HDTenEightyP/NetNews huggingface dataset:
From: rh@smds.com (Richard Harter)
Newsgroups: rec.puzzles
Subject: Re: An(other) *easy* puzzle.
Date: 10 Jan 93 04:33:42 GMT
Reply-To: rh@ishmael.UUCP (Richard Harter)
Organization: Software Maintenance & Development Systems, Inc.

In article <1993Jan9.163703.24700@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.)

Stop there.  The assertion is false.  For a counter example, color all
points with rational coordinates red and those with irrational coordinates
blue.

For a simple proof, consider this figure (equilateral triangular net);:

                 0
                1 2
               3 4 5
              6 7 8 9

This figure contains a same-colored equilateral triangle.  Proof:
Suppose it does not.   Then 1-5-7 contains both colors; one is the same
as the color of 4.  Without loss of generality we can suppose that 1 and
4 are red and that at least one of 5 and 7 are blue, which gives us:


                 0
                R 2
               3 R 5
              6 7 8 9

Then it follows that 2 and 3 must be blue and, to keep 2-3-8 multi-colored,
8 must be red.  In turn this implies that 5 and 7 are both blue, giving us

                 0
                R B
               B R B
              6 B R 9

Now from triangle 3-6-7 6 must be R, from triangle 2-7-9 9 must be R,
and from 0-3-5 0 must be R, so that 0-6-9 is all R, contrary to the
assumption.  Q.E.D.

-- 
Richard Harter: SMDS Inc.  Net address: rh@smds.com Phone: 508-369-7398 
US Mail: SMDS Inc., PO Box 555, Concord MA 01742.    Fax: 508-369-8272
In the fields of Hell where the grass grows high
Are the graves of dreams allowed to die.
From: loeb@greco-prog.fr (Daniel LOEB)
Newsgroups: rec.puzzles
Subject: pick a number
Date: 7 Jan 93 09:20:27 GMT
Organization: GRECO Programmation du CNRS - Bordeaux,France

A contest being run by a French computer magazine for their 100th
issue includes the following tie breaking question. (The rest of the
questions are fairly easy, so the tie breaking question is needed to
win a prize.)

"Pick a number from 1 to 1,000,000,000. 
Your number should be as close as possibly to four-fifthes of the
average of the numbers chosen by all of the participants."

How would you play this game? (Send me email, I'll post a summary, and
indicate which of you would have won.)

Theoretically, one could reason as follows.
The numbers 800,000,001 to 1,000,000,000 are losers, so no one will
choose them. 
But in that case, the numbers 640,000,001 to 800,000,000 are also
losers and no one will choose them either.
Similarly, 512,000,001 to 640,000,000 are losers....
etc...

Such reasoning eliminates ALL numbers except 1 and 2.

HOWEVER, if even one person refuses to reason in this way, then the
average is NOWHERE near 1 or 2.


-- 

Yours, Daniel Loeb				loeb@geocub.greco-prog.fr
HOME 	150, cours Victor-Hugo; Appt D45; 33000 Bordeaux France
WORK	LABRI; Universite de Bordeaux I; 33405 Talence Cedex France
Newsgroups: rec.puzzles,soc.culture.japan
From: hiraga@Csli.Stanford.EDU (Yuzuru Hiraga)
Subject: Re: Help needed on puzzle
To: wsbusup2@urc.tue.nl
Followup-To: rec.puzzles
Keywords: puzzle
Cc: hiraga
Organization: Stanford University CSLI
Date: Tue, 5 Jan 1993 22:27:37 GMT

In article <wsbusup2.726247893@rw8.urc.tue.nl> wsbusup2@urc.tue.nl writes:
>I am working on a puzzle in a local newspaper for which I need some
>help.
>One part of the puzzle consist of sequences, that must be finished.
>The seuences are:
>  ...
>	...,Mori,Tsutsumi

OK, Tsutsumi is the owner of a Japanese pro-baseball team (Seibu lions),
while Mori is the (ex?) head coach.
So what are we to expect? The team captain is Akiyama, I think.

# but is this kind of knowledge required by a "local" newspaper?

An alternative possibility is that Tsutsumi was once ranked the
richest person by FORTUNE magazine, and also Mori (differenet from above)
also ranked high (perhaps top, too).
So we need a runner-up or once-top-ranked billionaire.
Queen Elizabeth comes to mind.

