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Interview prep / Brainteaser/Logic

Unit cubes in the shell of a 10-cube

Question

A large cube measuring 10×10×1010\times10\times10 is assembled from unit cubes. Its entire outer layer of unit cubes falls away. How many unit cubes come off?

Short answer

488. What remains is an 8×8×88\times8\times8 core, so the shell holds 103−83=1000−512=48810^3-8^3=1000-512=488 cubes.

Adapted from Crack, Heard on the Street, Q1.9, p.11; question and answer rewritten by SelfMadeQuant.com.

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