Dice
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Cheat Sheets
Study MaterialDice – Cheat Sheet
Dice problems are frequently tested in Logical Reasoning and Aptitude sections of SSC, Banking, Railway, UPSC, Defence, Insurance, CAT, and other competitive examinations.
This cheat sheet helps candidates solve dice problems involving standard dice, non-standard dice, opposite and adjacent faces, open dice configurations, and dice verification. It covers rules, formulas, and shortcut techniques for quick problem-solving.
About This Cheat Sheet
Complete guide to Dice problems for competitive exams:
Standard Dice
- Opposite Faces Sum = 7
- 1 opposite 6
- 2 opposite 5
- 3 opposite 4
Non-Standard Dice
- No Fixed Sum Rule
- Different Configurations
- Letter Dice
- Symbol Dice
Opposite Faces
- Finding Opposites
- Common Face Method
- Elimination Method
- From Multiple Positions
Adjacent Faces
- Sharing Common Edge
- Not Opposite
- From Given Positions
- Rotation Rules
Open Dice
- Net Patterns
- Cross Pattern
- Line Pattern
- T-Pattern
Dice Verification
- Valid Dice Identification
- Invalid Dice Identification
- Net to Cube Formation
- Condition Checking
Types of Dice
- Number Dice (1-6)
- Letter Dice (A-F)
- Symbol Dice
- Color Dice
Shortcut Techniques
- Quick Opposite Finding
- Rotation Tricks
- Elimination Method
- Exam-Oriented Tips
Topics Covered
This cheat sheet covers all important Dice topics for quick revision:
| Topic | Description | Key Rule / Formula |
|---|---|---|
| Standard Dice | Dice where opposite faces sum to 7 | 1↔6, 2↔5, 3↔4 |
| Non-Standard Dice | Dice with no fixed opposite sum rule | No sum rule applies |
| Opposite Faces | Faces that cannot be seen together | Find using common face/elimination |
| Adjacent Faces | Faces that share a common edge | All faces except opposite are adjacent |
| Open Dice - Cross Pattern | Net with 4 faces in a row and one on each side | Top↔Bottom, Left↔Right, Front↔Back |
| Open Dice - Line Pattern | Net with faces in a straight line | Position 1↔6, 2↔5, 3↔4 |
| Open Dice - T-Pattern | Net with T-shaped configuration | Opposite pairs at specific positions |
| Common Face Method | Finding opposites from two dice positions | If a face is common, other faces are opposite |
| Dice Verification | Checking if a dice can be formed from a net | Opposite faces must not be adjacent in net |
Key Rules & Patterns
Standard Dice Opposites
| Face | Opposite |
| 1 | 6 |
| 2 | 5 |
| 3 | 4 |
| A (1) | F (6) |
| B (2) | E (5) |
| C (3) | D (4) |
Open Dice - Cross Pattern
Left Center Right
Bottom
Opposite Pairs: Top↔Bottom, Left↔Right, Front↔Back
Open Dice - Line Pattern
Opposite Pairs: 1↔6, 2↔5, 3↔4
Dice Positions
| Position | Meaning |
| Top Face | Face on top |
| Bottom Face | Opposite of top |
| Front Face | Face facing viewer |
| Back Face | Opposite of front |
| Left/Right | Side faces |
Why This Cheat Sheet is Important
Master Opposite Faces
Learn to quickly find opposite faces using common face and elimination methods.
Solve Open Dice Problems
Identify valid dice configurations from net patterns with confidence.
Apply Shortcut Techniques
Use rotation rules and elimination methods for fast problem-solving.
High Exam Weightage
Dice questions appear frequently in reasoning sections of all competitive exams.
Competitive Exams Covered
- SSC CGL
- SSC CHSL
- SSC MTS
- Bank PO & Clerk
- IBPS Exams
- Railway Recruitment Exams
- UPSC CSAT
- Defence Exams
- Insurance Exams
- CAT
- State Government Exams
Quick Exam-Oriented Examples
Question 1:
In a standard dice, which number is opposite to 4?
Step 1: In a standard dice, opposite faces sum to 7.
Step 2: Face opposite to 4 = 7 - 4 = 3
Answer: 3
Question 2:
In a standard dice, which number is opposite to 2?
Step 1: In a standard dice, opposite faces sum to 7.
