Problem of the Week?

Question

A cube is made of a white material, but the exterior is
painted black. If the cube is cut into 125 smaller
cubes of exactly the same size, how many of the
cubes will have 2 of their sides painted black?

Answer 1

Exactly 2 sides painted black? 36.

(Exactly 3 sides painted black? 8.)

At least 2 sides painted black? 44.

Answer 2

The only ones with exactly two black sides will be the ones along the 12 edges, minus the corner ones. To get 125 smaller cubes, each edge would have to have 5 cubes (5x5x5), but two of those are corners. That leaves 3 along each of the 12 edges, for a total of 36 cubes with exactly two black sides.

Answer 3

To get 125 cubes you need the length of each edge of the big cube to be 5 small cubes in length. The small cubes with 2 sides pained black will be along the edges (but not in the corner). There are 5 cubes along each edge but 2 of them are corners. So there are 3 small cubes per edge with 2 black faces. There are 12 edges. The total number of small cubes with 2 black faces is 12*3 = 36

Answer 4

none