Every positive integer can be expressed in a unique way as the sum of powers of 2. Express 2008 as the sum of powers of 2.
I don't know if this is what you were looking for, but I got an answer:
42^2 + 12^2 + 10^2 = 2008
I started by squaring 45 and then moving back from there with 44, 43 and so on. I then subtracted this squared value from 2008. When I got to 42^2, which equals 1764, I subtracted it from 2008 and got 244.
244 = 144 + 100
244 = 12^2 + 10^2
I then added these two squares to 42^2 and got 2008.