Lists of NP-Complete problems

Yes, these are difficult problems.

- A compendium of NP optimization problems (here)
- An Annotated List of Selected NP-complete Problems (here)

And here are some discussions of how the Universe manages to solve them (or work around them...):
- NP-complete Problems and Physical Reality (here):
''Can NP-complete problems be solved efficiently in the physical universe? I survey proposals including soap bubbles, protein folding, quantum computing, quantum advice, quantum adiabatic algorithms, quantum-mechanical nonlinearities, hidden variables, relativistic time dilation, analog computing, Malament-Hogarth spacetimes, quantum gravity, closed timelike curves, and “anthropic computing.”''
- Optical solutions to NP-Complete problems (here)