Fascinating number

What this digit-property puzzle tests

This is a medium-difficulty puzzle that combines basic arithmetic with systematic reasoning. It asks you to find a three-digit number satisfying a specific constraint that relates its individual digits through different operations (addition, squaring, and cubing).

To solve problems like this, you typically set up an equation using the digits as variables, then search through the valid range methodically. The puzzle rewards both careful algebraic setup and efficient enumeration—you need to check candidates in a way that avoids wasted effort while ensuring you find the largest number meeting the constraint, not just any number that works.

• Positional notation and digit extraction
• Algebraic constraint formulation
• Bounded search and optimization