Dices
Dices questions in Analytical Reasoning test your ability to visualize dice orientations, deduce opposite faces, and apply logical rules based on given conditions. These problems are closely related to cube visualization but focus specifically on the faces of a dice and their relationships.
Types of Dice Problems
| Type | Description | Example |
|---|---|---|
| Standard Dice (Sum Rule) | In a standard dice, the sum of numbers on opposite faces is always 7 (1–6, 2–5, 3–4). | If 2 is opposite 5, then 1 is opposite 6 or 3 depending on orientation. |
| Non-Standard Dice | Opposite faces are not based on the 7-sum rule; must be deduced logically. | If 4 is opposite 2 and 6 is opposite 3, then 1 is opposite 5. |
| Same Dice Different Views | Two or more views of the same dice are given; you must deduce opposite/adjacent faces. | Dice showing 1,2,3 on one view and 2,4,1 on another → deduce opposite faces. |
| Different Dice (Comparison) | Two dice are compared to find common faces and infer opposites. | If face 3 is adjacent to 1 and 2 in both dice, opposite face must be deduced. |
| Rotation and Orientation | A dice is rotated, and you must figure out which face is on top, bottom, or side. | Dice rotated 90° clockwise around vertical axis → which number is now on top? |
Key Rules for Dice Questions
- Standard Dice Rule: Opposite faces add up to 7.
- Opposite Face Deduction Rule: If two different dice positions share two common numbers, then the third number in each position is opposite.
- Adjacency Rule: Opposite faces can never appear together in the same view.
- Rotation Principle: Visualize or sketch rotations to confirm the new orientation.
- Comparison Trick: Align common faces from two dice to quickly spot opposites.
How to Solve Step by Step
- Check if it’s standard or non-standard: Apply sum-to-7 rule only if standard dice is specified.
- Compare multiple views: Identify common numbers across dice views.
- Apply opposite face rule: Deduce opposites logically.
- Use elimination in MCQs: Options with impossible adjacencies can be ruled out quickly.
- Sketch when stuck: Simple sketches of rotations help avoid confusion.
Conceptual Tips and Common Mistakes
- Don’t always assume “sum = 7”: Many exam questions use non-standard dice.
- Be careful with adjacency: Opposite faces will never be visible together.
- Track rotations properly: Left ↔ right or up ↔ down rotations change visible faces differently.
- Symmetry traps: Dice may look identical but orientations differ—check carefully.
Examples
Example 1 — Standard Dice Opposites
If opposite faces sum to 7, then:
- 1 ↔ 6
- 2 ↔ 5
- 3 ↔ 4
Example 2 — Non-Standard Dice
Given: 2 is opposite 4; 6 is opposite 3.
Answer: Remaining pair is 1 opposite 5.
Example 3 — Same Dice Different Views
View 1: Faces {1, 2, 3} visible.
View 2: Faces {2, 4, 1} visible.
Common faces: 1 and 2.
→ Therefore, 3 is opposite 4.
Example 4 — Dice Rotation
A dice has 5 on top and 2 in front. If rotated forward, 2 goes to the bottom, 5 moves to front, and the back face comes on top.