Cube & Dice

Standard dice numbering rules and cube-painting/cutting problems — a compact, visualization-heavy topic.

📖 ~4 min read 🧠 RRB NTPC / Group D — Reasoning

Standard Dice Rule

On a standard dice, opposite faces always sum to 7: 1↔6, 2↔5, 3↔4

Finding Opposite Faces from Two Views

If two different views of the same dice share a common face, the remaining two faces (not shown, not shared) are opposite to each other
Use elimination: whichever numbers never appear adjacent to a given number across multiple views must be opposite it

Cube Painting & Cutting

A cube is painted on all outer faces, then cut into n³ smaller identical cubes. Standard results:

Smaller Cube Position	Painted Faces
Corner cubes	3 faces painted
Edge cubes (non-corner)	2 faces painted
Face-centre cubes	1 face painted
Fully internal cubes	0 faces painted (not on any outer surface)

💡 Example: A cube cut into 4×4×4=64 smaller cubes has 8 corner cubes (3 faces painted) — corner count is always 8, regardless of cube size (as long as n≥2).

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