UPSC Prelims 2017 · CSAT (Paper 2) · Q58

General Mental Ability

Medium · Cube painting combinatorics

The outer surface of a 5cm x 5cm x 5cm cube is painted completely in red. It is sliced parallel to the faces to yield 125 unit (1cm x 1cm x 1cm) cubes. How many of the small cubes have no painted faces at all?