Pariksha SaathiCubes and Dice Questions with Solutions
On a standard die, opposite faces always add up to 7 — that single fact is the key to almost every question in this topic, from finding a hidden face to totalling what’s visible on a stack of dice. Here’s the concept, four fully worked examples, and a few to try yourself.
The concept, quickly
- The core rule: on a standard die, numbers on opposite faces always sum to 7 (1↔6, 2↔5, 3↔4).
- To find a face opposite a given number, subtract it from 7.
- The six faces of one die always sum to 1+2+3+4+5+6 = 21 — a fast way to find the total of several hidden faces is "21 minus whatever’s visible," instead of adding up each hidden face individually.
- When two dice are joined face-to-face, the two touching faces are both hidden — find their sum, then subtract it from the combined total (42 for two dice) to get everything visible on the outside.
Worked examples
1. On a standard die, the numbers on opposite faces always add up to 7. If one face shows 2, what number is on the face opposite to it?
Solution
- 7 − 2 = 5.
Answer: 5
2. A standard die shows 1, 3 and 5 on three visible faces meeting at a corner. What is the sum of the numbers on the three hidden faces?
Solution
- The six faces of a die always total 1+2+3+4+5+6 = 21.
- Hidden sum = 21 − (1 + 3 + 5) = 21 − 9 = 12.
Answer: 12
3. On a standard die, if the face showing 4 is on top, which number is on the bottom face?
Solution
- The bottom face is opposite the top face: 7 − 4 = 3.
Answer: 3
4. Two standard dice are placed together so that the face showing 6 on one die touches the face showing 6 on the other. What is the sum of all the numbers visible on the outside of this combined block?
Solution
- Two dice together have a total face-sum of 2 × 21 = 42.
- The two touching (hidden) faces both show 6, so their sum is 6 + 6 = 12.
- Visible sum = 42 − 12 = 30.
Answer: 30
Try these yourself
Use the opposite-faces-sum-to-7 rule, then check against the answer.
1. On a standard die, if one face shows 6, what number is on the opposite face?
Answer: 1
2. A standard die shows 2, 4 and 6 on three visible faces at a corner. Find the sum of the three hidden faces.
Answer: 9
3. Two standard dice are placed together so that the face showing 3 on one die touches the face showing 4 on the other. What is the sum of all the numbers visible on the outside of this combined block?
Answer: 35
Where this comes up
Cubes and Dice is a regular topic in the Reasoning/General Intelligence section of every exam Pariksha Saathi covers — SSC CGL, SSC MTS, SSC CHSL, IBPS PO, IBPS Clerk, SBI PO and SBI Clerk.
Practice more Cubes and Dice questions
This page covers the concept and a handful of worked examples. Pariksha Saathi has full topic-wise practice sets for Cubes and Dice (and every other Reasoning/Quant/English topic) with instant scoring and explanations — free, no account required.
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