly as many balls as 
 > >there are (standard) natural numbers. Consider the following thought 
 > >experiment. At 1 minute to 12 p.m. balls numbered 1 through 10 are placed 
 > >in the urn, and ball number 1 is withdrawn; at  1/2 minute to 12 p.m.,
 > balls 
 > >numbered 11 through 20 are placed in the urn, and ball number 2 is 
 > >withdrawn; at 1/4 minute to 12 p.m., balls numbered 21 through 30 are 
 > >placed in the urn and ball number 3 is withdrawn; at 1/8 minute to 12 p.m. 
 > >balls numbered 31 through 40 are placed in the urn, and ball number 4 
 > >is withdrawn, and so on. How many balls are in the urn at 12 p.m. and
 > >what are their labels?
 > >One answer is that the urn is empty at 12 p.m. For,  
 > >consider any ball, say, ball number n. At some time prior to 
 > >12 p.m. [in fact, at (1/2)n-1minutes to 12 p.m.], this ball is withdrawn 
 > >from the urn. Hence for each n, ball number n is not in the urn at 12
 > p.m.; 
 > >therefore, the urn must be empty at that time. 
 > >This is, however, very remarkable, because, when 12 p.m.is approaching,
 > the 
 > >number of balls inside the urn grows above all bounds. At 12 p.m., 
 > >instantaneously, infinitely many balls disappear from the urn.  

 
G'day... 
 
I personally don't see any remarkable paradox with this puzzle, as 
appears to be a simple matter of context manipulation. By defining 
the analogy of a clock, a linear perception of time is established 
whereby the difference between 11:59:59 and 12:00:00 is the same as 
the difference between 11:59:58 and 11:59:59.
 
However, within this environment we have 
and infinite series whereby 12:00 is mathematically infinity. The 
fault with the puzzle is that an infinite series has been defined 
within a finite time span. As 12:00 approaches it would take an 
infinatly small amount of time to add and remove balls from the urn. 
If you insist that 12:00 be eventually reached by looking at it from 
the linear perspective, then it would take zero time to add or 
remove balls; thus time itself would be meaningless. 
 
Regards,
Tim
 * Origin: I am serious ... and don't call me Shirley. (3:635/526)
From: irw@bharh58.bnr.co.uk (Ian Woollard)
Newsgroups: rec.puzzles
Subject: Re: gays and condoms
Date: 10 Nov 92 14:12:28 GMT
Organization: BNR Europe Ltd, London Road, Harlow, England.
NNTP-Posting-Host: 47.131.128.36

In article <hoens.721384948@gmd.de> hoens@gmd.de (Guenter Hoens) writes:
>
>i think, for 7 gays 14 condoms is the maximum. one for active use and one for
>passive use by each person.
>

I think this problem is in pretty poor taste BTW. Why just not say
everyone has to shake hands with everyone else, and there is a limited
number of sterile gloves and someone has some death plague? Not quite
the same kick to it I admit ;-)

Anyway as stated:

If we assume *mighty* strong condoms and that two can be worn at
once, and you can turn them inside out: the answer is 5 condoms...

One guy is 'lucky' he only shares everybody elses clean condom once
each way (i.e. turning inside out), after that every other pair wears
two (each way)...  (the sides that he 'dirtied' together).  There's an
obscene joke about menage a' trois there somewhere.

Self infection might be a problem though... still if you must do that
kind of thing what do you expect?

>--
>-----------------------------------------------------------------
>* Guenter Hoens, GMD - I8, 
>* German National Research Center for Computer Science
>* hoens@gmd.de    (02241) 14-2408

Safe sex my foot! (Condoms are one shot devices) :- 6 gays == 60 condoms

-Ian.
Newsgroups: rec.puzzles.crosswords