I just quickly wrote a script, but made a typo and got 13 instead of 23 :)
You could have used wolframalpha, it basically does all the work for you: 1+[(x^y*y^x-1)(mod9)]
Ah, so in that case I got lucky that you goofed a bit the first time :D Sorry to say but I like free stuff, so if I win I'll probably keep it.
I've used wolframalpha actually for my calculus and diff.eq whenever I'm having integral problems. But of course the goofy thing bugs on me a bunch and will mistake a variable for a physics equation or something.
Oh, no, actually it all good. I'm not interested in the prize and should not have posted my answer in the first place :)
Actually I solved the 'title' riddle accidentally I believe. The answer just popped out when I was playing with wolfram and trying to program it to solve the main riddle.