Step 2: Face opposite to 2 = 7 - 2 = 5
Answer: 5
Question 3:
Two positions of a dice are shown below. Find the number opposite to 3.
Step 1: In both positions, 1 is common at the top.
Step 2: Faces adjacent to 1 in Position 1: 2 and 3
Step 3: Faces adjacent to 1 in Position 2: 4 and 5
Step 4: The face opposite to 3 is the one not adjacent to 1 in any position.
Step 5: Remaining faces: 2, 3, 4, 5, 6. 3 is opposite to 6.
Answer: 6
Question 4:
Two positions of a dice are shown. Find the face opposite to A.
Step 1: A is common in both positions.
Step 2: Faces adjacent to A: B, C, D, E
Step 3: The remaining face F must be opposite to A.
Answer: F
Question 5:
Two positions of a non-standard dice are shown. Find the face opposite to 2.
Step 1: 2 is common in both positions.
Step 2: Faces adjacent to 2: 3, 4, 5, 6
Step 3: The only face not adjacent to 2 is 1.
Answer: 1
Question 6:
An open dice (net) is shown below. Which face is opposite to the face with 3?
2 3 4
5
Step 1: This is a cross pattern open dice.
Step 2: In cross pattern, opposite pairs are: Top↔Bottom, Left↔Right, Front↔Back
Step 3: 3 is at the center. Its opposite is the face not adjacent to it in the net.
Step 4: In cross pattern, center is opposite to the face behind it (not shown).
Step 5: The face opposite to 3 is 6 (the face not in the net).
Answer: 6
Question 7:
An open dice net is shown in a line: [A] [B] [C] [D] [E] [F]. Which face is opposite to C?
Step 1: In a line pattern, opposite pairs are: 1↔6, 2↔5, 3↔4
Step 2: Here A=1, B=2, C=3, D=4, E=5, F=6
Step 3: C is at position 3, so its opposite is position 4 = D
Answer: D
Question 8:
Can the following dice be formed from the net shown?
Step 1: In line pattern, opposites: 1↔6, 2↔5, 3↔4
Step 2: Check: 2 and 5 are opposite, 4 and 3 are opposite, 6 and 1 are opposite.
Step 3: In the dice, Top=2, Front=4, Right=6
Step 4: 2, 4, 6 are all adjacent to each other (not opposite).
Step 5: This is possible because none of these are opposite pairs.
Answer: Yes, the dice can be formed
Question 9:
Can the following dice be formed from the net shown?
Step 1: In line pattern, opposites: 1↔6, 2↔5, 3↔4
Step 2: In the dice, Top=1 and Front=6
Step 3: 1 and 6 are opposite faces.
Step 4: Opposite faces cannot be adjacent (they cannot be seen together).
Step 5: But here 1 and 6 are shown together (top and front).
Answer: No, the dice cannot be formed (1 and 6 are opposite)
Question 10:
A dice has letters A, B, C, D, E, F on its faces. Two positions are shown:
Which letter is opposite to C?
Step 1: A is common in both positions.
Step 2: Faces adjacent to A: B, C, D, E
Step 3: The remaining face F must be opposite to A.
Step 4: C is adjacent to A, and its opposite is the face not seen with A.
Step 5: From the positions, C is opposite to E.
Answer: E
Question 11:
A dice has symbols: ★, ●, ■, ▲, ◆, ♥ on its faces. Two positions are shown:
Which symbol is opposite to ■?
Step 1: ★ is common in both positions.
Step 2: Faces adjacent to ★: ●, ■, ▲, ◆
Step 3: The remaining symbol ♥ must be opposite to ★.
Step 4: ■ is adjacent to ★, and its opposite is the face not seen with ★.
Step 5: From the positions, ■ is opposite to ◆.
Answer: ◆
Final Takeaway
Dice problems test your ability to visualize 3D objects and determine relationships between faces. The key is to understand the rules of standard dice, identify opposite and adjacent faces, and apply open dice patterns correctly.
Regular practice of standard dice, non-standard dice, open dice configurations, and dice verification problems will significantly improve your speed and accuracy. This cheat sheet serves as a complete revision resource for mastering Dice problems in competitive examinations.
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Everything You Need for Dice Problems Revision
Explore standard dice rules, non-standard dice, opposite and adjacent faces, open dice patterns, dice verification, and shortcut techniques in one place for quick and effective revision.
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