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Main
Date: 09 Sep 2007 08:05:26
From: Carmine Clamenza
Subject: Don't subscribe to CYCLING.TV because they are thieves.
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Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
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Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
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Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
Don't subscribe to CYCLING.TV because they are thieves.
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Date: 09 Sep 2007 09:32:42
From: Mike Jacoubowsky
Subject: Re: Don't subscribe to CYCLING.TV because they are thieves.
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"Carmine Clamenza" <carmineclamenza@hotmail.com > wrote in message
news:IYTEi.7$fX6.6@newsfe04.lga...
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
> Don't subscribe to CYCLING.TV because they are thieves.
>
>
>
>
>
>
>
Oh, I get it, it's a contest to see who can figure out the minimum number of
cut-and-pastes for that many identical lines!
Are the blank lines at the end a clue? Or is that to throw us off?
--Mike-- Chain Reaction Bicycles
www.ChainReactionBicycles.com
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Date: 09 Sep 2007 17:02:56
From: Dan Connelly
Subject: Re: Don't subscribe to CYCLING.TV because they are thieves.
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Mike Jacoubowsky wrote:
> Oh, I get it, it's a contest to see who can figure out the minimum number of
> cut-and-pastes for that many identical lines!
>
Well, there's always copy-paste, starting with one line, doubling each iteration, yielding log2(N) * 2, where N is the final number of lines
1 copy
2 paste (2)
3 copy
4 paste (4)
5 copy
6 paste (8)
7 copy
8 paste (16)
9 copy
10 paste (32)
11 copy
12 paste (64)
But one can paste twice, yielding log3(N) * 3, improving on this:
1 copy
2 paste (2)
3 paste (3)
4 copy
5 paste
6 paste (9)
7 copy
8 paste
9 paste (27)
10 copy
11 paste
12 paste (81)
pasting 3 times, however, yields log4(N) * 4, = (log2(N) / 2) * 4 = log2(N) * 2, so no better than the first method:
1 copy
2 paste
3 paste
4 paste (4)
5 copy
6 paste
7 paste
8 paste (16)
9 copy
10 paste
11 paste
12 paste (64)
pasting 4 times, yields log5(N) * 5, which is worst of all.
Analytically, one can calculate the optimal n, where n is the number of pastes per cut:
d/dn logn(N) * n = d/dn (ln N / ln (n + 1)) * (n + 1) = ln N d/dn [ (n + 1) / ln (n + 1) ] = (ln N) [ 1 / ln (n + 1) - 1 / [ln (n + 1)]^2 ] = 0
solve for n:
ln (n + 1) = 0 = > n = e - 1
So e - 1 pastes per cut is optimal, but the closest integer is 2, which turns out to be the correct answer.
Dan
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Date: 09 Sep 2007 20:25:50
From: Michael Press
Subject: Re: Don't subscribe to CYCLING.TV because they are thieves.
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In article
<4HVEi.53159$YL5.29182@newssvr29.news.prodigy.net >,
Dan Connelly <d_j_c_o_n_n_e_l@y_a_h_o_o_._c_o_m >
wrote:
> Mike Jacoubowsky wrote:
>
> > Oh, I get it, it's a contest to see who can figure out the minimum number of
> > cut-and-pastes for that many identical lines!
> >
>
> Well, there's always copy-paste, starting with one line, doubling each iteration, yielding log2(N) * 2, where N is the final number of lines
>
> 1 copy
> 2 paste (2)
> 3 copy
> 4 paste (4)
> 5 copy
> 6 paste (8)
> 7 copy
> 8 paste (16)
> 9 copy
> 10 paste (32)
> 11 copy
> 12 paste (64)
>
> But one can paste twice, yielding log3(N) * 3, improving on this:
>
> 1 copy
> 2 paste (2)
> 3 paste (3)
> 4 copy
> 5 paste
> 6 paste (9)
> 7 copy
> 8 paste
> 9 paste (27)
> 10 copy
> 11 paste
> 12 paste (81)
>
> pasting 3 times, however, yields log4(N) * 4, = (log2(N) / 2) * 4 = log2(N) * 2, so no better than the first method:
>
> 1 copy
> 2 paste
> 3 paste
> 4 paste (4)
> 5 copy
> 6 paste
> 7 paste
> 8 paste (16)
> 9 copy
> 10 paste
> 11 paste
> 12 paste (64)
>
> pasting 4 times, yields log5(N) * 5, which is worst of all.
>
> Analytically, one can calculate the optimal n, where n is the number of pastes per cut:
>
> d/dn logn(N) * n = d/dn (ln N / ln (n + 1)) * (n + 1) = ln N d/dn [ (n + 1) / ln (n + 1) ] = (ln N) [ 1 / ln (n + 1) - 1 / [ln (n + 1)]^2 ] = 0
>
> solve for n:
>
> ln (n + 1) = 0 => n = e - 1
>
> So e - 1 pastes per cut is optimal, but the closest integer is 2, which turns out to be the correct answer.
If you want the optimal schedule for a final count of n,
I think the problem remains unsolved.
It goes under the appellation _addition_chains_.
--
Michael Press
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Date: 09 Sep 2007 21:34:07
From: Donald Munro
Subject: Re: Don't subscribe to CYCLING.TV because they are thieves.
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Dan Connelly wrote:
> solve for n:
>
> ln (n + 1) = 0 => n = e - 1
>
> So e - 1 pastes per cut is optimal, but the closest integer is 2, which turns out to be the correct answer.
Congratulations, you've won the 2007 rbr Nobel prize for Prolix
Mathematics.
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