HDTenEightyP/NetNews huggingface dataset:
From: imc@comlab.ox.ac.uk (Ian Collier)
Newsgroups: rec.puzzles
Subject: Re: Diameter of earth?
Date: 5 Oct 92 12:55:17 GMT
Organization: Oxford University Computing Laboratory, UK
X-Local-Date: Monday, 5th October 1992 at 1:55pm BST
Originator: imc@msc3.comlab

In article <1992Oct5.031617.18844@cs.cornell.edu>, karr@cs.cornell.edu
(David Karr) wrote:
>                                                           it isn't
>even necessary for the two observers to be on exactly the same line of
>longitude.  They'll make their observations a few minutes apart since
>each goes according to local noon, but the difference will be wiped
>out by other errors of measurement.

...that "difference" being, of course, the error in the measured distance -
not any difference in time: doing both observations at local noon ensures
that the rotation of the Earth will cancel out any east-west component in the
separation of the points, but this will mean that the points are actually
closer together than you thought.  However, even if your "north" is 10
degrees away from true north, the error in the measured distance will be
less than 2%.

Ian Collier
Ian.Collier@prg.ox.ac.uk | imc@ecs.ox.ac.uk
Newsgroups: rec.puzzles
From: amorgan@csd-d-3.Stanford.EDU (Crunchy Frog)
Subject: Re: Diameter of earth?
Originator: amorgan@csd-d-3.Stanford.EDU
Organization: /usr/lib/news/organizatoin
Date: Sun, 4 Oct 1992 18:54:42 GMT

In article <1alpsdINNg1n@gap.caltech.edu> carl@SOL1.GPS.CALTECH.EDU writes:
>In article <7451@charon.cwi.nl>, dik@cwi.nl (Dik T. Winter) writes:
>>I like this.  When is it noon?  How do you find out when it is noon?
>
>Find a level piece of ground.  Drive a stake into it vertically.  When the
>shadow of the stake is shortest, it's noon, and the shadow is pointing due
>north.

Yes, that is fine for the person at the stake.  The point behind your
method is that two people at different places must measure the
angle of the sun *at the same time*.  You have the stake.  You are in
Slobovia.  I am in Afbonistan.  We both make measurements of the suns
angle when it is noon in Slobovia.  How do *I* know when it is noon in
Slobovia?

C Frog
From: clong@remus.rutgers.edu (Chris Long)
Newsgroups: rec.puzzles
Subject: Re: One Vowel... Two Syllables
Date: 1 Oct 92 03:39:47 GMT
Organization: Rutgers Univ., New Brunswick, N.J.

In article <1992Sep25.180902.18685@questrel.com>, Chris Cole writes:

> Vowels
> longest one vowel strengths (9,1)  

This is the NI3 record, but "tsktsking" ties it in the OSPD.
-- 
Chris Long, 265 Old York Rd., Bridgewater, NJ  08807-2618
From: acheng@ncsa.uiuc.edu (Albert Cheng)
Newsgroups: rec.puzzles
Subject: Re: Chess-problem
Date: 2 Oct 92 20:08:20 GMT
Organization: Nat'l Ctr for Supercomp App (NCSA) @ University of Illinois
Originator: acheng@shalom.ncsa.uiuc.edu


In article <1992Oct2.182648.1904@news.eng.convex.com>, Dave Dodson <dodson@convex.COM> writes:
>Onar, I'd like to check my understanding of your puzzle.  I think you are
>assuming that all the queens will placed on the board first such that the
>king will be in checkmate no matter where it is placed.  Is this correct?
>
>If so, I see such a position for 7 queens.

6 queens can do too.  Put them from b2 to b7.  All rows from 2 to 7
are checked.  a8 to c8 checked by queen at b7.  d8 to h8 checked by
queens at b6 to b2 respectively.  Same for the row 1.  All squares
checked.
Newsgroups: rec.puzzles
From: Dave Dodson <dodson@convex.COM>
Subject: Re: Chess-problem
Originator: dodson@bach.convex.com
Date: Fri, 2 Oct 1992 18:26:48 GMT
Reply-To: dodson@convex.COM (Dave Dodson)
Organization: Engineering, CONVEX Computer Corp., Richardson, Tx., USA
X-Disclaimer: This message was written by a user at CONVEX Computer
              Corp. The opinions expressed are those of the user and
              not necessarily those of CONVEX.

