TNPSC Group II · Bite-size lessons
Dice
About 6 min · Aptitude and Mental Ability · English
Time worked out from the lesson's 442 words at 150 words a minute, plus a minute for each question.
Dice problems are part of the Aptitude and Mental Ability section in TNPSC exams. These questions test your spatial reasoning and ability to visualize three-dimensional objects from two-dimensional representations. The core skill is determining which faces are opposite to each other and understanding how a die rotates.
Key ideas
- Standard Die Rule: On a standard die, opposite faces always sum to 7. So, 1 is opposite 6, 2 is opposite 5, and 3 is opposite 4.
- Cube Structure: A cube has 6 faces, 8 vertices (corners), and 12 edges. Any face shares edges with exactly 4 other faces and is opposite to 1 face.
- Adjacent Faces: If you can see two faces simultaneously in any view of a die, they are adjacent (share an edge), never opposite.
- Common Face Method: When two positions of a die share a common visible face in the same orientation, the remaining two visible faces in each position help identify opposite pairs.
- Rotation Principle: When a die is rotated, the top and bottom faces (or front and back, or left and right) swap positions depending on the axis of rotation.
Watch out for
- Assuming all dice are standard: Many exam questions use non-standard dice. Don't blindly apply the "sum = 7" rule unless the question specifies a standard die.
- Confusing adjacent with opposite: Just because two faces are near each other in an unfolded net doesn't mean they're opposite. When the net folds, faces separated by exactly one face in a straight line become opposite, not adjacent.
- Ignoring orientation when comparing views: When two positions share a common face, ensure the common face is in the exact same position (e.g., both times on top). If it's rotated, the comparison changes.
Quick reference
- Standard die: 1↔6, 2↔5, 3↔4 (opposites sum to 7)
- Two faces visible together → always adjacent, never opposite
- Maximum 3 faces visible at once; they meet at one corner
- Net rule: faces sharing an edge when folded are adjacent
- If a face never appears with another across all views → likely opposite
Check yourself: 3 questions
1. A standard dice is thrown twice. If the sum of the numbers on the top face is 8, which of the following pairs could NOT appear on the top faces?
2. Three different positions of a dice are shown: Position 1: 1, 2, 3 are visible Position 2: 2, 4, 5 are visible Position 3: 1, 5, 6 are visible Which number is opposite to 2?
3. A cube is painted red on all faces and then cut into 64 smaller identical cubes. How many smaller cubes have exactly two faces painted?
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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