Cubes and dice — Logical reasoning for kids

How to think it through

Corners, edges, faces, inside — “where a small cube sits tells you how many of its faces are painted”

1. Find n, the number of small cubes along one edge (27 small cubes → n = 3).
2. 3 faces: 8 corners. 2 faces: 12 × (n − 2). 1 face: 6 × (n − 2)². No face: (n − 2)³.
3. Dice: opposite faces add up to 7 (1–6, 2–5, 3–4).

Use it for: Cube and dice questions in Olympiads and aptitude tests, and building 3D sense.

Worked example: A wooden cube is painted on all six faces, then cut into 27 equal small cubes. How many small cubes have exactly two painted faces? → 12

✏️ Practice

Work it out in your head or on paper, type the answer and press Check. Stuck? Press “Show me how”.

🏁 Lesson 19 test

20 questions. Check each answer, then go to the next one. Get 16 or more right to pass.

🏅 Sign in with Google to earn the 🎲 Dice Decoder badge when you pass — and a certificate when you finish all 10 lessons of Part 2 · Order and arrangement. You can still take the test without signing in.

🖨️ Cube and Dice Worksheet

• Worksheet set 1 (PDF)
• Worksheet set 2 (PDF)
• Worksheet set 3 (PDF)