In article <1992Oct2.121459.27750@hsr.no> onar@hsr.no (Onar Aam) writes:
>Given that you have a chessboard and one black king, how many white queens is
>the least that is required to checkmate the king without moving the queens?
>
>presumptions:
>there is no white king on the board
>the black king can be placed at any vacant spot.

Onar, I'd like to check my understanding of your puzzle.  I think you are
assuming that all the queens will placed on the board first such that the
king will be in checkmate no matter where it is placed.  Is this correct?

If so, I see such a position for 7 queens.

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

Dave Dodson		                             dodson@convex.COM
Convex Computer Corporation      Richardson, Texas      (214) 497-4234
From: bjackson@mentor.cc.purdue.edu (Ben Jackson)
Newsgroups: rec.puzzles
Subject: Re: One Vowel... Two Syllables
Date: 1 Oct 92 19:18:58 GMT
Organization: Purdue University Computing Center

In article <Sep.30.23.39.46.1992.6244@remus.rutgers.edu> clong@remus.rutgers.edu (Chris Long) writes:
>In article <1992Sep25.180902.18685@questrel.com>, Chris Cole writes:
>
>> Vowels
>> longest one vowel strengths (9,1)  
>
>This is the NI3 record, but "tsktsking" ties it in the OSPD.

NI3, Nitrogen tri-iodide, is a pretty potent contact-explosive.  I am
assuming from this you mean some OTHER NI3. :)

\\_//
 o o    Ben Jackson
< ^ >   bjackson@mentor.cc.purdue.edu
 \~/         ...@glia.biostr.washington.edu
  V     "Natural laws have no pity."
From: carl@SOL1.GPS.CALTECH.EDU (Carl J Lydick)
Newsgroups: rec.puzzles
Subject: Re: Diameter of earth?
Date: 4 Oct 1992 19:18:24 GMT
Organization: HST Wide Field/Planetary Camera
Reply-To: carl@SOL1.GPS.CALTECH.EDU
NNTP-Posting-Host: sol1.gps.caltech.edu

In article <1992Oct4.185442.14447@CSD-NewsHost.Stanford.EDU>, amorgan@csd-d-3.Stanford.EDU (Crunchy Frog) writes:
>In article <1alpsdINNg1n@gap.caltech.edu> carl@SOL1.GPS.CALTECH.EDU writes:
>>In article <7451@charon.cwi.nl>, dik@cwi.nl (Dik T. Winter) writes:
>>>I like this.  When is it noon?  How do you find out when it is noon?
>>
>>Find a level piece of ground.  Drive a stake into it vertically.  When the
>>shadow of the stake is shortest, it's noon, and the shadow is pointing due
>>north.
>
>Yes, that is fine for the person at the stake.  The point behind your
>method is that two people at different places must measure the
>angle of the sun *at the same time*.  You have the stake.  You are in
>Slobovia.  I am in Afbonistan.  We both make measurements of the suns
>angle when it is noon in Slobovia.  How do *I* know when it is noon in
>Slobovia?

That's why I said that you wanted to be at the same longitude.  That way, noon
is at the same time both places.  Picking two places at the same longitude but
separated by a large enough distance to make the estimate reliable is a matter
of figuring out to sufficient precision which way north is, and then some
surveying.  Not a trivial task, but not impossible, either.
--------------------------------------------------------------------------------
Carl J Lydick | INTERnet: CARL@SOL1.GPS.CALTECH.EDU | NSI/HEPnet: SOL1::CARL

Disclaimer:  Hey, I understand VAXen and VMS.  That's what I get paid for.  My
understanding of astronomy is purely at the amateur level (or below).  So
unless what I'm saying is directly related to VAX/VMS, don't hold me or my
organization responsible for it.  If it IS related to VAX/VMS, you can try to
hold me responsible for it, but my organization had nothing to do with it.
From: lsonko@pearl.tufts.edu (FLOCCINAUCHINIHILIPIPIFICATION- LOOK IT UP)
Newsgroups: rec.puzzles
Subject: Re: Packing problem
Date: 6 Oct 92 22:28:00 GMT
Organization: Tufts University - Medford, MA
News-Software: VAX/VMS VNEWS 1.41

