[gauravk_newton]

A cube is made of a blue-coloured material, but the exterior is painted red. If now the cube is cut into 125 smaller cubes which are of exactly the same size, how many of the cubes will have 2 of their sides painted red?

[gauravk_newton]

ANSWER: There will be 96 cubes with two or three red faces.
72 cubes will have ONLY 2 faces painted red.
Remaining 24 will have there three faces painted red.

Hope you don't mind replying if its correct.

[Capuchin]

I think you're wrong, only cubes on the vertex will have 2 red sides, that's 3 per vertex, 12 vertices, so I think it's 36 cubes with 2 sides painted.

the 8 corners will have 3 sides painted red. So that's 8

the 9 cubes on each sice will have 1 side painted red, so that'll be 9*6, 54

then that leaves the central 3x3x3 block which is 27 with no red paint.

27+54+8+36 = 125

[galactus]

See here where a similar problem was addressed. There is a general formula for these.

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