HDTenEightyP/NetNews huggingface dataset:
From: mag@cs.uiuc.edu (Tom Magliery)
Subject: Re: Manhole covers - why circular?
Reply-To: mag@cs.uiuc.edu
Organization: University of Illinois at Urbana-Champaign
Date: Tue, 5 Jan 1993 18:50:08 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, and why does a circular shape satisfy it?

spoiler alert...

Wouldn't want it dropping through its own hole, now, would we?

>What other shapes would also satisfy the condition?

Trivially, anything with a circle as its convex hull (e.g., a planar
donut).  I can't think of any others, without using to my advantage
the width of the little ridge that the manhole cover is resting on.
This is not to say there aren't any.

mag
-- 
Tom Magliery ** Dept of CS ** 1304 W Springfield ** Champaign IL 61820 ** USA
Organization: School of Computer Science, Carnegie Mellon, Pittsburgh, PA
Newsgroups: rec.puzzles
Date: Tue, 12 Jan 1993 13:23:09 -0500 
From: "Andrew C. Plotkin" <ap1i+@andrew.cmu.edu>
Subject: Re: A question on the game "SET"

Excerpts from netnews.rec.puzzles: 10-Jan-93 A question on the game
"SET" Mark Kobayashi@hpindda.c (696)

> 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).

> 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?)

Ha -- I just subscribed to rec.puzzles for the sole purpose of asking
that question :-)

Since you seem to have left out the game rules, let me do so:

Each card shows a figure. The figure has N independent attributes; each
attribute has 3 possible values. So there are 3^N possible cards. The
deck contains exactly one of each.

In the deck sold, N=4, so there are 81 cards. The attributes are 
	shape (diamond / oval / squiggle)
	shade (solid / striped / hollow)
	color (red / green / blue)
	number (one copy / two copies / three copies)

Three cards form a "set" if: 
For every attribute, either all three cards' values match, or the three
cards' values are all different.

So, for the standard deck (N=4):
 (one solid red diamond)  (two solid red diamond)  (three solid red
diamond) is a set.
So is (one solid blue diamond)  (two solid green diamond)  (three solid
red diamond)
And (one hollow blue diamond)  (two striped green oval)  (three solid
red squiggle)
Three identical cards would form a set, except that there is only one of
each card in the deck.
But  (one solid blue oval)  (two solid green diamond)  (three solid red
diamond) is not a set; it fails for the attribute of shape. 

Again, the question is: what is the maximum number of cards you can lay
out without any three of them forming a set?

I've thought about this for a few days now. My first guess was 2^N, but
that's wrong; I found arrangements of 9 cards with no set in the N=3
case, and 18 cards for N=4.

Bonus question (easier, I have an answer and proof): How does the answer
change if you allow repeated cards?

BTW, it's a very cool game, and only costs $10 or $12. The game is just
laying out cards and trying to find sets as fast as possible.

--Z
Xref: sparky rec.puzzles:8321 rec.org.mensa:9178
From: jgregory@ub.d.umn.edu (jennifer gregory)
Newsgroups: rec.puzzles,rec.org.mensa
Subject: Simple thoughts on a math/puzzle
Date: 11 Jan 1993 02:56:12 -0600
Organization: University of Minnesota, Duluth
Distribution: world
NNTP-Posting-Host: ub.d.umn.edu


Just lying in bed thinking the other night I came up with this little
problem... kind of simple, but I've only been through high-school
pre-calc... if you figure it out, mail me with the answer... I'll respond
if you're right (or wrong I guess too) but I don't want the answer posted
until people have had a chance to mull over it.

Another note before the puzzle - I'm not exactly sure why this works, but
it does... and it works rather well... :)  So if you can explain the
reason behind the equation, I'd appreciate it... I just play around with
numbers in my head (turn words into numbers and add, etc. :) and I came up
with it... without further ado:

What is the significance of this equation?
x(.5(abs(x)+1))=y

If you work with it I'm sure you can figure it out... it's not too hard...
just kind of interesting if you like working with numbers. :)


Newsgroups: rec.puzzles
From: hiraga@Csli.Stanford.EDU (Yuzuru Hiraga)
Subject: Re: Manhole covers - why circular?  [SPOILER]
Organization: Stanford University CSLI
Date: Tue, 5 Jan 1993 22:16:14 GMT

In article <1993Jan5.193711.7525@cs.cornell.edu> karr@cs.cornell.edu (David Karr) writes:
>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.

