I lost you. Not a math person here.
That could be a problem, because you cannot check my derivation. So far, everything about my suggestions depends on the assumptions I made in coming up with the formula in step 5. You need to be able to understand this enough to be able to state whether or not I have understood this and made the right assumptions.

Assuming I have done it right, the answer to your question is in the equation in step 5 (edited here so that the buckets are numbered from 1 to 9 instead of 0 to 8).
y/x1=2^n-1
In this equation:
y= total sum (2044 in your case)
x1= the value in bucket 1 (4 in your case)
n= the number of buckets (9 in your case)
2044/4=2^(9)-1 (you should be able to verify this).

If you give it the total (y) and the value in the first bucket (x1), you should easily be able to solve for n. You may need to review your high school algebra on how to solve exponential equations (http://www.purplemath.com/modules/solvexpo2.htm is a good tutorial). You should get something like n=log(2044/4+1,2)