Twenty seven small cubes are glued to make a big cube and the exterior is painted yellow. How many among each of the 27 small cubes would have been painted yellow on :

1. only one of its faces

2. two of its faces

3. three of its faces.

Please send an explanation to the answers

Only one of the pointed faces = marked by 1 = 1

Since, there are six such faces, so number of cubes with only one of its faces pointed = 6 × 1 = 6

cubes with 2 faces pointed are marked by 2.

Number of cubes with 2 faces pointed in top layer = 4

Number of cubes with 2 faces pointed in middle layer = 4

Number of cubes with 2 faces pointed in bottom layer = 4

So, number of cubes with 2 faces pointed = 4 + 4 + 4 = 12

Number of cubes with three of its faces pointed in top layer = 4.

Number of cubes with three of its faces pointed in bottom layer = 4

Number of cubes with three of its faces pointed in middle layer = 0

So, number of cubes with three of its faces pointed = 4 + 4 = 8

∴ 1. Only one of its faces = 6

2. Only two of its faces = 12

3. Three of its faces = 8

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