How to compute number of possible paths in directed Traveling Salesman problem?
The way you have written your question makes it very difficult to understand, but let me try to answer one of your points as simply as I can.

Using a "super computer" (however you might define that) will not help us to make significant progress on the travelling salesman problem. The reason is that the time taken to solve a travelling salesman problem increases exponentially with the number of cities.

So suppose we can solve problems with up to 50 cities in a reasonable time on an "ordinary" computer (I have made this number up as an illustration). But let's also suppose that the running time of our most efficient algorithm is $O(2^n)$ - in other words, every time we add a city the time needed to find a solution doubles.

If we had a super computer that was a thousand times faster than an ordinary computer then it could solve problems with $60$ cities in the same time as an ordinary computer took for $50$ cities. This is because adding $10$ cities increases the problem difficulty by a factor of $2^{10} \approx 1000$.

So the super computer gives us a small improvement. But to solve  problems with $100$ cities in a reasonable time we would need a computer that was a million million ($10^{12}$) times faster again.