There is a bulky book (several hundred pages) on this subject
by Prof. Shigetake Matsuura (Kyoto Univ.).
Unfortunately, I know it only in Japanese.

-Yuzuru Hiraga
From: grayt@Software.Mitel.COM (Tom Gray)
Newsgroups: rec.puzzles
Subject: Re: Port Holes
Date: 11 Jan 93 17:21:09 GMT
Organization: Mitel. Kanata (Ontario). Canada.

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?




-- 
i.sinature
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: Sat, 9 Jan 1993 20:09:59 GMT

In article <1993Jan9.163703.24700@zip.eecs.umich.edu> kanad@quip.eecs.umich.edu (Kanad Chakraborty) writes:
>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.)

Suppose I chose point A to be the origin.  Suppose also that the
positive x-axis is colored red.  Now what is the (or a) point colored
red nearest to A?

-- David Karr (karr@cs.cornell.edu)
Newsgroups: rec.puzzles
From: asimov@wk223.nas.nasa.gov (Daniel A. Asimov)
Subject: Re: closed form for a sum (SPOILER)
Organization: NAS, NASA Ames Research Center, Moffett Field, California
Date: Wed, 13 Jan 93 02:31:58 GMT

In article <1iv1enINNnq6@master.cs.rose-hulman.edu> goddard@NeXTwork.Rose-Hulman.Edu (Bart E. Goddard) writes:
>
>Evaluate: 
>        \infinity 
>          ___
>         \        sin(n)/n
>         /___
>         n = 1
>The solution is nice.
>--
>Bart Goddard                            |Behold, thy King cometh unto thee,
>Math. Dept. Rose-Hulman Inst. of Tech.  |meek, and sitting upon an ass, and
>goddard@nextwork.rose-hulman.edu        |a colt, the foal of an ass.


The sum is (pi - 1)/2.

(Sketch):  Identify the sum as the imaginary part of sum (exp(in)/n).
Consider sum (z^n/n) and e.g. by differentiating this, identify it with
log(1/(1-z)). Now plug in exp(in) for z, take the imaginary part, and
use the half-angle formula to see that it is (pi-1)/2.


Dan Asimov
Mail Stop T045-1
NASA Ames Research Center
Moffett Field, CA 94035-1000

asimov@nas.nasa.gov
(415) 604-4799

Newsgroups: rec.puzzles
From: hiraga@Csli.Stanford.EDU (Yuzuru Hiraga)
Subject: Re: Manhole covers - why circular?  [SPOILER]
Organization: Stanford University CSLI
Date: Tue, 5 Jan 1993 22:09:49 GMT

In article <1993Jan5.193711.7525@cs.cornell.edu> karr@cs.cornell.edu (David Karr) writes:
>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."...
> ...
>An example of such a shape is three 60-degree circular arcs attached
>end-to-end to form an "equilateral triangle" with bulging sides....

True, but add another requirement that the cover can be fit in
regardless of its (planar) orientation, that is, there is no need to
rotate it to place it in a fitting position.
THEN we are left with only the circle.

# And I think this is practically important.

>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.

The problem is that they can't be used as "wheels" (not rollers),
because you can't put an axis that maintains constant height while
rotating (they make good toys, though).
Even as rollers, there may be problems; because:
* they have a particular orientation of stability (with the pointed edge
  up, lowest center of mass) so that the motion may be jerky (though
  this won't be a problem if we use multiple rollers with different
  orientations), and
* the pointed edge may damage the supported object (as well as the road
  surface).

