Determining the least expensive path for a new subway line underneath a metropolis like New York City is a colossal planning challenge—involving thousands of potential routes through hundreds of city ...

The original version of this story appeared in Quanta Magazine. Imagine a town with two widget merchants. Customers prefer cheaper widgets, so the merchants must compete to set the lowest price.

You may be among the 45% of adults who snore at least occasionally or you likely know someone who does. They may be the brunt of jokes ("Uncle Joe snores so loudly he rattles the windows!"), but ...