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Mathematics

Hamiltonian Cycles and the Traveling Salesman Problem

Quick fact

The traveling salesman problem is NP-hard, meaning that no known algorithm can solve it exactly in time that grows merely polynomially with the number of cities—even though a proposed solution can be checked instantly.

Why this is interesting

You have to visit every city on your list exactly once and return home—but which route is shortest? The answer may seem simple, yet it hides one of the deepest mysteries in computer science.