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#1 2007-11-01 14:04:38

tony123
Member
Registered: 2007-08-03
Posts: 228

how many

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

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#2 2007-11-01 18:02:49

Devantè
Real Member
Registered: 2006-07-14
Posts: 6,400

Re: how many

My guess would be 38 or 40. I managed to fit in 38 using Microsoft Paint. I will double-check my answer on paper.

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#3 2007-11-02 02:46:45

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: how many

Here's a way to put fit 39 squares in there, but that's sticking to regular structures. It's possible that there's a counter-intuitive arrangement that can hold more.

4tonyje0.png

Using the areas of both shapes, you can definitely fit no more than 50 squares into the circle. There could be a more complex argument to reduce that upper bound though.

So at the moment, our best answer is "somewhere between 39 and 50".


Why did the vector cross the road?
It wanted to be normal.

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#4 2007-11-02 07:50:02

Devantè
Real Member
Registered: 2006-07-14
Posts: 6,400

Re: how many

If we didn't stick to regular structures, then we could use rotated squares against the edges of the circle. I can definitely see that you can fit 42 this way, at least.

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