20110404, 23:41  #1 
"Lucan"
Dec 2006
England
194A_{16} Posts 
Smoker's packing probllem
2D: I resorted to a pack of 20 today.
(Having broken an arm recently, I find rolling up slightly tricky ATM) They were packed in 3 rows (as usual) but 776 instead of the more usual 767. OK fags are a bit squashy so this was conceivably down to transport or storage. I smoked one from the first 7 row considering the ugliness of the arrangement, and decided to arrange it better. Funnily enough I found the remaining 19 stacked appropriately enough in a neat 676 arrangement. David Last fiddled with by davieddy on 20110404 at 23:52 
20110405, 00:20  #2 
6809 > 6502
"""""""""""""""""""
Aug 2003
101Γ103 Posts
19×499 Posts 
Smoking fags has a completely different meaning in the USA.
As does throwing a bunch of fags into a roaring fire. 
20110405, 02:30  #3  
"Lucan"
Dec 2006
England
2·3·13·83 Posts 
Quote:
My next installment was going to be the 3D version entitled "stacking faggots". (Meatballs to us over here) David Last fiddled with by davieddy on 20110405 at 02:35 

20110405, 11:18  #4  
"Brian"
Jul 2007
The Netherlands
7×467 Posts 
Quote:
Quote:


20110405, 11:37  #5 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
13743_{8} Posts 

20110405, 13:22  #6 
Mar 2005
2×5×17 Posts 
milk bottles
It suggests something close to a puzzle I've been thinking about for some time* Its a variant of the milkcrate problem: what is the smallest square crate into which bottles can be packed more densely than a square lattice? i'm allowing a crate of otherthaninteger side length to make it nontrivial. It would work with ciggies if ciggies were sold in square packets: its a problem about unit discs within a square. For small numbers of discs the densest packing is a square lattice; for large numbers densest will be hexagonal. I'm asking where the 'crossover' comes.) Apologies if the answer is wellknown: I haven't googled an answer. Richard *this means I haven't solved it yet. 
20110405, 14:06  #7  
Aug 2006
3^{2}×5×7×19 Posts 
Quote:
Depending on your interpretation it's either 2 + sqrt(2) or 2 + sqrt(2)/2 + sqrt(6)/2. Scale these by 1/2 if you want diameter 1 instead of radius 1. Last fiddled with by CRGreathouse on 20110405 at 14:11 

20110405, 14:26  #8  
"Forget I exist"
Jul 2009
Dumbassville
20300_{8} Posts 
Quote:


20110405, 15:32  #9  
"Lucan"
Dec 2006
England
14512_{8} Posts 
Quote:
unaccustomed use of my left hand. OK, as warned, I am half blind, but the cause of the injury was simply falling over. David 

20110405, 15:43  #10  
Undefined
"The unspeakable one"
Jun 2006
My evil lair
5·1,223 Posts 
Quote:
Quote:
Sympathy shall now be dispensed as is appropriate ... ... oh wait, that was empathy. Let's try again ... 

20110405, 17:06  #11 
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
2992_{16} Posts 

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