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Large Cube and Painted Faces

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Author: Annie Fetter
Description: Geometry, difficulty level 3. Unit cubes form a larger cube. Some faces of the larger cube are painted. When the large cube is taken apart, 24 of the unit cubes have no paint on them. How big was the large cube and which of its faces were painted?
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Problem page: http://mathforum.org/geopow/archive/solutio87.html
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