HDTenEightyP/NetNews huggingface dataset:
From: matthew@base.cs.ucla.edu (Matthew Merzbacher)
Subject: Connect the Dots (original)
Organization: UCLA, Computer Science Department
Date: 12 Jan 93 23:48:13 GMT

I was thinking about this in a research meeting today...

Suppose you have four dots, arranged in a square:

   A.  .B

   C.  .D

We want to connect the dots by straight line segments (no bends allowed).

How many ways can you draw a single continuous path of line segments from 
dot-to-dot that does not intersect itself?

In the example, we can draw:
  
  ABCD
  ABDC
  ACBD
  ACDB

but not ADCB or ADBC (since those paths intersect themselves).

Along with the symmetric paths that start at the other three points, 
there are a total of 16 possible paths.

QUESTIONS (ranging in difficulty):

1. How many circuits are there (instead of paths)?  Remember that a circuit
   is a path that has the same dot as both endpoints.  Example: ABDCA (but
   not ABCDA!).

2. Suppose you have 9 dots in a 3x3 square.  
   How many valid paths are there now?

   .A  .B  .C

   .D  .E  .F

   .G  .H  .I

   Note that a path is considered to have crossed itself if it goes through
   a dot that it previously passed through.  So, AG is not part of any
   legitimate path since it goes through D.

3. How many valid circuits are there in the 3x3 problem?

4. Supppose you have an NxN square. 
   How many valid paths are there through such a square?

5. How many valid circuits are there through an NxN square?

6. Suppose that we have blots instead of dots.  That is, our dots
   are now circles with non-zero circumference.  You are forbidden from
   passing through any part of a blot (unless you are going to that blot
   as part of the path).
   
   Clearly this makes the problem (very) difficult.  Is there an easy
   solution to any of the previous questions in general?

   Example:

   +--+A  oB
   |  |
   +--+
   oC  oD

   Now the segment BC will always intersect A, so it can't be part of any
   path.  In this case, the blots have different size (well, A does, anyhow).
   What if they all have the same (non-zero) size?
--

Matthew Merzbacher	ARPA:	matthew@CS.UCLA.EDU
Moo - Moo Moo  		UUCP:	...!{uunet|rutgers|ucbvax}!cs.ucla.edu!matthew
               		This time, *with* the oys
Newsgroups: rec.puzzles
From: hector@sci.ccny.cuny.edu (Hector Garcia)
Subject: Re: 19
Keywords:  SPOILER
Organization: City College of New York - Science Computing Facility
Date: Tue, 12 Jan 1993 15:59:44 GMT

In article <1993Jan7.080754.14350@dde.dk> ct@dde.dk (Claus Tondering) writes:
>What computer operating system could be spelled thus:
>
>		19
>

Could it be UN=1 , and IX=9. UNIX?
-------------------------------------------------------------------------------
Hector Garcia       hector@sci.ccny.cuny.edu   City College
-------------------------------------------------------------------------------
From: nichael@bbn.com (Nichael Cramer)
Newsgroups: rec.puzzles
Subject: Re: Manhole covers - why circular?
Date: 5 Jan 93 13:49:17
Organization: BBN, Interzone Office
Reply-To: ncramer@bbn.com
NNTP-Posting-Host: kariba.bbn.com
In-reply-to: robertw@informix.com's message of 5 Jan 93 17:34:40 GMT

robertw@informix.com (Robert Weinberg) writes:

   Manhole covers are manufactured in circular shape, rather than oval or square, to  
   satisfy one paramount condition.

   What is the condition ...

The cover can't fall down the hole.

   ... and why does a circular shape satisfy it?

Because: DIAMETER_HOLE <= DIAMETER_COVER
for all possible values of DIAMETER_HOLE and DIAMETER_COVER.

   What other shapes would also satisfy the condition?

Given the above, for any fully convex shape, I don't _think_ there are
any others.

Probably if I was clever enough (and/or had more time) perhaps I could
come up with some more complicated shape.

(Implicit in the above is the assumption that what's really keeping
the lid from dropping is a narrow lip around the edge of the hole.  If
we could play with the width of the lip, we could surely get other
allowable shapes, but the problem would quickly become uninteresting.)

