Refueling cars on circular racetrack puzzle > Suppose there are a number of cars at the start line of circular racing track with a fueling station. Each car can carries enough fuel to drive exactly half a lap. The cars can either refuel at the finish line or transfer any amount of fuel from one car to another when they are next to each other. I am tasked to find the minimum number of cars required for at least one car to finish a loop. My intuition tells me to approach this problem using a geometric series, but I don’t even know how to model the problem correctly. Please advise, and thank you!

If cars can go _backwards_ and refuel at the _start_ line, then 3 cars are enough:

* Cars A and B both go out to the 0.2 lap mark and wait there.
* Car C now uses one full tank to go out to the 0.2 lap mark, donate fuel for 0.1 lap to either A or B, and return to the start line.
* Repeat the above step four times. Cars A and B now each has a full tank.
* Car C refuels one last time and all three cars proceed to the 0.3 lap mark. They now have fuel for exactly one lap between them, which they split between car A and B.
* A and B go together to the 0.5 lap mark.
* Car B has 0.3 lap of fuel, and donates 0.2 of it to A.
* A now has a full tank and completes the remaining half-lap alone.