# Can You Take the Scenic Route?

Say we are Car A. With only one car, we can be sure to never complete the loop, as we would run out of fuel halfway.

If we add in a second car, Car B, we can take Car A and Car B through 1/4 the loop, where B can refuel A with the remaining 1/2 of its tank, but then B will be stuck. If B gives A any less fuel, A cannot make it far enough on the other side to be refueled. Two cars could only be possible if one of the cars had even a single drop of fuel more in terms of capacity, in which case they can give said single drop at the 1/4 mark before heading back to the gas station. But because that is not the case, we need a third car.

Introduce a third car, Car C. Cars A, B, and C travel 1/8 around the loop, using 1/4 their fuel each. C gives A and B 1/4 a tank each and heads back to the station, having barely enough to make it. A and B then travel to the 1/4 point around the loop, where B gives A 1/4 a tank of fuel, allowing B to make it back with its remaining 1/2 tank to refuel. A, now with a full tank, can travel from 1/4 around the loop to 3/4 around the loop. Now B will meet A there, using 1/2 its tank to get there and giving A 1/4 its tank. Both A and B use the rest of their fuel to make it to the 7/8 point of the loop, where C meets them, gives them 1/4 a tank each. They all make it back to the station with the rest of their fuel.

Thus, it is possible to complete the scenic route with just three cars. Assuming this is the most optimal usage of fuel, we would need five full tanks of gas, or 100 gallons.

**Answer:** 3 cars

**Extra Credit:** 100 gallons