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Cubes and Dice — Questions and Answers

Cubes and Dice in the non-verbal section combines two question families: deducing opposite faces from different views of a cube, and counting painted faces when a large painted cube is cut into smaller ones. Both are governed by fixed formulas, so once the four painted-cube counts and the adjacency rule are memorised the topic becomes arithmetic.

8 solved questionsNon Verbal ReasoningFree · no signup

Cubes and Dice— Concepts, Formulas & Shortcuts

  • A cube has 6 faces, 12 edges and 8 vertices.
  • Faces visible together in one view are adjacent, never opposite.
  • On a standard die, opposite faces sum to 7.
  • Painted cube cut into n³ pieces: 8 have three painted faces, 12(n − 2) have two.
  • 6(n − 2)² have one painted face; (n − 2)³ have none.
  • If a face repeats across two views, use it as the pivot to pair the remaining faces.

Cubes and Dice Practice Questions with Answers

Attempt each question first, then open the explanation. All 8 questions below are free to read and require no signup.

  1. Q1.How many vertices does a cube have?

    Easy
    • A6
    • B8
    • C12
    • D16
    +Show Answer & Explanation

    Answer: B. 8

    Explanation: A cube has 8 vertices, 12 edges and 6 faces.

    Cubes and Dice question 1 of 8

  2. Q2.A painted cube is cut into 27 equal cubes. How many have exactly one face painted?

    Moderate
    • A4
    • B6
    • C8
    • D12
    +Show Answer & Explanation

    Answer: B. 6

    Explanation: 6(n − 2)² with n = 3 gives 6 × 1 = 6 — the centre of each face.

    Cubes and Dice question 2 of 8

  3. Q3.A painted cube cut into 64 pieces has how many with three painted faces?

    Easy
    • A6
    • B8
    • C12
    • D24
    +Show Answer & Explanation

    Answer: B. 8

    Explanation: Only the 8 corner cubes touch three outer faces, whatever the cut.

    Cubes and Dice question 3 of 8

  4. Q4.On a standard die, if 6 is on top, the bottom face shows:

    Easy
    • A1
    • B2
    • C3
    • D5
    +Show Answer & Explanation

    Answer: A. 1

    Explanation: Opposite faces sum to 7, so 7 − 6 = 1.

    Cubes and Dice question 4 of 8

  5. Q5.Two faces of a cube seen together in one view are:

    Moderate
    • AOpposite
    • BAdjacent
    • CIdentical
    • DParallel
    +Show Answer & Explanation

    Answer: B. Adjacent

    Explanation: Opposite faces can never be visible simultaneously, so any two seen together must be adjacent.

    Cubes and Dice question 5 of 8

  6. Q6.A painted cube cut into 125 pieces has how many with exactly two faces painted?

    Difficult
    • A24
    • B36
    • C48
    • D54
    +Show Answer & Explanation

    Answer: B. 36

    Explanation: 12(n − 2) with n = 5 gives 12 × 3 = 36.

    Cubes and Dice question 6 of 8

  7. Q7.How many small cubes are completely unpainted when a painted cube is cut into 64 pieces?

    Moderate
    • A4
    • B6
    • C8
    • D12
    +Show Answer & Explanation

    Answer: C. 8

    Explanation: (n − 2)³ = 2³ = 8 interior cubes.

    Cubes and Dice question 7 of 8

  8. Q8.The sum of the numbers on all faces of a standard die is:

    Easy
    • A18
    • B20
    • C21
    • D24
    +Show Answer & Explanation

    Answer: C. 21

    Explanation: 1 + 2 + 3 + 4 + 5 + 6 = 21.

    Cubes and Dice question 8 of 8

Cubes and Dice — Frequently Asked Questions

How many small cubes have exactly two painted faces?+

12(n − 2), where n is the number of cuts per edge. These are the edge cubes excluding the corners, so a cube cut into 4 per edge gives 12 × 2 = 24.

How do I deduce opposite faces from two views?+

Find the face that appears in both views and treat it as fixed. The other faces have rotated around it, which pairs up the remaining faces as opposites.

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