MathDB
Painted Cube Probability

Source:

September 7, 2024
probability2024

Problem Statement

Amelia has 2727 unit cubes. She selects one and paints one of its faces. She then randomly glues all 2727 cubes together to form a 3×3×33 \times 3 \times 3 cube (with all possible arrangements of the unit cubes being equally likely). Compute the probability that the resulting cube appears unpainted.
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