-Yuzuru Hiraga
From: ct@dde.dk (Claus Tondering)
Newsgroups: rec.puzzles
Subject: 19
Date: 7 Jan 93 08:07:54 GMT
Organization: Dansk Data Elektronik A/S

What computer operating system could be spelled thus:

		19


-- 
Claus Tondering
Dansk Data Elektronik A/S, Herlev, Denmark
E-mail: ct@dde.dk
------------------------------- Why do they never serve pizza on airplanes?
Newsgroups: rec.puzzles
From: acheng@ncsa.uiuc.edu (Albert Cheng)
Subject: Re: Bus Stop Puzzle
Originator: acheng@shalom.ncsa.uiuc.edu
Organization: Nat'l Ctr for Supercomp App (NCSA) @ University of Illinois
Date: Thu, 7 Jan 1993 20:10:25 GMT


In article <C0HD3p.1u4@dcs.ed.ac.uk>, 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?

stop 2.  It takes 1 more minute to get to stop 1 than stop 2.  So, if
you can catch the bus at stop-1, you sure can catch it at stop-2; it is
not true the other way.  Also, if you are 30 seconds away from stop-2
and see the bus coming, you can run like crazy with waving arms as
Dagwood does.  (Actually he is in carpool now.)
Newsgroups: rec.puzzles
From: myrberger@e.kth.se
Subject: New 3x3x3 cube puzzle list
Reply-To: myrberger@e.kth.se
Organization: KTH, Royal Institute of Technology, School of Electrical Engineering
Date: Thu, 7 Jan 1993 15:21:53 GMT

A new version of my list with puzzles that in their final state
are a 3x3x3 cube is ready.

If you'd like a copy just send me a MAIL.

Enjoy,

Johan Myrberger

MAIL: myrberger@e.kth.se
Newsgroups: rec.puzzles
From: an1060@anon.penet.fi
Subject: Re: Manhole covers - why circular?
Organization: Anonymous contact service
X-Anonymously-To: rec.puzzles
Date: Tue, 5 Jan 1993 22:48:13 GMT

X-Anon-To: rec.puzzles

Anything with a CONSTANT HEIGHT will do.  Circles are the most popular 
examples, also "triangles" with circular edges (the Mazda Rotary engine uses
such a design).... Can anyone think of other shapes with a constant height??
(i.e. shapes that when rolled on a surface along their perimeter yield a
constant height from the surface)...

Abe

mantell@ama.sunysb.edu

-------------------------------------------------------------------------
To find out more about the anon service, send mail to help@anon.penet.fi.
Due to the double-blind system, any replies to this message will be anonymized,
and an anonymous id will be allocated automatically. You have been warned.
From: torbenm@diku.dk (Torben AEgidius Mogensen)
Newsgroups: rec.puzzles
Subject: Re: RANDOM NUMBERS ON A COMPUTER
Date: 8 Jan 93 13:43:52 GMT
Organization: Department of Computer Science, U of Copenhagen

tjgerman@53iss6.Waterloo.NCR.COM (Trevor German) writes:


>	Someone wants to know hos to create random numbers on a computer.


>	This sounds trivial but it is not. First you need a good definition
>	of a random number. The definition required is as follows.


>	1. The number shall be contained within a range, say 0 - 255

>	2. The probability of selecting and number at any time will
>	 be 1:256.

>	3. No sequencies shall exist, ever.....

I assume you mean "no cycles will occur", in the sense that the
infinite sequence of numbers does not repeat after a while.

>	If an algorithm is used than sooner or later some condition will
>	be met that restarts the sequence. This is why these routines are 
>	usually called pseudo-random generators.

It is in fact possible to make non-repeating pseudo-random number
generators. The 'pseudo' doesn't refer to repetition, but to
predictability: if the numbers are generated by an algorithm, you can
predicat the next number if you know the current state. Therefore the
numbers are not truly random. So your condition 2 can not hold, as the
probability for any number is either 0 or 1. However, you can require
that the distribution of numbers approach the even distribution in the
limit, as the length of the sequence increases.

To make a non-repeating sequence of random numbers you need unbounded
memory (like on a Turing machine), but you will only a finite amount
of it at any time.

