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Some identical cubes are arranged in a pyramid-like form with 5 layers. Starting from the bottom layer, the number of cubes in the layers are 5 x 5, then 4 x 4, then 3 x 3, then 2 x 2, then 1 x 1. The whole exterior of the pyramid is painted including the bottom. How many of the cubes will have none of their faces painted?
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