Inspired by Alisa Meier
A school consists of 100 students that are in 10 classes. The students scored \(1, 2, 3, \ldots, 100\) in a test. The Head of Department gets the bright idea of rearranging the classes so as to maximize the average of the 10 class averages.
What is the maximum average that can be achieved?
Note: Each class needs to have at least 1 student.