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        riddles >> medium >> how many non overlapping
        
(Message started by: tony123 on Nov 1^st, 2007, 7:37pm)

Title: how many non overlapping
Post by tony123 on Nov 1^st, 2007, 7:37pm

how many non overlapping 2 by 2 squares will fit into a circle with radies 8

Title: Re: how many non overlapping
Post by mikedagr8 on Nov 2^nd, 2007, 1:56am

I'll have a go at 16

Title: Re: how many non overlapping
Post by towr on Nov 2^nd, 2007, 2:32am

I can fit at least 33, and that's without really trying..

[e]39 with a bit more care[/e]

Title: Re: how many non overlapping
Post by mikedagr8 on Nov 2^nd, 2007, 2:35am

I see why I have so few, I read 'radii' as diameter. So that's where I 've gone wrong... :P

Title: Re: how many non overlapping
Post by towr on Nov 2^nd, 2007, 2:42am

on 11/02/07 at 02:35:30, mikedagr8 wrote:

I see why I have so few, I read 'radii' as diameter. So that's where I 've gone wrong... :P

Ah, that would make a bit of a difference, yes.
Although then you'd have a greater area in squares than your circle.. 16*2² > (8/2)²*http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/pi.gif

Title: Re: how many non overlapping
Post by mikedagr8 on Nov 2^nd, 2007, 2:55am

on 11/02/07 at 02:42:07, towr wrote:

Ah, that would make a bit of a difference, yes.
Although then you'd have a greater area in squares than your circle.. 16*2² > (8/2)²*http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/pi.gif

Yes, that'd be annoying. But all fixed now.

Title: Re: how many non overlapping
Post by Grimbal on Nov 2^nd, 2007, 4:10am

I found a page that can fit 35 in a circle of radius 7.3 roughly. It is listing the smallest circle that fits a given number of squares up to 35.
Given the relation between number of squares and radius listed there, I would estimate the maximum number for radius 8 to about 42.

Title: Re: how many non overlapping
Post by mikedagr8 on Nov 2^nd, 2007, 4:13am

Are you going to write a program to prove your suspicion, or should I just be patient? :)

Title: Re: how many non overlapping
Post by Grimbal on Nov 2^nd, 2007, 5:23am

When I look at the solutions up to 35
http://www.stetson.edu/~efriedma/squincir/
it should be far from obvious.

Title: Re: how many non overlapping
Post by towr on Nov 2^nd, 2007, 5:55am

I got up to 40 now.. Using parallel rows of 3,6,7,7,7,6,4