N
From: tvaughan@buphyk.bu.edu (Timothy Vaughan)
Newsgroups: rec.puzzles
Subject: Re: Manhole covers - why circular?  [SPOILER]
Date: 5 Jan 93 18:34:54 GMT
Organization: Boston University Physics Department

They are round so that they cannot fall through the manhole,
regardless of the orientation.

Any regular polygon can be oriented to fall through the hole,
unless the lip or ridge in the manhole is wide enough.

Other shapes, anyone?

Tim
Newsgroups: rec.puzzles
From: jimbo@statsci.com (Jimbo Harris)
Subject: Re: Manhole covers - why circular?
Organization: Statistical Sciences, Inc
Date: Fri, 8 Jan 1993 02:21:18 GMT

ghazel@eskimo.com (Geoff Hazel) writes:

>In article <C0EHKG.AL5@watdragon.uwaterloo.ca> deghare@daisy.uwaterloo.ca (Dave Hare) writes:
>>In article <1993Jan5.173440.10482@informix.com> robertw@informix.com (Robert Weinberg) writes:
>>>Manhole covers are manufactured in circular shape, rather than oval or square, to  
>>>satisfy one paramount condition.
>>>
>>>What is the condition, and why does a circular shape satisfy it?
>>
>>Actually, access covers are circular for many reasons, and I often use this
>>as a game with kids to get them to stretch their brains.
>>
>>I don't know which reason you have in mind, but here are some:
>>
>>    - It is orientation free: it will fit in any position
>             ^^^^^^^^^^^^^^^^^

>In fact, I read that they were round in order to minimize the number
>of decisions the sewer workers had to make.

I heard it was to minimize the number of fatal head injuries caused by
manhole covers falling through manholes upon men that are down 
above mentioned manholes. (You have to figure that any job that you 
could possibly get where you MIGHT be expected to jump down a manhole
CAN'T require more brains than, say, a squirrel...)

-Jimbo Harris
From: landman@hal.COM (Howard Landman)
Newsgroups: rec.puzzles
Subject: Re: Manhole covers - why circular?
Date: 10 Jan 93 06:57:59 GMT
Organization: HaL Computer Systems, Inc.
NNTP-Posting-Host: bang.hal.com

In article <72940@cup.portal.com> ISW@cup.portal.com (Isaac S Wingfield) writes:
>The other shape that satisfies the condition is an equilateral triangle.

No, it doesn't.  Cut a hole in a piece of paper and see why.

	Howard A. Landman
From: Haavard.Johnsbraaten@tmlh.no (Haavard Johnsbraaten)
Newsgroups: rec.puzzles
Subject: Re: Solution wanted on a nice Christmas problem
Date: 7 Jan 93 13:48:31 GMT
Organization: Telemark College of Education


I see that I haven't stated that the problem is two-dimentional.  So please 
insert "in the plane" somewhere in the text.

 o            o
Havard Johnsbraten, Telemark College of Education, Notodden, Norway
E-mail  haavard.johnsbraaten@tmlh.no  or
G=haavard;S=johnsbraaten;O=tmlh;P=uninett;A= ;C=no
From: torbenm@diku.dk (Torben AEgidius Mogensen)
Newsgroups: rec.puzzles
Subject: Re: Bus Stop Puzzle (Spoiler)
Date: 7 Jan 93 13:45:14 GMT
Organization: Department of Computer Science, U of Copenhagen

tk@dcs.ed.ac.uk (Tommy Kelly) writes:

>Every morning, I take a train to the city, then have to take a bus to
>Uni.  There are two bus stops within easy walking distance of the train
>station.

>Bus stop 1 is 4mins 20 seconds away, and is the earlier on the route (the bus
>visits it before bus stop 2).

>Bus stop 2 is 3mins 20 seconds away.

>The bus takes about 30 seconds to travel from stop 1 to stop 2.

>Bus interarrival time is 15 minutes, and can effectively be at any point
>in their run when I begin my walk from the train station.

>a. On average, which bus stop should I walk to minimize my time in travelling
>   to the University?

Surely it is stop 2. Even if they are at the same distance, you can
catch an earlier bus at stop 2. Since stop 2 is also closer than stop
1, there is no contest.

