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 Sphere Cube (Posted on 2004-02-09)
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In a cube of side 4, I pack eight spheres of unit radius.

What is the largest sphere I can place in the center (such that it doesn't overlap any of the other spheres)?

 Submitted by SilverKnight Rating: 3.0000 (5 votes) Solution: (Hide) Think of a smaller cube, with vertices at each sphere's center. This smaller cube would have sides of 2. The long diagonal of this cube would then be 2√3, and this is also equal to twice the larger spheres' radius plus twice the smaller sphere's radius. Since twice the larger spheres' radius equals 2, the equation is 2√3 = 2 + 2(smaller sphere's radius), solving for the smaller sphere's radius shows the largest sphere that can be placed has radius √3 - 1

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 Subject Author Date Puzzle Thoughts K Sengupta 2023-06-30 07:53:08 No Subject prashant 2004-03-29 08:00:56 Less otherworldly Dan Porter 2004-02-15 00:22:56 re(3): another dimension SilverKnight 2004-02-13 15:43:19 re(2): another dimension Tristan 2004-02-13 15:01:39 re: another dimension SilverKnight 2004-02-13 14:44:54 another dimension pleasance 2004-02-13 14:06:31 my solution is completely wrong...:-) John 2004-02-13 12:55:12 a try John 2004-02-13 12:24:38 re(2): Different Sulution York 2004-02-11 08:46:33 i'll give it a swing superfuous_nut 2004-02-10 18:54:03 Stumbling merrily away Phil 2004-02-09 19:12:09 re: Different Sulution Charlie 2004-02-09 11:19:57 Different Sulution York 2004-02-09 10:01:16 solution retiarius 2004-02-09 07:26:20 More balls than most Phil 2004-02-09 07:03:53

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