```Date: Apr 7, 1995 8:07 AM
Author: DAVE_LUNSFORD@gcccd.cc.ca.us
Subject: re: how many coins?

From:	tad@midget.towson.edu on	Fri Apr 7>Does anyone have a proof to the following:>>Given a rectangular region of 2cm by 1000cm.  You can fit 2011>(I think  it was 2011.  It is more than 2000) coins of 1cm>diameter in this region.>>On the surface, it appears that the answer should be 2000, but>someone at  the Bell Lab apparently proved that you can fit more>(which, by the way,  is very significant for communication folks>since each "coin" can be a  fiberoptic cable in an underground>cable cases).>************************************************************************As Jim Austin points out, there need to be at least 3 rows foreconomy in packaging.  Three rows of 1 cm diameter "rigid" coinscan be fit into a 2000 sq. cm. rectangle that is approximately2.7321 cm by 732.04 cm.  Two rows (top and bottom) will contain732 coins while the middle row will contain 731 for a total of2195 coins in 2000 sq. cm. of space.QUESTION #1:  What is the maximum number of "rigid" coins 1 cm indiameter that can be fit into a rectangular area of 2000 sq. cm.?QUESTION #2:  What is the maximum number of "rigid" coins 1 cm.in diameter that can be fit into a rectangle of area A sq. cm.Questions #3, 4, 5, ...:  Change Q #2 by replacing rectangle withtriangle, hexagon, circle, ...Anybody for ping pong????
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