I can't talk about the Java part, but CW is literally full of mathmematical katas (not to mention you could ultimately analyze almost any kata in mathematical terms), so I see no reason to worry here :)

You could consider the mathematical approach as a way to skip a brute-forcish approach and do things the smarter way :)

Math is an essential part of software engineering, and if you think you can be a good engineer without math side, than I can assure you that you are hardly mistaken. Unless you want to be designer or "web-front-design-fancy-interface" type of programmer, which is not really software engineering.

I had the names in an array that put a copy of the 1st name in the end. rotate once and repeated as many times as possible. worked for low numbers but for large numbers timed out. From that point I figured it had something to do with math and lost interest.

While question is indeed quite mathematical, I managed to finally solve it "almost" empirically through trial-and-error using programming as a tool for my experiments. It was fun. The task looks simple but bites hard.