As an example, generate the (infinite) binary expansion of pi. To do
this requires more and more memory (and time) for each successive bit.
To generate a pseudo-random number sequence with numbers in the range
0-255, group the bits eight at a time. The sequence will never repeat
(as pi is not rational), and it will have an even limit-distribution
of numbers.

>        Hardware random number generation can be done using something that
>        counts random events, like the atmospheric noise froma tuned out
>        radio etc. 

Noise from a diode has often been used. Note that you will not
normally have an even distribution of values from such a source, but
see the discussion about unfair coins for how to generate even
distribution from an uneven source with unknown distribution.

	Torben Mogensen (torbenm@diku.dk)
Newsgroups: rec.puzzles
From: kanad@quip.eecs.umich.edu (Kanad Chakraborty)
Subject: Re: An(other) *easy* puzzle.
Organization: University of Michigan EECS Dept., Ann Arbor
Date: Sat, 9 Jan 1993 16:37:03 GMT

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:
>>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.

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
distance AB = x units.  Then any equilateral triangle with A
as one vertex and side < x units has all three vertices colored
blue, for obvious reasons.

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

If x > 1 cm in the previous proof, the above is possible. Otherwise,
I don't see right off hand a way to construct such an equilateral triangle.

>-YH


Kanad
From: landman@hal.COM (Howard Landman)
Newsgroups: rec.puzzles
Subject: Re: Help me with MH puzzle, also, a new puzzle.
Date: 10 Jan 93 06:45:19 GMT
Organization: HaL Computer Systems, Inc.
NNTP-Posting-Host: bang.hal.com

In article <1i7cb6INNe0@mirror.digex.com> adric@access.digex.com (William Johnson) writes:
>	A) Spin shoot spin shoot
>	C) Shoot spin shoot
>
>But I don't see the difference between A and C, unless in case C you know
>in advance that where you put the bullet either was or was not in the
>next chamber to be fired.

The gun was handed to you by someone who just fired and had an empty chamber.
Now do you see why A is better?

	Howard A. Landman
Newsgroups: rec.puzzles
From: potamian@hpl.hp.com (Spyros Potamianos)
Subject: Unfair coin
Date: Tue, 5 Jan 1993 20:46:28 GMT
Reply-To: potamian@hpl.hp.com
Organization: Hewlett-Packard Company

Here's a little probability problem I thought on my way to work (yes, it's
a looooong drive! :-)

Given an unfair coin (with unknown probabilities for head/tail) how can you
approximate a given probability P ?
I.e. try to devise a sequence of tosses and a "winning" combination of
results, so that the probability of achieving this combination is P',
where
    abs(P'-P) < e
for any given error margin 'e'

a) For what values of P the simulation is exact, i.e. you can achieve P=P'
   with a finite number of tosses ?
b) In general, as e-->0, the number of tosses needed in the worst case
   goes to infinity. However the average number of tosses is finite. Find
   it!

Spyros Potamianos
potamian@hpl.hp.com

P.S. Here is a hint from the FAQ...... 


==> probability/unfair.p <==
Generate even odds from an unfair coin.  For example, if you
thought a coin was biased toward heads, how could you get the
equivalent of a fair coin with several tosses of the unfair coin?

Solution follows....


==> probability/unfair.s <==
Toss twice.  If both tosses give the same result, repeat this process
(throw out the two tosses and start again).  Otherwise, take the first
of the two results.
Newsgroups: rec.puzzles
From: aa382@Freenet.carleton.ca (Marc Sira)
Subject: Re: Port Holes
Reply-To: aa382@Freenet.carleton.ca (Marc Sira)
Organization: The National Capital Freenet
Date: Thu, 7 Jan 1993 18:29:28 GMT


In a previous article, deghare@daisy.uwaterloo.ca (Dave Hare) says:

>And an even more serious question is: Why are airplane windows (roughly)
>round?

Actually, they're rounded rectangles, but "why are they rounded" is a good
question. It occurs to me that the window+hull interface is stronger with
rounded corners than without, in terms of distributing pressure (which may
be what you mean by "an even more serious question?"). I don't know if the
same applies to submerged portholes on ships, at least in terms of the
design decision.

