@billobillo

You will never understand this question unless you yourself sit and work with the numbers.

May I suggest that you cut the question down to 100 balls an let K=8.

List the smallest eight numbers. What is

List the larest eight numbers. What is

List any eight numbers. What is

Now what is the maximum for ?

Now what is the minimum for ?

Now what is ?

The think about number partitions?

When you have done that. Tell us what you find.