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Clay Mathematics Institute: 2 puzzles worth knowing

2 puzzles from Clay Mathematics Institute, each explained in a minute and credited to the original work. Free on Savvy.

• Find the shortest route between cities. A million dollars says you can't — efficiently

  Given a list of cities and the distances between them, find the shortest possible route that visits every city exactly once and returns to the start. For a handful of cities it's e…

  — Clay Mathematics Institute, P vs NP Millennium Prize Problem

• If you can quickly check an answer, can you always quickly find it?

  Some problems are easy to verify but seem brutally hard to solve — like finding a short route through a huge map of cities, versus just checking whether a given route is short enou…

  — Clay Mathematics Institute, P versus NP problem

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