Cube and Dice Worksheet

Logical reasoning lesson 19: Cubes and dice · Set 16 · 40 questions

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

1. 1.A wooden cube is painted on all six faces, then cut into 125 equal small cubes. How many small cubes have at least one painted face?
2. 2.A wooden cube is painted on all six faces, then cut into 125 equal small cubes. How many small cubes have exactly three painted faces?
3. 3.On a standard dice, opposite faces add up to 7. The dice shows 5 on top. What number is on the bottom face?
4. 4.A wooden cube is painted on all six faces, then cut into 27 equal small cubes. How many small cubes have at least one painted face?
5. 5.On a standard dice, opposite faces add up to 7. The dice shows 3 on top. What number is on the bottom face?
6. 6.A wooden cube is painted on all six faces, then each edge is cut into 5 equal parts, making small cubes. How many small cubes have no painted face?
7. 7.A wooden cube is painted on all six faces, then each edge is cut into 3 equal parts, making small cubes. How many small cubes have exactly one painted face?
8. 8.Two standard dice show 4 and 4 on top. Opposite faces of a dice add up to 7. What is the total of the two bottom faces?
9. 9.On a standard dice, opposite faces add up to 7. The dice shows 1 on top. What number is on the bottom face?
10. 10.A wooden cube is painted on all six faces, then each edge is cut into 6 equal parts, making small cubes. How many small cubes have exactly two painted faces?
11. 11.A wooden cube is painted on all six faces, then cut into 216 equal small cubes. How many small cubes have exactly one painted face?
12. 12.Two standard dice show 4 and 6 on top. Opposite faces of a dice add up to 7. What is the total of the two bottom faces?
13. 13.A wooden cube is painted on all six faces, then cut into 64 equal small cubes. How many small cubes have exactly three painted faces?
14. 14.Two standard dice show 2 and 1 on top. Opposite faces of a dice add up to 7. What is the total of the two bottom faces?
15. 15.A wooden cube is painted on all six faces, then cut into 27 equal small cubes. How many small cubes have exactly three painted faces?
16. 16.Two standard dice show 5 and 3 on top. Opposite faces of a dice add up to 7. What is the total of the two bottom faces?
17. 17.Two standard dice show 1 and 4 on top. Opposite faces of a dice add up to 7. What is the total of the two bottom faces?
18. 18.Two standard dice show 2 and 3 on top. Opposite faces of a dice add up to 7. What is the total of the two bottom faces?
19. 19.A wooden cube is painted on all six faces, then cut into 125 equal small cubes. How many small cubes have exactly one painted face?
20. 20.On a standard dice, opposite faces add up to 7. The dice shows 4 on top. What number is on the bottom face?
21. 21.On a standard dice, opposite faces add up to 7. The dice shows 6 on top. What number is on the bottom face?
22. 22.A wooden cube is painted on all six faces, then each edge is cut into 6 equal parts, making small cubes. How many small cubes have exactly three painted faces?
23. 23.Two standard dice show 5 and 2 on top. Opposite faces of a dice add up to 7. What is the total of the two bottom faces?
24. 24.Two standard dice show 3 and 2 on top. Opposite faces of a dice add up to 7. What is the total of the two bottom faces?
25. 25.Two standard dice show 2 and 5 on top. Opposite faces of a dice add up to 7. What is the total of the two bottom faces?
26. 26.Two standard dice show 5 and 1 on top. Opposite faces of a dice add up to 7. What is the total of the two bottom faces?
27. 27.A wooden cube is painted on all six faces, then each edge is cut into 5 equal parts, making small cubes. How many small cubes have exactly two painted faces?
28. 28.Two standard dice show 6 and 5 on top. Opposite faces of a dice add up to 7. What is the total of the two bottom faces?
29. 29.Two standard dice show 4 and 3 on top. Opposite faces of a dice add up to 7. What is the total of the two bottom faces?
30. 30.Two standard dice show 6 and 1 on top. Opposite faces of a dice add up to 7. What is the total of the two bottom faces?
31. 31.Two standard dice show 6 and 3 on top. Opposite faces of a dice add up to 7. What is the total of the two bottom faces?
32. 32.Two standard dice show 1 and 3 on top. Opposite faces of a dice add up to 7. What is the total of the two bottom faces?
33. 33.A wooden cube is painted on all six faces, then cut into 64 equal small cubes. How many small cubes have no painted face?
34. 34.A wooden cube is painted on all six faces, then each edge is cut into 4 equal parts, making small cubes. How many small cubes have no painted face?
35. 35.Two standard dice show 1 and 1 on top. Opposite faces of a dice add up to 7. What is the total of the two bottom faces?
36. 36.A wooden cube is painted on all six faces, then each edge is cut into 4 equal parts, making small cubes. How many small cubes have exactly one painted face?
37. 37.A wooden cube is painted on all six faces, then cut into 125 equal small cubes. How many small cubes have exactly two painted faces?
38. 38.Two standard dice show 3 and 1 on top. Opposite faces of a dice add up to 7. What is the total of the two bottom faces?
39. 39.A wooden cube is painted on all six faces, then each edge is cut into 3 equal parts, making small cubes. How many small cubes have exactly three painted faces?
40. 40.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?

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