SOLUTION: A solid rectangular prism with sides of 6 m by 9 m by 17 m is painted orange and then cut into 1 m^3 cubes. How many cubes are orange on fewer than 2 sides?

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Question 1189472: A solid rectangular prism with sides of 6 m by 9 m by 17 m is painted orange and then cut into 1 m^3 cubes. How many cubes are orange on fewer than 2 sides?
Answer by ikleyn(52781) About Me  (Show Source):
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A solid rectangular prism with sides of 6 m by 9 m by 17 m is painted orange and then cut into 1 m^3 cubes.
How many cubes are orange on fewer than 2 sides?
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In all, there are 6*9*17 = 918 small cubes.


Of them, 8 corner cubes has 3 faces painted,

and  4*(6-2) + 4*(9-2) + 4*(17-2)  small cubes along the edges (excluding corner cubes) have two faces painted.


So, the number of cubes with 2 or more faces painted is 4*(6-2) + 4*(9-2) + 4*(17-2) + 8 = 112.


We subtract 112 from 918 and obtain the number of small cubes with less than 2 faces painted


    918 - 112 = 806.    ANSWER

Solved.