DICE

Important Formulas & Rules for Dice Problems

• Opposite Faces Sum to 7: On a standard dice, opposite faces add up to 7.
  (1 & 6), (2 & 5), (3 & 4)
• Sum of numbers on opposite faces is always 7.
• Faces adjacent to a face do not include its opposite face.
• To find the number on opposite face:
  Opposite face = 7 - (given face)
• To solve dice problems: Visualize or draw the dice net (unfolded dice) to determine adjacent faces.
• Common types of questions: Finding opposite face, adjacent faces, or the number on faces after rotation or when dice are stacked.

Explanation & Examples

Example 1: What is the number on the face opposite to 3 on a standard dice?

Solution: Opposite face = 7 - 3 = 4

Example 2: If the top face of a dice shows 2 and the front face shows 5, what number is on the right face?

Solution: Since opposite of 2 is 5 (given front), right face is adjacent to both 2 and 5.
The numbers adjacent to 2 and 5 are 1, 3, and 6. Because 5 is front and 2 is top, the right face is 1 or 3 or 6 depending on orientation. Usually, the right face is 1.

Previous Year Questions with Solutions

1. SSC CGL 2020: A dice is rolled. The number on the top face is 5. What is the number on the bottom face?
   Answer: 7 - 5 = 2
2. SSC CHSL 2019: The faces opposite to 1, 2, and 3 are shown on the same dice. What is the number on the face opposite to 2?
   Answer: 5 (Because opposite of 2 is 5)
3. RRB NTPC 2018: If the face opposite to 4 is 3 and the face opposite to 6 is 1 on a dice, what number is on the face adjacent to both 4 and 6?
   Answer: 2 or 5 (depending on dice orientation)
4. SSC GD 2019: A dice is thrown three times. If the numbers obtained are 1, 3, and 5, what is the sum of the numbers on the opposite faces of these three numbers?
   Answer: (7-1) + (7-3) + (7-5) = 6 + 4 + 2 = 12
5. HSSC Constable 2018: If the face opposite to 2 is 5, and the face opposite to 6 is 1, which number is adjacent to both 2 and 6?
   Answer: 3 or 4 (both are adjacent)