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A cube has edge length x (an integer). three faces meeting at a corner are painted blue.

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A cube has edge length x (an integer). three faces meeting at a corner are painted blue. The cube is then cut into smaller cubes of unit length. If exactly 343 of these cubes have no faces painted blue, then the value of x is ________ .

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(x – 1)3 = 343

⇒ x – 1 = 7

⇒ x = 8

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