In article <1992Oct6.020647.4651@ils.nwu.edu>, blum@news.ils.nwu.edu (Daniel Blum) writes...
>A few years ago, this puzzle appeared in the newsletter of the company
>I was working for:
> 
>   Given an infinitely long rectangular strip which is two units wide,
>and circles with diameters of one unit, one can pack them in parallel
>rows of two, like so:
>                      _____________________________
>                      |oooooooooooooooooooooooooooo...
>                      |oooooooooooooooooooooooooooo...
>                      -----------------------------
>However, there is a more efficient packing.  What is it?
> 
>Unfortunately, I left the company before the solution was given, and
>as fas as _I_ can see, there is no solution.  Any ideas?  
>(Note: I assumed that "more efficient," or whatever the exact original
>phrase was [definitely similar] means that the ratio of covered to
>uncovered area is higher than that of the "obvious" packing - I can't
>think of what else it COULD mean.)

I know I know I know!  (grin)     at least I think I do...

but let me give another question in reply to yours!

a freighter was to carry a shipment of ball bearings to a bicycle plant down
the river.  The captain of the ship noted the volume of his hold and the
density of steel (what the bearings were made of, of course).  He then told the
guy loading the ship to only fill the ship three quarters full, lest the ship
sink under the weight of the bearings.  The loader thought about this for a
moment and told the captain not to worry.  Despite the captain's objections, he
loaded the holds to their maximums. Low and behold, the ship did not sink and
everyone lived happily ever after (especially the captain who moved more
bearings than he expected, making a large bonus).

What did the loader know?

enjoy,
lee
Newsgroups: rec.puzzles
From: lrm28@cas.org ()
Subject: Another poser
Summary:  vowels to consonants
Keywords: That would be telling...
Organization: Chemical Abstracts Service, Columbus, Ohio
Date: Wed, 30 Sep 1992 17:33:17 GMT

List words of 4 letters or more which have the highest ratio
of vowels to consonants.

Ex.  eerie has 4 vowels to one consonant, or 80% vowels.

Now where did I put that dictionary...
-- 
Luke Mayercin  lrm28@cas.org  "Why does ear wax taste like it does?"
Chemical Abstracts Service is not responsible for these comments.
From: bultman@dgw.rws.nl (G.W.Bultman)
Newsgroups: rec.puzzles
Subject: Solution 1-26 (LaTeX)
Date: 6 Oct 1992 08:29:40 -0500
Organization: UTexas Mail-to-News Gateway
NNTP-Posting-Host: cs.utexas.edu

% Assuming that almost everybody has either LaTeX or a PostScript printer
% or both) here is the solution for the 1-26 puzzle.
\documentstyle[dina4]{article}
\pagestyle{\empty}
\begin{document}
\noindent{\bf Puzzle}: 

\noindent Make the numbers 1-26 using only 2's and 6's and the operators
$+$,$-$,$\times$,$/$,$!$,$\sqrt{\phantom{0}}$ and $**$ (exponentiation).
An extra conditon is that for each number an {\bf equal} number of 2's and 
6's must be used.

\bigskip

\noindent{\bf Solution}:

% make the strut 6pt taller and 6pt deeper than the entry for 17
\setbox0=\hbox{$\frac{6\times6-2}{2}$}%
\dimen0=\ht0 \advance\dimen0 by 6pt
\dimen2=\dp0 \advance\dimen2 by 6pt
\setbox\strutbox\hbox{\vrule width0pt depth\dimen2 height \dimen0 }

\begin{center}
\begin{tabular}{|rc|rc|}
\multicolumn{1}{c}{\rule{1.5cm}{0pt}}&
\multicolumn{1}{c}{\rule{5cm}{0pt}}&
\multicolumn{1}{c}{\rule{1.5cm}{0pt}}&
\multicolumn{1}{c}{\rule{5cm}{0pt}} \\ [-15pt]
\multicolumn{4}{c}{\bf \LARGE 26 } \\ \hline
 1: & $ \frac{26}{26}             $ & 14: &  $ 26-6\times2           $ \\ \hline
 2: & $ \sqrt{6-2}                $ & 15: &  $ 6\times2+\frac{6}{2}  $ \\ \hline
 3: & $ \frac{6}{2}               $ & 16: &  $ 6+6+2+2               $ \\ \hline
 4: & $ 6-2                       $ & 17: &  $ \frac{6\times6-2}{2}  $ \\ \hline
 5: & $ 2+2+\frac{6}{6}           $ & 18: &  $ 26-6-2                $ \\ \hline
 6: & $ \sqrt{6^2}                $ & 19: &  $ \frac{26}{2}+6        $ \\ \hline
 7: & $ 6-2+\frac{6}{2}           $ & 20: &  $ 6\times2+6+2          $ \\ \hline
 8: & $ 6 + 2                     $ & 21: &  $ 22-\frac{6}{6}        $ \\ \hline
 9: & $ \frac{6\times6}{2\times2} $ & 22: &  $ 22+6-6                $ \\ \hline
10: & $ 22-6-6                    $ & 23: &  $ 22+\frac{6}{6}        $ \\ \hline
11: & $ 6+6-\frac{2}{2}           $ & 24: &  $ (6-2)!                $ \\ \hline
12: & $ 6\times2                  $ & 25: &  $ \frac{62}{2}-6        $ \\ \hline
13: & $ 6+6+\frac{2}{2}           $ & 26: &  $ 26                    $ \\ \hline
\end{tabular}
\end{center}

