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A 10 by 10 by 10 cube is painted red.  The cube is cut into 1000 one by one by one cubes.  Find the number of small cubes that have exactly two red sides.

 May 20, 2020
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A 10 by 10 by 10 cube is painted red.  The cube is cut into 1000 one by one by one cubes.  Find the number of small cubes that have exactly two red sides.

 

The only cubes that will have two painted sides are the cubes along the edges of the large cube, but not the corners.  The corners will have three red sides.  So, along one edge, there will be 8 red cubes.  Since there are 12 edges on a cube, there will be 96 cubes with two red sides.  

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 May 21, 2020

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