how to figure possible set of scores for 15 students that would result in the class average of 66
Well, one set would be: everyone gets 66!
Then, if you just start adjusting some scores, adding and subtracting the same amounts here and there, the total does not change, so the average does not change. For example,
66 66 66 66 66 ...
64 68 65 67 70 62 ...