Number Puzzle #92
A 3x3x3 inches cube is painted with red color on all the outer surfaces. If the cube is cut into smaller cubes of 1*1*1 inches.
How many 1 inch cubes will have at least one surface painted ?
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All the corners will have 3 faces painted, there are total of 8 corners.
Cubes at the edge(except corners) will have 2 faces painted, there will a one such cube per edge, there are a total of 12 edges, thus 12 cubes will have 2 faces painted.
You can imagine one cube formed by exact center of a face will have only one face painted, there are a total of 6 faces in a cube, thus 6 such cubes will exists.
So total number of cubes with at least one face painted = 8 + 12 + 6 = 26
We can even confirm our calculation by counting the number of painted faces
Number of painted faces = 8*3 + 12*2 + 6 = 24 + 24 + 6 = 54 = 9*6(Each face of the original 3x3x3 cube is cut into 9 pieces.