I am having a difficult time understanding a problem...

The problem, in essence is the Pythagorean Theorem, and I see how it IS Pythagorean Theorem, but I want to go deeper than the answer.

The problem is this:

Superman starts at home, and decides to exercise, by running. He runs exactly one mile north, decides it isn't enough, and runs exactly one mile east. He then runs two miles south, two miles west, three miles north, three miles east, four miles south, four miles west, and so on until he has run a distance of 11,001 miles, at which point he rests, and flies directly home. What is the distance he had to fly to get home?

Now, the problem itself calls upon the 11,001 miles distance. I have figured this out, but my process was lengthy, as I actually got a large paper and drew it out, then calculated. That was a huge pain in the butt, and I'd rather have a set equation, or a simple process (i.e. no more than 5 minutes), but I don't quite comprehend how to simplify it.

So, my questions, in essence, are:

1. In the exact same problem, what would be the distance he had to fly home forxmiles?

2. Why is this?

Thank you in advance for any time spent on this!