Cube & Dice
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Dice: finding opposite faces from positions
Standard die
1+6 = 2+5 = 3+4 = 7
Opposite faces of a standard die.
Painted cube cut into small cubes
Two faces painted
12(n-2)
Cubes on the edges, excluding corners.
One face painted
6(n-2)^2
Cubes in the middle of each face.
No face painted
(n-2)^3
Hidden inner cube.