TNPSC Group IV · Bite-size lessons
Dice and Cubes
About 6 min · Aptitude and Mental Ability Test · English
Time worked out from the lesson's 404 words at 150 words a minute, plus a minute for each question.
Dice and Cubes is a listed topic in TNPSC Group IV's Aptitude and Mental Ability section. Questions test your ability to visualize three-dimensional objects mentally—a skill that separates high scorers from average performers.
Key ideas
- Standard Dice Rule: A standard dice always has opposite faces summing to 7. The pairs are: 1-6, 2-5, 3-4. TNPSC questions may use standard or non-standard dice—read carefully.
- Opposite Face Identification: When two positions of the same dice are shown, faces appearing together (adjacent) in any view can never be opposite to each other.
- Common Vertex Rule: When three faces meet at a corner, none of these three can be opposite to each other. The remaining three faces (not visible) form their opposites.
- Rotation Principle: A dice can be rotated in any direction, but opposite faces remain constant regardless of orientation.
- Painted Cube Concept: When a cube of side 'n' units is painted and cut into unit cubes, the position of smaller cubes determines how many faces are painted (corner = 3 faces, edge = 2 faces, face-center = 1 face, interior = 0 faces).
Watch out for
- Assuming all dice are standard → Always check if the question specifies "standard dice" or shows a non-standard configuration. Non-standard dice don't follow the sum-of-7 rule.
- Confusing adjacent with opposite → If two faces appear together in ANY view, they are adjacent, NOT opposite. Students often forget to cross-reference multiple views.
- Forgetting n ≥ 3 for interior cubes → For a 2×2×2 cube, there are no interior cubes and no cubes with exactly 1 face painted.
Quick reference
- Standard dice: opposite faces sum to 7 (pairs: 1-6, 2-5, 3-4)
- Faces visible together at a corner → all three are mutually adjacent, none opposite
- 3 faces painted = 8 (corners, always)
- 2 faces painted = 12(n−2) (edges)
- 1 face painted = 6(n−2)² (face centers)
Check yourself: 3 questions
1. A cube is painted red on all faces and then cut into 64 smaller cubes of equal size. How many smaller cubes will have exactly two faces painted red?
2. A cube is painted blue on all six faces. It is then cut into 125 identical smaller cubes. How many of the smaller cubes will have no face painted?
3. A solid cube of side 6 cm is painted on all faces and then cut into smaller cubes of side 1 cm. Among the smaller cubes, how many will have paint on exactly three faces?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 17 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.
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