You are given 64 1x1x1 cubes and asked to use them all to form one large cube. Afterward you paint all the sides of the larger in green. How many of the original 1x1x1 cubes will have no paint on them? How many of the original surfaces will have no paint on them (eg the top center cube would have 1 painted surface and 5 unpainted services)?
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Comments:
Heroka - 10 years, 3 months ago
The large cube will have dimensions 4*4*4. Therefore, the 'inside cube' will be 2*2*2 leading to 8 original cubes having no paint on them.
In total, there are 64*6 = 384 surfaces. Each side of the big cube contains 16 green surfaces, which means that 16*6=96 surfaces are green. 384 - 96 = 288 unpainted surfaces.
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