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TNPSC dice and cubes reasoning practice questions

By the PrepMatic team · Updated 9 Oct 2026 · 4 min read

Dice is named in the Group 4 reasoning syllabus. A dice question gives you one or two views of a die and asks which number is opposite another, and painted-cube questions in the same family ask how many small cubes have a certain number of coloured faces. Both are rule-based, so a short list of rules solves almost every case. The five questions below test them. The wider syllabus view is in TNPSC aptitude and mental ability.

What this topic covers

• Standard dice: numbers on opposite faces add up to 7 (1 with 6, 2 with 5, 3 with 4).
• Two or three views of one die: finding the face opposite a given number.
• Faces and sums: the total of all faces is 21.
• Painted cubes: a large cube painted on all faces and cut into smaller cubes.

For a large cube painted outside and cut into n × n × n small cubes (n at least 3):

Sample questions

Question 1

On a standard die, the numbers on opposite faces add up to 7. The number on the face opposite 2 is:

• A. 3
• B. 4
• C. 5
• D. 6

Question 2

Two positions of the same die are shown. In the first position the visible faces are 1, 2 and 3. In the second position the visible faces are 1, 3 and 4. Which number is on the face opposite 2?

• A. 4
• B. 5
• C. 6
• D. 3

Question 3

On a standard die (opposite faces add up to 7) the number 4 is on the top. The sum of the numbers on the four side faces is:

• A. 10
• B. 14
• C. 17
• D. 18

Question 4

A cube painted on all faces is cut into 27 equal small cubes (3 × 3 × 3). How many small cubes have exactly two faces painted?

• A. 6
• B. 8
• C. 9
• D. 12

Question 5

A cube painted on all faces is cut into 64 equal small cubes (4 × 4 × 4). How many small cubes have exactly one face painted?

• A. 24
• B. 16
• C. 32
• D. 8

Answers and explanations

1. C. The opposite face of 2 is 7 − 2 = 5. The other pairs are 1 with 6 and 3 with 4.
2. A. Faces seen together in one view touch each other. Faces 1 and 3 appear in both views and touch. Faces 2 and 4 are each next to both 1 and 3, and the only two faces that touch both are opposite each other. So 4 is opposite 2.
3. B. All six faces add up to 1 + 2 + 3 + 4 + 5 + 6 = 21. The top is 4 and the bottom is 7 − 4 = 3, so the sides total 21 − 4 − 3 = 14.
4. D. Cubes with two painted faces lie along the edges but not at the corners. A cube has 12 edges, and each edge of a 3 × 3 × 3 block has 3 − 2 = 1 such cube, so the count is 12 × 1 = 12.
5. A. Cubes with one painted face lie in the middle of a face. Each face has (4 − 2) × (4 − 2) = 4 such cubes, and there are 6 faces, so the count is 6 × 4 = 24.

How to prepare dice and cube questions

Memorise the opposite pairs of a standard die and the total of 21. That covers questions 1 and 3. If a question does not say "standard die", it expects you to deduce the opposite face from the views alone, as in question 2.

For two or three views, use the common-face method. Find the face that appears in both views, then compare the other faces. Faces that are next to the same two common faces are opposite each other. Sketch a small labelled cube instead of working it out in your head.

For painted cubes, learn the table above and reproduce it from memory. The four counts must add up to n cubed (8 + 12 + 6 + 1 = 27 for n = 3), which gives you an instant check. Then practise variations, such as a cube painted on only some faces, by counting from first principles.

For other spatial and logical practice, move to TNPSC puzzles practice and TNPSC logical reasoning practice.

Take the full topic test on PrepMatic

Dice and cube questions are quick once the rules are automatic, and a PrepMatic topic test (about 15 questions, 30 minutes) will tell you whether yours are. Full mocks follow the real 200-question, 180-minute Group 4 pattern, so you can also practise reasoning at the end of a long paper.

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