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[Brain Teaser] 10 x 10 x 10 Cube: On How Many of the Smaller Cubes is there any Paint?

Question:

You’ve got a 10 x 10 x 10 cube made up of 1 x 1 x 1 smaller cubes. The outside of the larger cube is completely painted. On how many of the smaller cubes is there any paint?

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Answer:

Larger cube is made up of 1,000 smaller cubes. 8 x 8 x 8 inner cubes are not painted which equals 512 cubes. Therefore, 1,000 – 512 = 488 cubes that have some paint. Alternatively, you can calculate this by recognizing that two 10 x 10 sides are painted (200) plus two 10 x 8 sides (160) plus two 8 x 8 sides (128): 200 + 160 + 128 = 488.

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