>b. In general, for times :
>	Tn - time to walk to stop n
>	dn - time for bus to travel from stop n to stop n+1
>	l  - bus interarrival time

>	which stop should I choose?

If Tn+dn > T(n+1) choose stop n+1 over stop n. Any bus you could catch
at stop n, you can also catch at stop n+1. You might even catch an
earlier bus.

If Tn+dn < T(n+1) choose stop n over stop n+1. Similar reasoning.

You can compare two non-adjacent stops in a similar way. If
Tn+dn+...+d(n+m-1) > T(n+m) choose stop n+m over stop n, and vice
versa. Since you can compare any two stops, you can sort the stops and
choose (one of) the best.

The interarrival time is irrelevant.

	Torben Mogensen (torbenm@diku.dk)
Newsgroups: rec.puzzles
From: hsieh@math.toronto.edu (Paul Hsieh)
Subject: Re: new year's problem
Organization: Department of Mathematics, University of Toronto
Distribution: rec
Date: Mon, 4 Jan 93 17:03:15 GMT

In article <1993Jan2.1584.7529@channel1> "eliot gelwan" <eliot.gelwan@channel1.com> writes:
>On 12-31-92 KEITH F. LYNCH  wrote:
>
>KFWhat property did 1987 have, that no year after it will have
>KFuntil 2013?
>
>Prime numbers
>
>KFWhat property did 1961 have, that no year
>after it will have until 6009?
>
>turn 'em upside down and see.
>

What property did 1991 have that I shared and wont share again until I am
33?
Newsgroups: rec.puzzles
From: karr@cs.cornell.edu (David Karr)
Subject: Re: Port Holes
Organization: Cornell Univ. CS Dept, Ithaca NY 14853
Date: Thu, 7 Jan 1993 00:40:12 GMT

In article <13797@grayt> grayt@Software.Mitel.COM (Tom Gray) writes:
>
>Why are ship port holes round?

Why, because they wouldn't look *nautical* otherwise, of course.
Imagine if your boat had square windows all over the hull; it would
look like some landlubber's *house*, for goodness' sake!

-- David Karr (karr@cs.cornell.edu)
Newsgroups: rec.puzzles
From: hiraga@Csli.Stanford.EDU (Yuzuru Hiraga)
Subject: An(other) *easy* puzzle.
Organization: Stanford University CSLI
Date: Sat, 9 Jan 1993 03:08:24 GMT

In article <1993Jan8.193314.3289@zip.eecs.umich.edu> kanad@quip.eecs.umich.edu (Kanad Chakraborty) writes:
>Here's a very *easy*, and nice, puzzle....

Along a similar vein	# no, it's not original.

A plane is totally colored with two colors.
* Show that there exist three points of same color that
  (when connected) form an equilateral triangle.
* How about one with a 1cm (no, not inch :-) edge?

-YH
Date: Saturday, 9 Jan 1993 14:10:42 EST
From: <RVESTERM@vma.cc.nd.edu>
Newsgroups: rec.puzzles
Subject: Re: An(other) *easy* puzzle.
 <1993Jan9.030824.13624@Csli.Stanford.EDU>
 <1993Jan9.163703.24700@zip.eecs.umich.edu>

bzzt.  try again.  it is not necessarily true that for a given blue point,
there is a "closest" red point.

draw a line through the plane.  color everything to one side of the line
blue.  color everything to the other side of the line red.  color the
line itself blue.

pick a blue point.  any blue point.  i don't care which.  your choice.
show me a red point.  any red point.  i don't care which.  your choice.

i'll show you a closer red point.

bob vesterman.

Xref: sparky rec.puzzles:8294 rec.org.mensa:9155
From: leon@unixg.ubc.ca (Leon ter Beek)
Newsgroups: rec.puzzles,rec.org.mensa
Subject: Re: Try this for a change!
Date: 8 Jan 1993 21:27:04 GMT
Organization: University of British Columbia, Vancouver, B.C., Canada
NNTP-Posting-Host: unixg.ubc.ca

In article <1993Jan8.205328.28113@sci.ccny.cuny.edu> hector@sci.ccny.cuny.edu (Hector Garcia) writes:
>GOAL:  Connect the pairs of boxes with the same label. ie [1] with [1],
>       [2] with [2], and [3] with [3]. The connections must be made by 
>       drawing a continuous line sourcing from one of the boxes
>       and terminating at the other.
>       By a continuous line I mean anything you can draw WITHOUT
>       lifting your pencil.
>RULES: 1)Lines connecting different pairs of boxes should not intersect.
>       2)No drawing is allowed outside of the big box.
 
