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Cubes

by Aman verma » Mon Jul 19, 2010 8:13 am
Q: A big cube is formed by rearranging the 160 coloured and 56 non-coloured similar cubes in such a way that the exposure of the coloured cubes to the outside is minimum . The percentage of exposed area that is coloured is :

a)25.9 %

b)35%

c)44.44%

d)50%

e)66.66%


OA[spoiler]c)44.44%[/spoiler]
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by nicolezl » Mon Jul 19, 2010 9:22 am
First of all, you can figure out that since there are a total of 216 small cubes, the big cube is 6x6x6 small cubes. Also, there are 152 small cubes visible on the outside of the big cube and 64 small cubes hidden inside. If you want minimal color exposure, then all 64 inside cubes should be colored. That leaves 96 colored cubes that must be visible. You can position these so that the middle 16 cubes on each of the 6 sides are colored. (That way only 1 side of each colored cube is exposed.)

So the percentage of exposed area that is colored is 96/216 = 4/9 = 44.44%

Sorry if that's really confusing.
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