Come to think of it, wouldn't round airplane windows be a sounder design
than the existing sort?


-- 
Marc Sira                    |
toh@micor.ocunix.on.ca       |  "Your god drinks...p-p-peach nectar!"
aa382@freenet.carleton.ca    '
From: wilson@gauss.cs.jhu.edu (Dwight Wilson)
Newsgroups: rec.puzzles
Subject: Re: Port Holes
Date: 7 Jan 93 00:57:42 GMT
Organization: The Johns Hopkins University CS Department

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!
>

No no, port holes are circles because they're noughtical.

-Dwight
From: davidm@erie.aruba.UUCP (David MacMahon)
Newsgroups: rec.puzzles
Subject: Re: Port Holes
Date: 8 Jan 93 17:27:09 GMT

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?
|> 
|> 
|> 
|> 
|> -- 
|> i.sinature

I'm not sure, but I think it has to do with the fact that it is much easier
to seal a round hole (no corners) than it is a non-round hole (corners).

David MacMahon
davidm@opl.com
From: grayt@Software.Mitel.COM (Tom Gray)
Newsgroups: rec.puzzles
Subject: Port Holes
Date: 6 Jan 93 21:09:44 GMT
Organization: Mitel. Kanata (Ontario). Canada.


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?




-- 
i.sinature
From: landman@hal.COM (Howard Landman)
Newsgroups: rec.puzzles
Subject: Re: Manhole covers - why circular?
Date: 10 Jan 93 06:53:44 GMT
Organization: HaL Computer Systems, Inc.
NNTP-Posting-Host: bang.hal.com

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?

That they can't fall into their holes, which are the same shape but slightly
smaller.  There's no way to get a diameter of the cover through the hole,
and no matter what orientation you choose you'll have to do that to fall in.

>What other shapes would also satisfy the condition?

At a minimum, any shape of constant diameter.  A non-circular example is the
shape formed by three circular arcs, each of which is 1/3rd of a circle.
(Start with an equilateral triangle, put the points of a compass at two
corners, draw the arc to the other corner; repeat for all three arcs.)

	Howard A. Landman
Newsgroups: rec.puzzles,rec.org.mensa
From: hector@sci.ccny.cuny.edu (Hector Garcia)
Subject: Palindrome (ORIGINAL)
Organization: City College of New York - Science Computing Facility
Date: Tue, 12 Jan 1993 22:46:57 GMT

Here is a palindrome I just thought about. I hope that you all enjoy it, and
that the given information makes it challenging, yet doable.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Those who score very low on IQ tests take me for an Egyptian deity.

_ _ _ _    _ _    _ _ _ _ _ _    _ _    _


Every dash stands for a letter. No offense of any kind is intended to anyone.
-----------------------------------------------------------------------------
Hector C. Garcia		hector@sci.ccny.cuny.edu
EE Dept. City College		eehcg@ees1s0.engr.ccny.cuny.edu
-----------------------------------------------------------------------------
Newsgroups: rec.puzzles
From: joelw@convex.com (Joel Williamson)
Subject: Re: 19
Date: Thu, 7 Jan 1993 13:59:23 GMT
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 <1993Jan7.080754.14350@dde.dk> ct@dde.dk (Claus Tondering) writes:
>What computer operating system could be spelled thus:
>
>		19
>

		Un-nix, perhaps.

Joel Williamson
-- 

Newsgroups: rec.puzzles,rec.org.mensa
From: hector@sci.ccny.cuny.edu (Hector Garcia)
Subject: Another palindrome (ORIGINAL)
Organization: City College of New York - Science Computing Facility
Date: Wed, 13 Jan 1993 00:33:16 GMT

A measure of the intellectual ability of the this medium was found to be
countable with fingers:

_ _ _ _    _ _    _ _    _ _ _


_________________________________________________________________________
Hector C. Garcia	hector@sci.ccny.cuny.edu	City College
EE- Dept.		eehcg@ees1s0.engr.ccny.cuny.edu