painting a cube with red color
Geometry
Level
2
A cube measuring 24 units on an edge is painted red. It is then cut into smaller cubes which measures 2 units on an edge. How many of the smaller cubes have no red face?
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1000
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1 solution
The initial cube is split into a 12 by 12 by 12 mesh of cubes. All the ones on the outside have at least one red face. Strip off the outside layer to reveal a 10 by 10 by 10 mesh of cubes with no red.