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# Cubes

A cube is a regular three-dimensional solid structure having 6 faces, 12 edges, and 3 corners. All the edges of a cube are equal and hence all the faces are square in shape. The questions based on cubes are generally of the following types:

1. A cube is cut making certain specified cuts and the number of identical pieces resulting out of the given cuts has to be found.
2. The number of identical pieces into which a cube is cut is given and the cuts have to be identified.
3. Some or all faces of the cube are given having been painted with one or more colours and then cut into specified numbers of identical The number of cubes that have 1, 2, or 3 faces painted etc has to be determined.

For the third type of problems, the following general deductions can be of help.

For n x n x n number of smaller cubes,

- The number of smaller cubes with three faces painted = 8

- The number of smaller cubes with two surfaces painted = (n – 2) x 12

- The number of smaller cubes with one surface painted = (n – 2) x (n – 2) x 6

- The number of smaller cubes which would not form any face of the larger cube and would not be painted on any side = (n – 2) x (n – 2) x (n – 2)

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