Geometry puzzles (contest style)

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Learn it Contest geometry often has an answer that doesn't depend on details ("wherever the point is"). Look for symmetry, ratios that cancel, and counting by position (corners, edges, faces).

Example: A 4 cm cube is painted and cut into 1 cm cubes. How many have exactly one red face?

One-face cubes are in the middle of each face, not on an edge.
Each face has a $2 \times 2$ middle = 4.
6 faces × 4 = 24.

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