This is a somewhat elegant problem from the 1987 Discover magazine’s Brain Bogglers by Michael Stueben:

“Each dot in the figure at left represents a factory. On which of the city’s 63 intersections should a warehouse be built to make the total distance between it and all the factors as short as possible? (A much simpler solution than counting and totaling the distances is available.)”

Note that the distance is the taxicab distance I discussed in my article South Dakota Travel Problem rather than the distance along straight lines between the warehouse and factories.

Answer.

See the Factory Location Problem for solutions.