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Problem 1083

AIME late

Number theory Difficulty 5.0 Find the answer BMO Round 1 · United Kingdom · 2011

Let $s$ be an integer greater than $6$ . A solid cube of side $s$ has a square hole of side $x < 6$ drilled directly through from one face to the opposite face (so the drill removes a cuboid). The volume of the remaining solid is numerically equal to the total surface area of the remaining solid. Determine all possible integer values of $x$ .

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