>	Jordan,Holyfield,...,Mansell

Jordan is the champ of ONE ball, Holyfield of TWO knuckles, and
Mansell of FOUR wheels.  So we need a champion of three-something.
# I have no idea.

>	Gorbatsjov,Kohl,...

Who's to be thrown out next? :-)

-Yuzuru Hiraga
Newsgroups: rec.puzzles
From: robert@labtam.labtam.oz.au (Robert Groom)
Subject: Re: Port Holes (Hint)
Organization: Labtam Australia Pty. Ltd., Melbourne, Australia
Date: Tue, 12 Jan 1993 05:08:30 GMT

grayt@Software.Mitel.COM (Tom Gray) writes:

>In article <1993Jan7.004012.29368@cs.cornell.edu> karr@cs.cornell.edu (David Karr) writes:
>>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!

>Well that may be one reason but there is a much more important reason.
>A Royal Navy destroyer sank because the builders were not aware of the
>reason. An ocaen liner had an elevator installed nad was almost completely
>destroyed in an instant because the designers forgot the reason.

>So - why are port holes round?

So there aren't any corners, of course. ;-)

Doesn't this question really belong in sci.stress.analysis?

-- 
Robert Q. Groom                            "My other computer is an EOS-1"
robert@labtam.oz.au
Labtam Australia Pty Ltd         phone: +61-3-587-1444 fax: +61-3-580-5581
Newsgroups: rec.puzzles
From: ping@bnlux1.bnl.gov (Shiping Zhang)
Subject: Re: Manhole covers - why circular?
Organization: Brookhaven National Laboratory, Upton, NY 11973
Date: Tue, 5 Jan 1993 22:30:30 GMT

In article <NICHAEL.93Jan5134917@kariba.bbn.com> ncramer@bbn.com writes:
>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.)

  Triangle shape also meets the condition.

-ping
Newsgroups: rec.puzzles
Subject: Re: Port Holes
From: jhsegal@wiscon.weizmann.ac.il (Livian)
Date: Sun, 10 Jan 1993 12:23:07 GMT
Organization: Weizmann Institute of Science, Computation Center

In article <C0HJKt.7vo@watdragon.uwaterloo.ca> deghare@daisy.uwaterloo.ca (Dave Hare) writes:
>In article <13797@grayt> grayt@Software.Mitel.COM (Tom Gray) writes:
>>
>>Man hole covers are round because man holes are round.
>>
>>The puzzle is:
>>Why are manholes round?
>>
>>A more serious problem is:
>>Why are ship port holes round?
>
>And an even more serious question is: Why are airplane windows (roughly)
>round?

And the most serious question of all is: Why are butt-holes round?
(I can bet you can't answer THAT! )

Livy
From: tvaughan@buphyk.bu.edu (Timothy Vaughan)
Newsgroups: rec.puzzles
Subject: Alternate cover shape [SPOILER]
Date: 5 Jan 93 19:43:53 GMT
Organization: Boston University Physics Department

I just thought of a non-circular shape that won't fall through.
I don't know what it is called, but it is the shape of the rotor
in a Wankel engine.  It has constant diameter, although not
constant radius.  It could be described nonrigorously as a "rounded
triangle."  I will try to derive the equation for it.

Tim
Newsgroups: rec.puzzles
From: russotto@eng.umd.edu (Matthew T. Russotto)
Subject: Re: Manhole covers - why circular?
Date: Wed, 06 Jan 93 00:57:44 GMT
Organization: Project GLUE, University of Maryland, College Park

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.

So you can't DROP the &(*@ing thing down the hole.
Circle satisies it because to get it down the hole you need to get a
diameter through, no matter how you turn it, and of course the hole is
smaller in diameter than the cover.
-- 
Matthew T. Russotto	russotto@eng.umd.edu	russotto@wam.umd.edu
Some news readers expect "Disclaimer:" here.
Just say NO to police searches and seizures.  Make them use force.
(not responsible for bodily harm resulting from following above advice)
Newsgroups: rec.puzzles
From: raph@panache.demon.co.uk (Raphael mankin)
Subject: Re: Manhole covers - why circular? [SPOILER] 
Distribution: world
Organization: Solvfield Ltd.
Reply-To: raph@panache.demon.co.uk
X-Mailer: Simple NEWS 1.90 (ka9q DIS 1.19)
Date: Sun, 10 Jan 1993 22:48:45 +0000