                                  This is the big box.
 	        _______________ /
 	       |    ---1       |
 	       |    |          |
 	       |    | ******** |
 	       |    | *2@@@  * |
 	       |    | *   @  * |
 	       |    | *   @  * |
 	       | 3  | *   @  3 |
 	       | *  | *** @    |
 	       | *  |   * @    |
 	       | *  |--1* @    |
 	       | *      * @    |
 	       | ******** @    |
 	       |       2@@@    |
 	       |_____ ___ _____|
 
 
>PS/ Topologists, and Graph Theoreticians shall prove the impossibility of this!

I'd like to see their 'proof'!

Leon
----------------------------------------------------------------------
"De wereld is mijn vaderland          Email: leon@nematic.chem.ubc.ca
 en wetenschap mijn religie"          Fax:   +1-604-82-22847
   -Christiaan Huygens-               Phone: +1-604-82-22603
Newsgroups: rec.puzzles
jhsegal
Newsgroups: rec.puzzles
Subject: Re: Port Holes
From: jhsegal@wiscon.weizmann.ac.il (Livian)
Date: Sun, 10 Jan 1993 12:20:08 GMT
Organization: Weizmann Institute of Science, Computation Center

In article <13797@grayt> grayt@Software.Mitel.COM (Tom Gray) writes:
>
>
>
>A more serious problem is:
>
>Why are ship port holes round?
>--
>i.sinature

Oh,come on! It is a known fact that the round shapes are more resistable to
pressure.So ship port holes are round to resist to the water pressure.
                                   ___
                                  (o o)
 ------------------------------ooO-(_)-Ooo------------------------------------
  __     __  __    ___ __     _     ___   __
    |      |   \     /   |     \       \    | VM/CMS:
    |      |    \   /    |    _ \       \   | JHSEGALL @ Weizmann.weizmann.ac.il
    |___   |       /     |    _  \    |  \  | UNIX:
        |  |      /      |   /    \   |     |  JHSEGAL  @ Wiscon.weizmann.ac.il
Newsgroups: rec.puzzles
From: potamian@apollo.HP.COM (Spyros Potamianos)
Subject: Re: An *easy* puzzle. (*SPOILER*)
Date: Fri, 8 Jan 1993 20:21:26 GMT
Reply-To: potamian@hpl.hp.com
Organization: Hewlett-Packard Company

In article <1993Jan8.193314.3289@zip.eecs.umich.edu>, kanad@quip.eecs.umich.edu (Kanad Chakraborty) writes:
|> Here's a very *easy*, and nice, puzzle.  This puzzle is a close
|> relative of the one I posted on New Years' eve.  No flames, please,
|> for posting something so simple. Simple things can be interesting 
|> sometimes, as some of you would undoubtedly agree.
|> 
|> Suppose you are given 3 colors and asked to assign a color
|> to each point in a plane such that (a) you *must* use more than one
|> color for the entire plane; (b) *every* pair of points 1 inch apart
|> are colored alike.  Can you make such an assignment ? The plane is
|> a continuum of points, it is not a grid.
|> 
|> Kanad


Obviously if two points X and Y are N inches apart (N = integer) they must
have the same color.
So, let A and B be two points with different colors.
Construct a triangle ABC, so that AC and BC have integer lengths (if measured
in inches!). Such a triangle can always be constructed, e.g. you can choose
AB = BC = ceiling(AB)
Then A has the same color as C, B has the same color as C, therefore A has
the same color as B, so......... no, you can not color the points of a
plane the way you described.

Nice little puzzle indeed!

Spyros Potamianos
potamian@hpl.hp.com
Newsgroups: rec.puzzles
From: rolls@cis.umassd.edu (Frank Pinto)
Subject: Re: 12 bolt puzzle HELP!
Organization: University of Massachusetts Dartmouth
Date: Wed, 13 Jan 1993 04:30:38 GMT

Scott
This is a typical "terniary" type of puzzle.

