- #1

Christian1992

- 2

- 0

I look for a solution for the following problen.

Determine all numbers, which can be written in exact 2010 different ways as a sum of powers of two with non-negative exponent, while all exponents are only allowed to appear maximal three times in one sum.

(All sums where only the order of the summands is changed are count as one sum.)

My problem is that I do not have any idea, how to find a solution to this task.

Therefore I started to determine in how many different sums I can write for example 2^4:

1. 2^4

2. 2*2^3

3. 2*2^2+2^3

4. 2*2+2^2+2^3

5. 2*2^0+2+2^2+2^3

6. 2*2^0+3*2+2^3

7. 2*2^0+3*2+2*2^3

Nevertheless, I did not find any coherenz zu the number and the number of different sums.

Do you have any tips?

Christian