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Mathematical conundrum


Redbaron

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I wrote a quick and dirty program that analyzed the literally trillions of permutations looking for the max balls and secondarily the most ideally shaped box. It said the most compact 50L box to fit 781 balls is 4x44x284, but you can get 780 in a more nicely shaped 24x52x40 box. All dimensions are in centimeters and this is with the primitive "stack the balls on top of each other" method. Computing more clever stacking arrangements is an exercise left for the student :)

 

Since we are in the technology section, thought I would also add an interesting benchmark. Since this program was such a number cruncher and my laptop has a 64-bit CPU, I compiled the code as both a 32-bit and 64-bit Windows application and compared the results. I was amazed to see the 64-bit version finished over 5 times faster! Anyone who doesn't buy a 64-bit processor these days is crazy. How else can you get a free 5x performance improvement! It's like I have a 15 gigahertz pentium all of a sudden!

 

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Neo said:

... Anyone who doesn't buy a 64-bit processor these days is crazy. How else can you get a free 5x performance improvement! It's like I have a 15 gigahertz pentium all of a sudden!

 

Are there (m)any 64-bit mainstream apps out there yet?

 

Wondering if it might be best to wait for more apps, at which time prices should be significantly lower.

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I don't think so, but remember 32-bit apps run just fine. It's kind of like asking if there are any games that need a video card better than an ATI 9600. Nope, but I wouldn't buy a video card just to run what's on the shelf right now. I'd want it to handle games coming out in the next years. Same for a processor.

 

Price will blow your mind. Pentium 3Ghz is $170US right now. Comparable AMD-64 3000 is just $149. Madness to buy a Pentium right now.

 

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BelgianBoy said:
A cube shape is the max volume

 

DOG

 

Dog,

 

Hmmmmm...... sorry, but max volume would be a sphere......

 

BB

 

Hi BB-

 

I'm thinkin' cube, too! In any given box, the biggest volume, choosing between a cube and a sphere, should always be the cube, no?

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Complicated.

 

As one sugested - pack in a single file, but this would waste paste. What you would want to do is not have the spheres not touching the outer edges of the adjacent sphere but the inner edges.

not this

X X X

 

X X X

 

X X X

 

X X X

 

but this

 

X X X

. X X

X X X

. X X

 

but to be done in a 3 dimensional format. sounds easy but it gets harder you think about it.

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