Originally posted by XanthosNZ
The car can hold as much fuel as it needs to.
Under those conditions, an onboard fuel tank which just gets portions from a cannister the driver picks up all the way, it seems to me you can find a starting point for which you cannot make it all the way around and a starting point for which you can make it all the way round, it all depends on the distribution. For instance, if the fuel was bunched up together 3 degrees apart and you start at the last fuel cannister you would never make it all the way round. If you started from the second fuel can on to the end you would not make it around.
So you have to start with the first container in line. If you had 1L cans every 36 degrees it would not matter at which can you started and it would be like my example of the ditch around the track so you would get around the track from every starting point, starting points presumable being where each can is located. I think because of those two examples it is always possible to find at least one location where you could make it around the track with any distribution of fuel.
A little harder to picture is uneven distributions with a system like 1,2,3 amd 4 L containers spaced unevenly, that might set up a condition where you cannot get all the way round. Like 1L at zero degrees and 2 L at 72 degrees, 3L at 144 degrees and 4 L at 324 degrees there may not be any point at which you can get all the way around. Those last numbers were just examples, I did not work it out.