All the manhole covers around here are square. Many have covers are two
triangles.  I haven't lifted any of them to see what shape the hole
is underneath.:-)
-- 
--------------
Raphael Mankin			Nil taurus excretum
From: wang@math.psu.edu (Feng Wang)
Newsgroups: rec.puzzles
Subject: Re: Help needed on puzzle
Keywords: puzzle
Date: 6 Jan 93 23:04:20 GMT
Organization: Penn State Department of Mathematics

In article <wsbusup2.726247893@rw8.urc.tue.nl> wsbusup2@urc.tue.nl writes:
>I am working on a puzzle in a local newspaper for which I need some
>help.
>
>One part of the puzzle consist of sequences, that must be finished.
>The seuences are:
>	110-20-...-11-10-6

	       12

	They are the same number: 6 in decimal system.
		base 2: 110
		base 3: 20
		base 4: 12
		base 5: 11
		base 6: 10
		base 7: 6
Newsgroups: rec.puzzles,sci.math
From: greil@guug.de (Anton Greil)
Subject: Re: Combinatorical problem
Organization: Technical University of Munich, Germany
Date: Tue, 12 Jan 1993 09:04:06 GMT

mnewman@comlab.ox.ac.uk (Matthew Newman) writes:

>Does anyone know the status on the following problem ?

>Let S(n) be the set of all permutations of the integers 1..n
>Let T(n) be the set of all transpositions (i.e. swapping
>two numbers).

>For which n can one find a set B(n) such that for all p in S(n)
>either p is in B(n), or p differs by exactly one transposition
>from an element of B(n), and such that no two elements from B(n)
>differ by exactly one transposition ?

I'd like to append with a more general question:

T(n) forms a generating system for S(n)  (for all n).
How can the combinatorics of this generating system be characterized?
Especially: does there exist a normal form of each generated element from
S(n) over the base T(n) ?

And - excuse please, yet more general - is there a connection to the general
Moebius groups of the Euclidean spaces R_n, where each such Moebius transfor-
mation can be generated by reflections, which are also elements of the
(group-) order 2 ?

Thank you!  
Toni Greil
Newsgroups: rec.puzzles
From: winkler@ifwsn4.ifw.uni-hannover.de (Max Winkler)
Subject: Re: Help needed on puzzle
Organization: University of Hannover (Germany), IFW
X-Newsreader: TIN [version 1.1 PL6]
Date: Wed, 6 Jan 1993 15:00:43 GMT

Yuzuru Hiraga (hiraga@Csli.Stanford.EDU) wrote:
: In article <wsbusup2.726247893@rw8.urc.tue.nl> wsbusup2@urc.tue.nl writes:
: >I am working on a puzzle in a local newspaper for which I need some
: >help.
: >One part of the puzzle consist of sequences, that must be finished.
: >The seuences are:
: >  ...
: >	...,Mori,Tsutsumi
: 
: OK, Tsutsumi is the owner of a Japanese pro-baseball team (Seibu lions),
: while Mori is the (ex?) head coach.
: So what are we to expect? The team captain is Akiyama, I think.
: 
: # but is this kind of knowledge required by a "local" newspaper?
: 
: An alternative possibility is that Tsutsumi was once ranked the
: richest person by FORTUNE magazine, and also Mori (differenet from above)
: also ranked high (perhaps top, too).
: So we need a runner-up or once-top-ranked billionaire.
: Queen Elizabeth comes to mind.
: 
: >	Jordan,Holyfield,...,Mansell
: 
: Jordan is the champ of ONE ball, Holyfield of TWO knuckles, and
: Mansell of FOUR wheels.  So we need a champion of three-something.
: # I have no idea.
: 
: >	Gorbatsjov,Kohl,...
: 
: Who's to be thrown out next? :-)

I think it should be 'Bush'. All three are/were head of a state and involved
in the new order in Europe.