\bigskip

\noindent{\bf Remarks}:

\noindent In choosing the `best' solutions, the solution with the least
number of digits always `won'; when tied, the solution using the least 
number of operators was preferred; in case of another tie, the solution 
with the least complex operators was chosen. 
Required brackets were counted as one operator:
$(\frac{6}{2})!$ has 3 operators (couting the brackets), 
$ (6-2)+\frac{6}{2} $ also has 3 operators.

\noindent The solution for 15 (JvdL) using the binomial operator is noted, but discarded.

\bigskip

\noindent{\bf Contributors}:

\begin{list}{$\bullet$}{\itemsep 0in \parsep 0in}
\item Hans Braker, $<$witajgb@dutinfh.tudelft.nl$>$
\item Janneke v.d. Linden, $<$linden@dgw.rws.nl$>$
\item Michael Maciolek, $<$mikem@ll.mit.edu$>$
\item T. Steidten, $<$Steidten@mathematik.tu-chemnitz.de$>$
\item Gert Bultman, $<$bultman@dgw.rws.nl$>$
\end{list}

\end{document}
From: acheng@ncsa.uiuc.edu (Albert Cheng)
Newsgroups: rec.puzzles
Subject: Re: Chess-problem
Date: 2 Oct 92 19:08:29 GMT
Article-I.D.: news.BvID66.3Dz
Organization: Nat'l Ctr for Supercomp App (NCSA) @ University of Illinois
Originator: acheng@shalom.ncsa.uiuc.edu


In article <1992Oct2.163046.18247@fid.morgan.com>, sethb@fid.morgan.com (Seth Breidbart) writes:
>In article <1992Oct2.121459.27750@hsr.no> onar@hsr.no (Onar Aam) writes:
>>Given that you have a chessboard and one black king, how many white queens is the
>>least that is required to checkmate the king without moving the queens?
>>
>>
>>presumptions:
>>there is no white king on the board
>>the black king can be placed at any vacant spot.

I interpret that means whichever square the black king is placed,
it is checkmated.

>You can always place two white queens such that the black king is
>under attack from both of them and after any possible move will still
>be under attack from at least one of them.

How come?  A queen can control at most 28 squares.  Two queens can't
control more than 56 squares (the control squares overlap too.)
So, there are at least 8 more squares for the black king to land on
safely.  Stalemate maybe, but not checkmate.
control 
Newsgroups: rec.puzzles
From: amorgan@csd-d-1.Stanford.EDU (Crunchy Frog)
Subject: Re: Packing problem
Originator: amorgan@csd-d-1.Stanford.EDU
Organization: /usr/lib/news/organizatoin
Date: Tue, 6 Oct 1992 20:47:53 GMT

In article <1992Oct6.020647.4651@ils.nwu.edu> 
  blum@news.ils.nwu.edu (Daniel Blum) writes:
>   Given an infinitely long rectangular strip which is two units wide,
>and circles with diameters of one unit, one can pack them in parallel
>rows of two, like so:
>                      _____________________________
>                      |oooooooooooooooooooooooooooo...
>                      |oooooooooooooooooooooooooooo...
>                      -----------------------------
>However, there is a more efficient packing.  What is it?

O O O
 O O    .........\
O O O            /

(I hope you get it from this, ascii isn't the best for this sort of thing).

