On a whim, I decided to pose a traveling salesman problem to Bing Chat Copilot, one of the many Large Language Models that have popped into the zeitgeist this year. I know the problem not generally solvable, but there are “close enough” solutions for reasonable numbers of stops.
“Prepare an itinerary for me to visit the county courthouse of every Texas county, visiting each in the daylight only, and staying overnight when needed”, I asked. It did not give me an itinerary. However, it confirmed it didn’t know basic math.
“To visit the county courthouse of every Texas county, you would need to travel a lot of miles and spend a lot of time on the road. According to one estimate, the shortest possible route that covers all the counties is about 3,000 miles long and would take about 60 hours of driving2. That means you would need at least 30 days to complete the trip, assuming you drive for two hours and visit one courthouse per day.”
At 3000 mines, that would give the average distance to the two closest other county courthouses is 11.7 miles. This should seem highly unlikely to anyone who has driven in Texas. So, I asked a simpler question, and it was able to answer reasonably. “What is the driving distance from the Harris County, Texas county courthouse to the courthouse of each neighboring county?” I chose that one only because I live in Houston.
According to the tool Driving Distance Calculator, the driving distance from the Harris County, Texas county courthouse to the courthouse of each neighboring county is as follows:
- Montgomery County: 43 miles or 69 kilometers
- Liberty County: 46 miles or 74 kilometers
- Chambers County: 47 miles or 76 kilometers
- Galveston County: 51 miles or 82 kilometers
- Brazoria County: 52 miles or 84 kilometers
- Fort Bend County: 29 miles or 47 kilometers
- Waller County: 44 miles or 71 kilometers
These distances are based on the shortest route between the county seats, which may not be the exact locations of the courthouses.
It did a good job of proving my point for me. Harris is most populace county, but not nearly the largest. To confirm, I asked “Which two Texas county courthouses are the closest to each other?”
…the two Texas county courthouses that are the closest to each other are the Brewster County Courthouse and the Presidio County Courthouse. They are located in the neighboring towns of Alpine and Marfa, respectively, and are only 26 miles …apart.
That pretty much seals that deal. And I’ve been to both of those as well. The math for two hours driving per day or one courthouse per day are wrong in so many directions; i don’t know where to start.. I’m pretty sure at one courthouse per day, you cannot visit 256 courthouses in 30 days.
The recent article Researchers Approach New Speed Limit for Seminal Problem in Quanta, reminded me of the task I’ve long wanted to accomplish.
