I asked for the solution for any number of gas stations.

Your solution only holds for a the circular track of exactly 1 gas station. In order for your solution to be correct, it would have to be provable that only the circular track of 1 gas station existed.

Let us, for example, apply your solution to the case of 2 gas stations. We'll call one gas station A and another gas station B. Let's say that A has 0 gas. Therefore, by definition of the circular track, B must have 1.00 gas (We're letting the amount required to traverse the circle be represented by a percentage). Your solution claims that A would be the correct solution. So I start at A with an empty tank, and fill my tank from the empty gas station, start driving around the circle only to not go anywhere.

Therefore your solution does not hold for 2 gas stations, and the argument can be expanded similarly to any number of gas stations larger than 1. Hence my statement that you did not traverse the circle; you did not explain to me how to traverse the circle in all cases, only one very specific case.

However, if you meant that there was no observable difference between starting at the initial gas station and ending at the initial gas station on a circular track then you would be correct. That does not changed the fact that you have not actually gone anywhere.