Dice and Cubes
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Introduction
Dice and Cubes questions test your ability to visualize 3D objects. A standard die is a cube with 6 faces numbered 1 to 6.
Types of Dice
2. General Die: The sum of opposite faces is not necessarily 7. Adjacent faces can never be opposite.
Open Dice Logic
When a cube is unfolded, alternate faces (in a straight line of 3 or 4 squares) are opposite to each other. Faces that touch at corners or edges are adjacent.
Cube Cutting Formulae
For a cube of side N units cut into smaller cubes of side 1 unit:
- Total smaller cubes = N┬│
- 3 faces painted (Corner) = 8 (always fixed)
- 2 faces painted (Edge) = 12 ├Ч (N - 2)
- 1 face painted (Face) = 6 ├Ч (N - 2)┬▓
- 0 faces painted (Inner) = (N - 2)┬│
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