Pariksha SaathiReasoning
Cubes and Dice: Practice Questions with Answers
15 practice questions on Cubes and Dice, with answers; most also have an explanation or a worked solution. Try each one before you open its answer.
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Q.1
A net has A, B, C, D in a horizontal strip, with E above B and F below B. Which face is opposite B?
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Answer: D
Solution:
- Keep B as the base. A and C fold up as two opposite side faces.
- E and F fold up as the other two side faces.
- D is attached beyond C and folds over to close the cube above B.
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Q.2
On a standard die, if the face showing 4 is on top, which number is on the bottom face?
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Answer: 3
Solution:
- The bottom face is opposite the top face: 7 − 4 = 3.
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Q.3
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?
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Answer: 12
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.
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Q.4
For the same 4 × 4 × 4 painted cube, count all four categories.
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Answer: 8 with three, 24 with two, 24 with one, 8 with none
Solution:
- Three painted faces: 8 corner cubes.
- Exactly two: 12 × 2 = 24. Exactly one: 6 × 2² = 24.
- Unpainted: 2³ = 8. Check: 8 + 24 + 24 + 8 = 64.
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Q.5
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?
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Q.6
On a cube labelled 1 to 6, one view shows 1, 2, 3 and another shows 1, 4, 5 meeting at corners. What is opposite 1?
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Answer: 6
Solution:
- The first view makes 2 and 3 neighbours of 1. The second makes 4 and 5 neighbours of 1.
- All four neighbours are now known. The only remaining label is 6.
- No standard-die assumption is needed.
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Q.7
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?
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Answer: 30
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.
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Q.8
A cube is painted on all outer faces and cut into 64 equal cubes. How many have exactly two painted faces?
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Answer: 24
Solution:
- 64 = 4³, so there are four small cubes along each edge.
- Exactly two painted faces occur on an edge, excluding its two corner cubes.
- There are 12 edges, with 4 − 2 = 2 qualifying cubes each: 12 × 2 = 24.
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Q.9
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?
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Q.10
An arbitrary cube has 2 next to 1, 3, 5 and 6. What is opposite 2?
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Answer: 4. It is the remaining label. Using 7 − 2 would incorrectly give 5, which is known to be adjacent.
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Q.11
On a standard die, if one face shows 6, what number is on the opposite face?
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Q.12
A cube painted on all sides is cut into 125 equal cubes. How many have exactly one painted face?
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Answer: 54. Since n = 5, each outer face has (5 − 2)² = 9 non-edge cubes; six faces give 54.
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Q.13
A standard die shows 2, 4 and 6 on three visible faces at a corner. Find the sum of the three hidden faces.
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Q.14
A painted cube is cut into 2 × 2 × 2 cubes. How many have exactly two painted faces?
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Answer: 0. All eight cubes are corners with three painted faces; there are no interior edge cubes.
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Q.15
For that 5 × 5 × 5 cube, how many small cubes have no paint?
How these questions were made
Written by Mahesh Srivastava, Founder of Pariksha Saathi. Published: 2026-10-03.