Due Friday, March 22, 2024 at 3 pm submitted to this Google form. You must be logged into your NAU gmail to submit via this form.

There is a circular road, along which travelers can drive in either direction. However, there is only one gas station on the loop. Driving the full loop in your car requires 40 gallons of gas, but your car’s fuel tank has a maximum capacity of 20 gallons. That said, you’d love to see every last spot along the route.

Of course, you can’t achieve this with just your own car. Fortunately, you can call on any number of your friends for, all of whom happen to have the same make and model car as you, each with a 20-gallon fuel tank and identical fuel efficiency.

Now, all the cars, including yours, must start and end at the gas station. However, only your car must cover the entire route. The gas station can be visited (and refueled at) by any car, any number of times. Cars may also transfer fuel from one to another, provided they meet up together at a spot along the route.

What is the smallest number of cars (including yours) needed for you to see every spot on the circular route?

(Note: There’s no “cheating” here. No towing or pushing of cars. Every car must be driven on its own, and by one person. No jerrycans for lugging around extra fuel, and so on and so forth.)