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Topic: re: how many coins?
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Posts: 6
Registered: 12/6/04
re: how many coins?
Posted: Apr 7, 1995 8:07 AM
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From: 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????

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