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401 unit diameter Circles in a 400 unit rectangle


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15 replies to this topic

#1 BMAD

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Posted 14 July 2013 - 04:41 AM

In a rectangle that's 2 by 200 units long, it's trivial to draw 400 non-overlapping unit-diameter circles.

But in the same rectangle, can you draw 401 circles?


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#2 bonanova

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Posted 14 July 2013 - 08:35 AM

Spoiler for must be ...

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
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#3 gavinksong

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Posted 14 July 2013 - 11:15 AM

I'm pretty sure you can fit way more than 401 circles in the rectangle.


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#4 BMAD

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Posted 14 July 2013 - 02:03 PM

I'm pretty sure you can fit way more than 401 circles in the rectangle.

what would your array be?


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#5 gavinksong

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Posted 14 July 2013 - 03:59 PM

 

I'm pretty sure you can fit way more than 401 circles in the rectangle.

what would your array be?

 

Sorry. There was an error in my thinking. Is Bonanova right? I think so. I can't possibly think of another way of doing this.


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#6 BMAD

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Posted 14 July 2013 - 04:30 PM

on the right track, but no sure answer yet


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#7 TimeSpaceLightForce

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Posted 14 July 2013 - 09:17 PM

Spoiler for


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#8 bonanova

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Posted 15 July 2013 - 05:28 AM

Spoiler for

 

Spoiler for It has to be different in the following way


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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#9 plasmid

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Posted 15 July 2013 - 06:06 AM

Spoiler for I think gavinksong's comment may have hinted at the answer ...


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#10 bonanova

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Posted 15 July 2013 - 07:35 AM

Spoiler for It looks possible


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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell




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