: 
: -Yuzuru Hiraga

Max Winkler




k
i

a
Newsgroups: rec.puzzles
From: lbaum@atc.boeing.com (Larry Baum)
Subject: Re: Revised Monty Hall problem
Organization: Boeing Computer Services
Date: Tue, 5 Jan 1993 17:40:27 GMT

>Leon ter Beek (leon@unixg.ubc.ca) writes:
>
>>I've made up another problem, similar to the Monty Hall problem. The
>>similarity is very obvious, but it does give it a different twist,
>>though.
>>
>>Disclaimer: First, I have been reading this group for just two days, so
>>excuse me if a similar extension has already been posted.
>>Second, I don't claim this to be a smart problem (what do you expect ;-)).
>>
>>There are five doors, behind two of them a car, and behind each of the
>>other three doors a goat. You pick a door and the quizmaster (who knows
>>what's behind the doors) opens a door with a goat behind it.
>>1) Should you change doors?
>>2) Why is the sum of the probability of changing and not changing not
>>equal to one?
>
The simple reason that the two probalities do not add up to one is that, unlike
the "classic" problem you can lose either way; i.e. even if you know for
certain that the door you chose originally was wrong, there are still 3 other
doors to chose from and only 2 winners...
Newsgroups: rec.puzzles
From: karr@cs.cornell.edu (David Karr)
Subject: Re: An *easy* puzzle. <SPOILER>
Organization: Cornell Univ. CS Dept, Ithaca NY 14853
Date: Fri, 8 Jan 1993 20:32:47 GMT

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 ?

<SPOILER> ...





For the following, assume unit = 1 inch for simplicity.

Pick a color for the origin, say, red.

Then since every point of the unit circle about the origin is exactly
1 inch from a red point, all points on the unit circle about the
origin are red.

Then since every point of the unit disk about the origin is exactly
1 inch from some point of the unit circle about the origin, all
points of the unit disk about the origin are red.

Now assume every point of the disk of radius N about the origin is red.
Every point of the disk of radius N+1 about the origin is exactly
1 inch from some point of the first disk, so all points of the
disk of radius N+1 about the origin is red.

By induction, all disks of integer radius about the origin are
completely red, and since every point of the plane is within such a
disk (I assume this is NOT a projective geometry) the entire plane is
red.

Ergo it is impossible to use two colors.

-- David Karr (karr@cs.cornell.edu)
From: deghare@daisy.uwaterloo.ca (Dave Hare)
Subject: Re: Manhole covers - why circular?
Organization: University of Waterloo
Date: Tue, 5 Jan 1993 21:41:04 GMT

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
    - It can't fall into the pipe
    - It gives maximal cross sectional area for a given amount of material
        (i.e., it is the most economical shape, assuming the covers are cast,
        and not cut)
    - It does not have to be carried, but can be rolled, so considerably
        less strength is required to manoeuver it
    - Human beings are roughly round in horizontal cross section (to varying
        degrees of accuracy, of course)
    - Orientation of the access hole with the ladder in the pipe below is not
        of concern

However, I think the paramount reason why access covers are round is that the
access opening they are covering is round :-)

Dave Hare
Newsgroups: rec.puzzles
From: karr@cs.cornell.edu (David Karr)
Subject: Re: An(other) *easy* puzzle.
Organization: Cornell Univ. CS Dept, Ithaca NY 14853
Date: Mon, 11 Jan 1993 15:25:43 GMT

In article <1993Jan9.030824.13624@Csli.Stanford.EDU> hiraga@Csli.Stanford.EDU (Yuzuru Hiraga) 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.

This was shown by numerous persons so I will not discuss it.

>* How about one with a 1cm (no, not inch :-) edge?

Try the following coloring of the plane:  Set w = sqrt(3)/2.  For each
point P=(x,y), find the integer n such that w*n <= y < w*(n+1).  Color
P red if n is even and blue if n is odd.

This way, the entire plane is colored in alternating w-cm-wide red
and blue strips, with the border between two strips colored the same
as the strip above.

Now let T be any triangle of side 1 cm with all vertices the same
color, WLOG they are all red.  The "highest" and "lowest" vertices
must differ by at least w in y-coordinates, so they cannot lie in the
same strip but must lie in consecutive red strips.  But then if the
third vertex lies in either red strip it must have a y-coordinate
difference greater than w from one of the first two points, which
cannot occur in any orientation of the triangle.  So the third point
is blue, a contradiction.

Ergo, the answer is "no" if the side of the triangle must be 1 cm.