Here are some hints:

Divide the bol
groups of 4.
weigh group 1 against group 2
either they balance or not. If they balance,
your problem is over (find group 3 and discover the
wrong bolt)
If they don't: look at this:
group1= b1,b2,b3,b4
group2= b5,b6,b7,b8
group3= b9,b10,b11,b12
 Well if group 1 does not balance with group
2, then group 3 has all
"good" bolts.
Now......
do the following:

weight the bolts:

b9,b1,b2,b3 against b4,b5,b6,b7

remember "b9" belongs to the group
which has all the "balanced" bolts.

well

95.9% of the problem is ssolved.

enjoy it

Frank Pinto
From: rmurphy@aludra.usc.edu (Bob Murphy)
Newsgroups: rec.puzzles
Subject: Re: An(other) *easy* puzzle.
Date: 10 Jan 1993 19:49:35 -0800
Organization: University of Southern California, Los Angeles, CA
NNTP-Posting-Host: aludra.usc.edu

>In article <1993Jan9.030824.13624@Csli.Stanford.EDU> hiraga@Csli.Stanford.EDU (Yuzuru Hiraga) writes:
>>In article <1993Jan8.193314.3289@zip.eecs.umich.edu> kanad@quip.eecs.umich.edu (Kanad Chakraborty) writes:
>>
>>A plane is totally colored with two colors.
>>* Show that there exist three points of same color that
>>  (when connected) form an equilateral triangle.
>
>Proof. WLOG, let the colors be red and blue.
>Choose a point A in the colored plane. Suppose, WLOG, that 
>A is colored blue. Find the (or a) point colored red _nearest_ to A 
>(Euclidean distance-wise). (This is always possible because both
                             ^^^^^^^^^^^^^^^^^^^^^^^
>colors have been used.) Call this point B. Suppose the
                    [stuff deleted]
>Kanad
 

It is NOT always possible to find such a nearest red point.
Suppose the plane is colored as follows:

   (x,y) is colored blue if x is rational
                 and red if x is irrational.

or a simpler coloring which shows this is the following:

   The point (0,0) is colored blue and every other point
   is colored red.

   This blue point clearly has no closest red point.


Bob Murphy (rmurphy@aludra.usc.edu)
From: gilhoosg@dcs.glasgow.ac.uk (Capt Scott (retired))
Newsgroups: rec.puzzles
Subject: 12 bolt puzzle HELP!
Date: 12 Jan 93 17:27:41 GMT
Organization: Glasgow University Computing Science Dept.

I was told a puzzle recently and it is driving me spare.
I have a feeling it is probably  standard puzzle so if anyone
can help me ....

This is it:-
	You have 12 bolts, totally identical except 1 is either 
lighter or heavier. Using a balance-scale 3 times find the 
Dud.

Any help appreciated
Scott

-- 
-----------------------------------------------------------------
 Scott Gilhooly             |The only thing more dangerous than |
 Glasgow University         |a programmer with a screwdriver is |
 gilhoosg@dcs.gla.ac.uk     |a user with an idea                |
From: landman@hal.COM (Howard Landman)
Newsgroups: rec.puzzles
Subject: Re: An *easy* puzzle.
Date: 10 Jan 93 07:14:14 GMT
Organization: HaL Computer Systems, Inc.
NNTP-Posting-Host: bang.hal.com

In article <1993Jan8.193314.3289@zip.eecs.umich.edu> kanad@quip.eecs.umich.edu (Kanad Chakraborty) writes:
>Suppose you are given 3 colors and asked to assign a color
>to each point in a plane such that (a) you *must* use more than one
>color for the entire plane; (b) *every* pair of points 1 inch apart
>are colored alike.  Can you make such an assignment ? The plane is
>a continuum of points, it is not a grid.

No.  Consider a single point of the first color.  All concentric rings of
integral radius around it must also be of the same color.  But since the
same holds true for each point on the ring of radius 1, we get that the
entire disk of radius 2 around any point must be exactly the same color!
This imples that the entire plane must be that color.

Conversely, if there WERE a point of the other color, the ring of radius 1
around it would be the other color too.  But where could you place this ring
without intersecting one of the concentric rings mentioned in the previous
paragraph?