C Frog
From: tolman%asylum.cs.utah.edu@cs.utah.edu (Kenneth Tolman)
Newsgroups: rec.puzzles
Subject: Diameter of earth?
Date: 3 Oct 92 22:39:47 GMT
Organization: University of Utah, CompSci Dept


  How can you measure the diameter of the earth, using everyday tools
that a typical person would have access to?  This means MEASURE, not look
up the answer someone else determined.  I want to measure the diameter of
the earth, and if some other people did to we could compare answers!
Newsgroups: rec.puzzles
From: de@cray.com (Duane Eitzen)
Subject: Re: Packing problem
Organization: Cray Research, Inc.
Date: 6 Oct 92 09:38:00 CDT

In article <1992Oct6.020647.4651@ils.nwu.edu> blum@news.ils.nwu.edu (Daniel Blum) writes:
>A few years ago, this puzzle appeared in the newsletter of the company
>I was working for:
>
>   Given an infinitely long rectangular strip which is two units wide,
>and circles with diameters of one unit, one can pack them in parallel
>rows of two, like so:
>                      _____________________________
>                      |oooooooooooooooooooooooooooo...
>                      |oooooooooooooooooooooooooooo...
>                      -----------------------------
>However, there is a more efficient packing.  What is it?
>
>Unfortunately, I left the company before the solution was given, and
>as fas as _I_ can see, there is no solution.  Any ideas?  
>(Note: I assumed that "more efficient," or whatever the exact original
>phrase was [definitely similar] means that the ratio of covered to
>uncovered area is higher than that of the "obvious" packing - I can't
>think of what else it COULD mean.)

If you take the top row of circles and shift it half a unit to the right,
it can pack a little closer to the bottom row. This actually loses a bit
of "efficiency" but its a fixed amount on an infinite problem. 

What this buys you is some headroom. I think that by breaking the lines of
circles into segments, and tilting the segments, you may be able to pack
things tighter than they were originally. I'll leave the math to someone else.

Duane.
From: isaak@aurora.com (Mark Isaak)
Newsgroups: rec.puzzles
Subject: Re: No vowels, One syllable
Summary: Some logical answers.
Date: 1 Oct 92 20:33:56 GMT
Reply-To: isaak@aurora.com (Mark Isaak)
Organization: The Aurora Group

"nth".

Which reminds me, "xor" could be considered a word with one vowel and
two syllables, at least as I usually hear it pronounced (ex-or), and
"iff" (if and only if) has one vowel and five syllables!

I know "nth" is sanctioned by some dictionaries, but I'm not so sure
about the others.
-- 
Mark Isaak           "Every generation thinks it has the answers, and every
isaak@aurora.com      generation is humbled by nature." - Philip Lubin
Newsgroups: rec.puzzles
From: amorgan@Xenon.Stanford.EDU (Crunchy Frog)
Subject: Re: Diameter of earth?
Organization: Computer Science Department, Stanford University.
Date: Sun, 4 Oct 1992 00:02:12 GMT

In article <1992Oct3.163947.17166@hellgate.utah.edu> 
  tolman%asylum.cs.utah.edu@cs.utah.edu (Kenneth Tolman) writes:
>  How can you measure the diameter of the earth, using everyday tools
>that a typical person would have access to?  This means MEASURE, not look
>up the answer someone else determined.  I want to measure the diameter of
>the earth, and if some other people did to we could compare answers!

Go to a nice, flat part of the Earth.  Determine the distance of the
furthest visible point on the ground (figuring out how to do this is
left as an exercise for the reader.  I have a few ideas).  Given the 
height of your eyes and that distance, computing the diameter of the 
Earth is trivial.

C Frog
From: bultman@dgw.rws.nl (G.W.Bultman)
Newsgroups: rec.puzzles
Subject: 'grading' 1-25,1-26 type puzzles
Date: 2 Oct 1992 02:16:44 -0500
Organization: UTexas Mail-to-News Gateway
NNTP-Posting-Host: cs.utexas.edu

Hi,

Thanks everybody, for your solutions. 
The 1-26 puzzle proved a lot easier than I thought, with hardly any 
surprises. The extension 26-62 was more difficult, and had as a pleasant
surprise the solution for 45 (Look for it in the posting next week, if
you didn't come up with it yourself). 
However, the 2nd series was very long and you may have found it a bit 
boring because it lacked enough challenge (a lot of easy solutions). 

