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re: how many coins?
Posted:
Apr 7, 1995 8:07 AM


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 for economy in packaging. Three rows of 1 cm diameter "rigid" coins can be fit into a 2000 sq. cm. rectangle that is approximately 2.7321 cm by 732.04 cm. Two rows (top and bottom) will contain 732 coins while the middle row will contain 731 for a total of 2195 coins in 2000 sq. cm. of space.
QUESTION #1: What is the maximum number of "rigid" coins 1 cm in diameter 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 with triangle, hexagon, circle, ...
Anybody for ping pong????