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






Organization: Carnegie Mellon, Pittsburgh, PA
Newsgroups: rec.puzzles
Date: Sat,  9 Jan 1993 16:16:03 -0500 
From: "Jonathan R. Ferro" <jf41+@andrew.cmu.edu>
Subject: A Rubik's Cube challenge

Just for fun, I would like a collection of simple Rubik's Cube move
sequences from START that lead to positions where no two adjacent
cubelet faces are the same color.  The simplest one at the top of the
list is, of course, RRLLFFBBUUDD, leading to the well-known checkerbox
pattern, but I have made several other ones by mistake and not been able
to find a simple sequence to recreate them.

Of course, since any combination of edge flips in the checkerbox pattern
will still have no adjacent same-color faces, the criterion for the list
will have to be an arbitrary sense of "interesting-ness" and shortness
of the sequence.

Please use the notation Right, Left, Front, Back, Up, Down to indicate
clockwise turns; either RR or R2 meaning a half-twist of the Right side;
R' meaning an anti-clockwise quarter-turn of the Right side.

-- Jon Ferro               Einsprachigkeit ist heilbar
Newsgroups: rec.puzzles
From: acheng@ncsa.uiuc.edu (Albert Cheng)
Subject: Re: Help me with MH puzzle, also, a new puzzle.
Originator: acheng@shalom.ncsa.uiuc.edu
Organization: Nat'l Ctr for Supercomp App (NCSA) @ University of Illinois
Date: Thu, 7 Jan 1993 19:20:43 GMT


In article <1i7cb6INNe0@mirror.digex.com>, adric@access.digex.com (William Johnson) writes:
>Damn.  Someone help, please.  I know people are sick of this one, but....
>
>I see two lines of reasoning, and the one I intuitively feel is correct
>is not the one that logically seems correct.
>
>Reasoning one:  Once Monty shows you a door, the remaining two are one right
>	and one wrong, making the choice 50/50.
>Reasoning two:  Once you pick, you have a 2/3 chance of being wrong, and so
>	if one of the two wrong answers is shown, switching give you a 2/3
>	chance of being RIGHT.

I have not seen the show.  I assume Monty shows a wrong door whether
you have picked the right door or not.  Here are all cases with equal
chance:
		Door
	1	2	3
	R	W	W
	W	R	W
	W	W	R

Say you pick door 1, then Monty shows you a wrong door.  If you stay,
you got the Right in case 1, but Wrong for case 2 and 3.  If you switch,
you got the Right door in case 2 and 3, but wrong for case 1.  This is
the same if you start out with door 2 or 3.  Therefore, switching give
you a 2/3 chance.

he 
From: mkoby@hpindda.cup.hp.com (Mark Kobayashi)
Date: Sun, 10 Jan 1993 21:25:48 GMT
Subject: A question on the game "SET"
Organization: HP Information Networks, Cupertino, CA
Newsgroups: rec.puzzles


I thought someone here might know the answer....

I bought the card game "SET" (matching off 3 cards at a time with
similar or unique combinations).

The game says to start out with 12 cards, although if no one
sees a set to continue to add 3 cards at a time.

There have been times where I've had 15 to 18 cards down, and
I'm saying to myself "gee, there's got to be a set, we're just
not seeing it..."

My question - what is the maximum number of cards which can 
be put down which would not contain any "set"? (or, what
number of cards would guarantee at least 1 set?)


                                         M. Kobayashi
                                         mkoby@hpindabw.cup.hp.com

Newsgroups: rec.puzzles
From: jes@downey.dev.macsch.com (John Schiermeier)
Subject: Re: Port Holes
Organization: The MacNeal-Schwendler Corporation
Date: Thu, 7 Jan 93 20:37:01 GMT

In article <C0HJKt.7vo@watdragon.uwaterloo.ca> deghare@daisy.uwaterloo.ca (Dave Hare) writes:
>In article <13797@grayt> grayt@Software.Mitel.COM (Tom Gray) writes:
>>
>>Man hole covers are round because man holes are round.
>>
>>The puzzle is:
>>Why are manholes round?
>>
>>A more serious problem is:
>>Why are ship port holes round?
>
>And an even more serious question is: Why are airplane windows (roughly)
>round?

The corners of the windows have been rounded to decrease the
likelihood of cracks as the plane goes through pressurization
cycles.  This is the same principle as fillets in machine parts.
One of the earlier passenger planes, the British Comet, had 
windows with corners.  Several of them crashed due to cracking.
(This is an example undergrad engineering professors love to 
cite in design classes.)

John

Newsgroups: rec.puzzles