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Message from discussion 2680 challenge
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The Last Danish Pastry  
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 More options Jan 24 2005, 5:01 pm
Newsgroups: sci.math, rec.puzzles
From: "The Last Danish Pastry" <cli...@gmail.com>
Date: Mon, 24 Jan 2005 22:01:16 -0000
Local: Mon, Jan 24 2005 5:01 pm
Subject: Re: 2680 challenge
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"Risto Lankinen" <rlank...@hotmail.com> wrote in message

news:dba955d3.0501241129.6e06321@posting.google.com...

> Clive Tooth wrote:
> > The text file
> > http://www.pisquaredoversix.force9.co.uk/2680.txt
> > consists of 2680 lines. Each line contains five integers. Each of these
> > integers is in the range 0 to 244. The challenge is to select 49 of the
2680
> > lines in such a way that each of the numbers from 0 to 244 is present in
the
> > selection.

> > I do not know if there is a solution to this challenge.

> This is a well-obfuscated way of asking if 5x7x7 box can be packed with
> the F-pentomino.  To see what is an F-pentomino, convert any line of the
> text file into base-7 and plot the (three) resultant 7:ary digits in 3D.

> There are 2680 orientations of an F-pentomino within a 5x7x7 box, and a
> quick (sample-based) check suggests that they are all represented in the
> text file.  Selecting a set of 49 non-overlapping integer lines hence is
> equivalent to finding a set of 49 F-pentominoes that fill the box.

> Quick scan of the net indicates that this may be an open problem in the
> art of packing theory...

> http://www.mathematik.uni-bielefeld.de/~sillke/PENTA/qu-prime

> [See "7) F1 box 5x7x7" near the end of the article.]

>  - Risto -

Yes, you have spotted what I was really asking.

The "48 line" set that I mentioned in another reply corresponds to the
packing (large and small) in this picture:
http://www.pisquaredoversix.force9.co.uk/48.png
The coin is a (Canadian) quarter.

My apologies to all for the deception... I was wondering if presenting the
question in the way that I did would lead to any new lines of attack on this
open problem.

--
Clive Tooth
http://www.clivetooth.dk


 
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