All Problems
Problem #45 MEDIUM

The Painted Cube

Amazon Meta Math Pattern Recognition

Problem Statement

A solid wooden cube measuring 4 x 4 x 4 units is painted red on all six of its outer faces. It is then cut into 64 smaller unit cubes (each measuring 1 x 1 x 1). If you pick one of these 64 small cubes completely at random, what is the probability that it has paint on exactly 2 of its faces? Generalise your approach for an n x n x n cube.

Answer & Quick Explanation

Logged-in Users Only

You must be logged in to view the answer and check your solution. Signing up is free and takes less than a minute.

Detailed Editorial Solution

Detailed Editorial Solution is Premium

Unlock detailed step-by-step mathematical proofs, logic explanations, and company-specific interview preparation pathways.