Honestly, I'm not a Java programmer either, that's probably why I'm having trouble with such a simple exercise. Basically, all I did was combine two previous exercises, one which validates that the input is an integer (first while loop), and one to then validate that it is within acceptable range.
Here's my confusion on the entire issue, the repeat only occurs once per interval. Basically, if I kept supplying "a" as the input for score 2, it would only have the glitch that first time. Just to be safe, I removed all the code after the first while loop to verify that none of it was influencing the issue, and got the same result. In short, unless my understanding on it is incorrect, the issue can't be a matter of clearing out the junk from the input stream, otherwise the glitch would occur every time, even on i = 1, which it doesn't. :S
I have statistics class in a few hours, I'm sure I'll have plenty of time to try out your code, though I still can't grasp how the glitch is occurring. Clearing out the junk shouldn't be a problem considering how specific the glitch is. :S