	Howard A. Landman
From: rick@daffodil.tymnet.com (Rick McFarland)
Newsgroups: rec.puzzles
Subject: Re: new year's problem <SPOILER?>
Date: 4 Jan 93 20:32:48 GMT
Distribution: rec
Organization: BT North America, San Jose, CA

In article <1993Jan4.170315.19491@math.toronto.edu>, hsieh@math.toronto.edu (Paul Hsieh) writes:
|> In article <1993Jan2.1584.7529@channel1> "eliot gelwan" <eliot.gelwan@channel1.com> writes:
|> >On 12-31-92 KEITH F. LYNCH  wrote:
|> >
|> >KF/What property did 1987 have, that no year after it will have
|> >KF/until 2013?
|> >
|> >Prime numbers
|> >
|> >KF/What property did 1961 have, that no year
|> >after it will have until 6009?
|> >
|> >turn 'em upside down and see.
|> >
|> 
|> What property did 1991 have that I shared and wont share again until I am
|> 33?



Is this correct?   You were 22 in 1991 and will be 33 in 2002.  Your age and the year are the same whem
written backwards.




------------------------------------------------
"ad astra per aspera"  
Newsgroups: rec.puzzles
From: klundqvi@abo.fi (Kurt Lundqvist AT)
Subject: Re: Port Holes
Organization: Abo Akademi University
Date: Thu, 7 Jan 1993 13:50:18 GMT


In article <13797@grayt> grayt@Software.Mitel.COM (Tom Gray) writes:
>
>Why are ship port holes round?
  
Ship port holes are round in order to avoid cracks in the hull that would 
start from sharp corners due to the stresses that appear in bad weather.

The constant diameter triangels as found in Wankel motors have one 
serious disadvantage that make them useless as manhole covers. 
If they are moved in wrong direction of some reason, they will turn 
into a vertical position because of the placement of the center of 
gravity. This will not happen with a circular cover. 
As manhole covers often are used in streets, I wouldn't like to be
the one driving into one hanging vertically in the manhole.

Kurt (klundqvi@ra.abo.fi)
Newsgroups: rec.puzzles
From: karr@cs.cornell.edu (David Karr)
Subject: Re: Manhole covers - why circular?  [SPOILER]
Organization: Cornell Univ. CS Dept, Ithaca NY 14853
Date: Tue, 5 Jan 1993 19:37:11 GMT

In article <106199@bu.edu> tvaughan@buphyk.bu.edu (Timothy Vaughan) writes:
>They are round so that they cannot fall through the manhole,
>regardless of the orientation.

Gee whiz, that's why!  I always thought it was because they are too heavy
to carry, so you want to be able to roll them.  :-) :-)

>Other shapes, anyone?

There are plenty of shapes that meet the "don't fall through" criterion.
They are called "curves of constant diameter."  There was a popular
article about them a few years ago; sorry, I don't recall the reference.
This topic was also covered in rec.puzzles last year, so there may be
some good stuff in the archive.

Another application of curves of constant diameter is that logs with
such a cross-section can be used as rollers, for example to move a
large block of stone.

An example of such a shape is three 60-degree circular arcs attached
end-to-end to form an "equilateral triangle" with bulging sides.
When you roll a block over this shape, as each "apex" of the shape
contacts the ground, it serves as the pivot for the arc bearing the
block, at whose center it happens to be.  A variant on this shape
is to draw a curve around it at a constant distance from the original
curve (e.g. roll a circle around the perimeter and trace the
envelope of its motion), resulting in a figure of six connected
circular arcs, three with smaller radius and three with larger radius.

I believe there are yet other shapes that have no circular arcs at
all, but can't recall one off-hand.

-- David Karr (karr@cs.cornell.edu)
From: @ee.surrey.ac.uk (null)
Newsgroups: rec.puzzles
Subject: I'm bored with manhole covers
Date: 11 Jan 93 10:33:23 GMT
Organization: University of Surrey, Guildford, Surrey, UK. GU2 5XH

As I was going up Guildford High Street on Saturday, I walked over a manhole cover.
It was square.

Can someone explain what is going wrong?

Yours mystifiedly,

J.H.B.D.