I'm always open to any suggestions for new puzzles of this type.

I have a whole stack of them, but I find that you have to take a rest from
them or they tend to get a bit tedious.

I'll post a new one around Christmas.

In the meantime, someone asked me for the 'optimal or most elegant solution'
which set me thinking about how to grade solutions to these puzzles.

I have sofar come up with a scheme that allocates certain amounts of points
to the digits and the operators; the idea is to declare the solution with the 
least number of points the winner. 

          A digit       4 points
          + - * /       1 point    (or should there be a difference between
                                    + - and * / ??)
          sqrt ^        2 points
          !             3 points

But my system is not watertight: should a solution with fewer digits always 
win? and if so, how do you give points so that a solution with fewer digits 
always wins? (maybe by omitting points for digits and just grading the 
opertors?)

Is sqrt(sqrt(8+8)) not more elegant than (8+8)/8 even though more complex 
operators are used?
And how about 3!! versus (3+3)!

I'm looking forward to sharing your ideas on this.

--

    o                                                                o   
  / | \    Gert Bultman <bultman@dgw.rws.nl>   Koningskade 4       / | \  
 o--o--o   Tidal Waters Division               2596 AA The Hague  o--o--o 
  \ | /    Rijkswaterstaat                     The Netherlands     \ | /  
    o                                                                o
From: carl@SOL1.GPS.CALTECH.EDU (Carl J Lydick)
Newsgroups: rec.puzzles
Subject: Re: Diameter of earth?
Date: 4 Oct 1992 03:53:49 GMT
Organization: HST Wide Field/Planetary Camera
Reply-To: carl@SOL1.GPS.CALTECH.EDU
NNTP-Posting-Host: sol1.gps.caltech.edu

In article <7451@charon.cwi.nl>, dik@cwi.nl (Dik T. Winter) writes:
>In article <1aleqmINNk87@gap.caltech.edu> carl@SOL1.GPS.CALTECH.EDU writes:
> > I prefer the originally published technique:  Measure the angle of the sun
> > from the horizon at noon from two places at the same longitude but different
> > latitudes, and a known distance apart.  Simple trigonometry will give you an
> > estimate of the diameter of the earth.
>I like this.  When is it noon?  How do you find out when it is noon?

Find a level piece of ground.  Drive a stake into it vertically.  When the
shadow of the stake is shortest, it's noon, and the shadow is pointing due
north.
--------------------------------------------------------------------------------
Carl J Lydick | INTERnet: CARL@SOL1.GPS.CALTECH.EDU | NSI/HEPnet: SOL1::CARL

Disclaimer:  Hey, I understand VAXen and VMS.  That's what I get paid for.  My
understanding of astronomy is purely at the amateur level (or below).  So
unless what I'm saying is directly related to VAX/VMS, don't hold me or my
organization responsible for it.  If it IS related to VAX/VMS, you can try to
hold me responsible for it, but my organization had nothing to do with it.
From: jw7348@norway.medtronic.com (Jeff Wilkinson)
Subject: Re: No vowels, One syllable
Organization: Medtronic, Inc., Minneapolis, MN
Date: Thu, 1 Oct 1992 13:16:08 GMT

In article <DV0wRB1w164w@cellar.org> kml@cellar.org (Scott Tiger) writes:
>Given that we've beaten the one-vowel, two-syllable puzzle into the ground,
>how about a no-vowel, one-syllable word.  I know of one in Webster's.
>I does not contain an A,E,I,O,U,or Y.
>
>Any takers?
>

Nth is in there, but it hardly seems like a "real" word.

wilk


Newsgroups: rec.puzzles
From: amorgan@csd-d-3.Stanford.EDU (Crunchy Frog)
Subject: Re: Packing problem
Originator: amorgan@csd-d-3.Stanford.EDU
Organization: /usr/lib/news/organizatoin
Date: Wed, 7 Oct 1992 00:13:21 GMT

In article <1992Oct6.220449.22024@ils.nwu.edu> 
  blum@news.ils.nwu.edu (Daniel Blum) writes:
>
>Wrong.  The efficiency of the original packing is pi/4.  The
>efficiency of this packing approaches (3*pi)/(8*sqrt(3)) as a limit,
>which is smaller.  This is assuming that I did the math correctly -

I'm sure you did (I didn't actually do any math - I was generalizing from
the multi-row case).  Sorry.

C Frog